Nothing
R/utils.R
In BayesSPsurv: Bayesian Spatial Split Population Survival Model
Defines functions
data_plots
JointCount
rllFun
llFun
mcmcfrailtySPlog
mcmcfrailtySP
mcmcSpatialLog
mcmcspatialSP
mcmcSPlog
mcmcSP
lambda.gibbs.sampling2
V.F.MH.sampling2
V.F.MH.sampling
V.F.post2
V.F.post
V.MH.sampling2
V.MH.sampling
V.post2
V.post
W.F.MH.sampling2
W.F.MH.sampling
W.F.post2
W.F.post
W.MH.sampling2
W.MH.sampling
W.post2
W.post
rho.post2
rho.post
gammas.post4
gammas.post3
gammas.post2
gammas.post
betas.post2
betas.post
rho.slice.sampling2
rho.slice.sampling
univ.gammas.slice.sampling4
univ.gammas.slice.sampling3
univ.gammas.slice.sampling
univ.gammas.slice.sampling2
gammas.slice.sampling4
gammas.slice.sampling3
gammas.slice.sampling2
gammas.slice.sampling
univ.betas.slice.sampling2
univ.betas.slice.sampling
betas.slice.sampling2
betas.slice.sampling
formcall
#' @useDynLib BayesSPsurv
#' @importFrom stats dgamma runif rgamma dnorm model.frame as.formula model.matrix model.response na.omit
#' @importFrom MCMCpack riwish
#' @importFrom coda mcmc
#' @import grDevices
#' @import graphics
#' @importFrom FastGP rcpp_rmvnorm rcpp_log_dmvnorm
#' @importFrom dplyr distinct
#' @importFrom reshape2 acast
#' @export
.onUnload <- function (libpath) {
library.dynam.unload("BayesSPsurv", libpath)
}
nameob <- c('capdist', 'numa', 'numb', 'kmdist', 'midist')
if(getRversion() >= "2.15.1"){
utils::globalVariables(c(nameob))
utils::suppressForeignCheck(c(nameob))
}
formcall <- function(duration,
immune,
Y0,
LY,
S = NULL,
A = NULL,
data,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
form,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
prop.varV = NULL,
prop.varW = NULL,
model = character())
{
formula1 <- as.formula(duration)
formula2 <- as.formula(immune)
variable <- unique(c(all.vars(formula1), all.vars(formula2)))
mf1 <- model.frame(formula = duration, data = data)
mf2 <- model.frame(formula = immune, data = data)
X <- model.matrix(attr(mf1, "terms"), data = mf1)
Z <- model.matrix(attr(mf2, "terms"), data = mf2)
Y <- as.matrix(model.response(mf1))
C <- as.matrix(model.response(mf2))
Y0 <- data[,Y0]
LY <- data[,LY]
burn <- burn
if (is.null(w)) w <- c(1,1,1) else w <- w
if (is.null(m)) m <- 10 else m <- m
if (is.null(ini.beta)) ini.beta <- 0 else ini.beta <- ini.beta
if (is.null(ini.gamma)) ini.gamma <- 0 else ini.gamma <- ini.gamma
if (is.null(ini.W)) ini.W <- 0 else ini.W <- ini.W
if (is.null(ini.V)) ini.V <- 0 else ini.V <- ini.V
form <- form
cnx <- colnames(X)
cnz <- colnames(Z)
if(model == "SPsurv"){
dataset <- data.frame(cbind(Y, Y0, C, LY, X, Z))
dataset <- na.omit(dataset)
Y <- as.matrix(dataset[,1])
Y0 <- as.matrix(dataset[,2])
C <- as.matrix(dataset[,3])
LY <- as.matrix(dataset[,4])
X <- as.matrix(dataset[,5:(4+ncol(X))])
Z <- as.matrix(dataset[,(5+ncol(X)):ncol(dataset)])
colnames(X) <- cnx
colnames(Z) <- cnz
fm <- list(Y = Y, Y0 = Y0, C = C, LY = LY, X = X, Z = Z, N = N, burn = burn,
thin = thin, w = w, m = m, ini.beta = ini.beta, ini.gamma = ini.gamma, form = form)
} else {
prop.varV <- prop.varV
prop.varW <- prop.varW
S <- data[, S]
dataset <- data.frame(cbind(Y, Y0, C, LY, S, X, Z))
dataset <- na.omit(dataset)
Y <- as.matrix(dataset[,1])
Y0 <- as.matrix(dataset[,2])
C <- as.matrix(dataset[,3])
LY <- as.matrix(dataset[,4])
S <- as.matrix(dataset[,5])
X <- as.matrix(dataset[,6:(5+ncol(X))])
Z <- as.matrix(dataset[,(6+ncol(X)):ncol(dataset)])
colnames(X) <- cnx
colnames(Z) <- cnz
fm <- list(Y = Y, Y0 = Y0, C = C, LY = LY, X = X, Z = Z, S = S, N = N, burn = burn,
thin = thin, w = w, m = m, ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V,
form = form, prop.varV = prop.varV, prop.varW = prop.varW)
}
if(!is.null(A)) fm$A <- as.matrix(A)
return(fm)
}
# @title betas.slice.sampling
# @description slice sampling for betas
#
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
betas.slice.sampling = function(Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
w,
m,
form) {
p1 = length(betas)
for (p in sample(1:p1, p1, replace = FALSE)) {
betas[p] = univ.betas.slice.sampling(betas[p], p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w, m, form = form)
}
return(betas)
}
# @title betas.slice.sampling2
# @description slice sampling for betas
#
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
betas.slice.sampling2 = function(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, form) {
p1 = length(betas)
for (p in sample(1:p1, p1, replace = FALSE)) {
betas[p] = univ.betas.slice.sampling2(betas[p], p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, form = form)
}
return(betas)
}
# @title univ.betas.slice.sampling
# @description univariate slice sampling for betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.betas.slice.sampling = function(betas.p,
p,
Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
b0 = betas.p
b.post0 = betas.post(b0, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
e.b.post0 = exp(b.post0)
if (is.infinite(e.b.post0)){e.b.post0 = exp(700)}
if (exp(b.post0) > 0) { b.post0 = log(runif(1, 0, e.b.post0))}
u = runif(1, 0, w)
L = b0 - u
R = b0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (betas.post(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (betas.post(R, p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (betas.post(L, p, Sigma.b, Y,Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (betas.post(R, p, Sigma.b, Y,Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
b1 = runif(1, L, R)
b.post1 = betas.post(b1, p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, form)
if (b.post1 >= b.post0) break
if (b1 > b0) {
R = b1
} else {
L = b1
}
}
return(b1)
}
# @title univ.betas.slice.sampling2
# @description univariate slice sampling for betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.betas.slice.sampling2 = function(betas.p, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
b0 = betas.p
b.post0 = betas.post2(b0, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
e.b.post0 = exp(b.post0)
if (is.infinite(e.b.post0)){e.b.post0 = exp(700)}
if (exp(b.post0) > 0) { b.post0 = log(runif(1, 0, e.b.post0))}
u = runif(1, 0, w)
L = b0 - u
R = b0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (betas.post2(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (betas.post2(R, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, is.numeric(m)))
K = (is.numeric(m) - 1) - J
while (J > 0) {
if (L <= lower) break
if (betas.post2(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (betas.post2(R, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
b1 = runif(1, L, R)
b.post1 = betas.post2(b1, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
if (b.post1 >= b.post0) break
if (b1 > b0) {
R = b1
} else {
L = b1
}
}
return(b1)
}
# @title gammas.slice.sampling
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling = function(Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
w,
m,
form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling(gammas[p], p, Sigma.g, Y,Y0, eXB, Z, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling2
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling2 = function(Sigma.g,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
w,
m,
form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling2(gammas[p], p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling3
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling3 = function(Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling3(gammas[p], p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling4
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling4 = function(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling4(gammas[p], p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title univ.gammas.slice.sampling2
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling2 = function(gammas.p,
p, Sigma.g,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
g0 = gammas.p
g.post0 = gammas.post2(g0, p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post2(L, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post2(R, p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post2(L, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post2(R, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post2(g1, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
g0 = gammas.p
g.post0 = gammas.post(g0, p, Sigma.g, Y, Y0,eXB, Z,gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post(L, p, Sigma.g, Y,Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post(R, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post(L, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post(R, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post(g1, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling3
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling3 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
g0 = gammas.p
g.post0 = gammas.post3(g0, p, Sigma.g, Y, Y0, eXB, Z,gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post3(L, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post3(R, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post3(L, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post3(R, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post3(g1, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling4
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling4 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
g0 = gammas.p
g.post0 = gammas.post4(g0, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post4(L, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post4(R, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, is.numeric(m)))
K = (is.numeric(m) - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post4(L, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post4(R, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post4(g1, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title rho.slice.sampling
# @description univariate slice sampling for rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
#
# @return One sample update using slice sampling
#
rho.slice.sampling = function(Y,
Y0,
eXB,
delta,
C,
LY,
rho,
w,
m,
lower = 0.01,
upper = +Inf) {
l0 = rho
l.post0 = rho.post(Y, Y0,eXB, delta, C, LY, l0)
e.l.post0 = exp(l.post0)
if (is.infinite(e.l.post0)){e.l.post0 = exp(700)}
if (exp(l.post0) > 0) { l.post0 = log(runif(1, 0, e.l.post0))}
u = runif(1, 0, w)
L = l0 - u
R = l0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (rho.post(Y, Y0,eXB, delta, C, LY, L) <= l.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (is.na(rho.post(Y, Y0,eXB, delta, C, LY, R))) #browser()
if (rho.post(Y, Y0,eXB, delta, C, LY, R) <= l.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (rho.post(Y, Y0,eXB, delta, C, LY, L) <= l.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (is.na(rho.post(Y, Y0,eXB, delta, C, LY, R))) #browser()
if (rho.post(Y, Y0,eXB, delta, C, LY, R) <= l.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
l1 = runif(1, L, R)
l.post1 = rho.post(Y, Y0,eXB, delta, C, LY, l1)
if (l.post1 >= l.post0) break
if (l1 > l0) {
R = l1
} else {
L = l1
}
}
return(l1)
}
# @title rho.slice.sampling2
# @description univariate slice sampling for rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
#
# @return One sample update using slice sampling
#
rho.slice.sampling2 = function(Y, Y0, eXB, delta, C, LY, rho, w, m, lower = 0.01, upper = +Inf) {
l0 = rho
l.post0 = rho.post2(Y, Y0, eXB, delta, C, LY, l0)
e.l.post0 = exp(l.post0)
if (is.infinite(e.l.post0)){e.l.post0 = exp(700)}
if (exp(l.post0) > 0) { l.post0 = log(runif(1, 0, e.l.post0))}
u = runif(1, 0, w)
L = l0 - u
R = l0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (rho.post2(Y, Y0, eXB, delta, C, LY, L) <= l.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (is.na(rho.post2(Y, Y0, eXB, delta, C, LY, R))) #browser()
if (rho.post2(Y, Y0, eXB, delta, C, LY, R) <= l.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (rho.post2(Y, Y0, eXB, delta, C, LY, L) <= l.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (is.na(rho.post2(Y, Y0, eXB, delta, C, LY, R))) #browser()
if (rho.post2(Y, Y0, eXB, delta, C, LY, R) <= l.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
l1 = runif(1, L, R)
l.post1 = rho.post2(Y, Y0, eXB, delta, C, LY, l1)
if (l.post1 >= l.post0) break
if (l1 > l0) {
R = l1
} else {
L = l1
}
}
return(l1)
}
# @title betas.post
# @description log-posterior distribution of betas with pth element fixed as betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
betas.post = function(betas.p,
p, Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
form) {
betas[p] = betas.p
eXB = exp(-(X %*% betas) + W)
lprior = rcpp_log_dmvnorm(Sigma.b, rep(0, length(betas)), betas, FALSE)
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title betas.post
# @description log-posterior distribution of betas with pth element fixed as betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Log Lokelihood)
#
# @return log- posterior density of betas
#
betas.post2 = function(betas.p, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) {
betas[p] = betas.p
eXB = exp(-(X %*% betas) + W)
lprior = rcpp_log_dmvnorm(Sigma.b, rep(0, length(betas)), betas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikWeibull(Y, Y0,eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post2
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post2 = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB, Z, V, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikWeibull(Y, Y0,eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post3
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Log Likelihood)
#
# @return log- posterior density of betas
#
gammas.post3 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post4
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post4 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title rho.post
# @description log-posterior distribution of rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
rho.post = function(Y,
Y0,
eXB,
delta,
C,
LY,
rho,
a = 1,
b = 1) {
lprior = dgamma(rho, a, b, log = TRUE)
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title rho.post2
# @description log-posterior distribution of rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
rho.post2 = function(Y, Y0, eXB, delta, C, LY, rho, a = 1, b = 1) {
lprior = dgamma(rho, a, b, log = TRUE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W (Weibull or exponential)
#
W.post = function(S,
A,
lambda,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
lprior = lprior + dnorm(S_uniq[s, 2], W_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W (Log likelihood)
#
W.post2 = function(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
lprior = lprior + dnorm(S_uniq[s, 2], W_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.MH.sampling
# @description MH Sampling for W
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.MH.sampling = function(S,
A,
lambda,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.post(S, A, lambda, Y, Y0,X, W_new[S], betas, delta, C, LY, rho)
w1[which(w1==-Inf)] <- -740
w2 = W.post(S, A, lambda, Y,Y0, X, W_old[S], betas, delta, C, LY, rho)
w2[which(w2==-Inf)] <- -740
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.MH.sampling2
# @description slice sampling for W
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.MH.sampling2 = function(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.post2(S, A, lambda, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
#w1[which(w1==-Inf)] <- -740
#w1[which(w1==Inf)] <- exp(700)
w2 = W.post2(S, A, lambda, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
#w2[which(w2==Inf)] <- exp(700)
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.F.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W
#
W.F.post = function(Sigma.w,
S,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.w[s,s])
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.F.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W
#
W.F.post2 = function(Sigma.w, S, Y, Y0, X, W, betas, delta, C, LY, rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.w[s,s])
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.F.MH.sampling (Cure Model with Frailties)
# @description MH sampling for W
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.F.MH.sampling = function(Sigma.w,
S,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.F.post(Sigma.w, S, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
w2 = W.F.post(Sigma.w, S, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.F.MH.sampling2 (Cure Model with Frailties)
# @description MH sampling for W
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.F.MH.sampling2 = function(Sigma.w, S, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.F.post2(Sigma.w, S, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
w1[which(w1==-Inf)] <- -740
w2 = W.F.post2(Sigma.w, S, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
w2[which(w2==-Inf)] <- -740
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title V.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas
#
V.post = function(S,
A,
lambda,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
vj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
lprior = lprior + dnorm(S_uniq[s, 2], V_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (log likelihood)
#
V.post2 = function(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
vj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
lprior = lprior + dnorm(S_uniq[s, 2], V_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.MH.sampling
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.MH.sampling = function(S,
A,
lambda,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.post(S, A, lambda, Y,Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
v1[which(v1==-Inf)] <- -740
v2 = V.post(S, A, lambda, Y, Y0,eXB, Z, V_old[S], gammas, C, LY, rho)
v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.MH.sampling2
# @description slice sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.MH.sampling2 = function(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.post2(S, A, lambda, Y, Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
#v1[which(v1==-Inf)] <- -740
#V1[which(V1==Inf)] <- exp(700)
v2 = V.post2(S, A, lambda, Y, Y0, eXB, Z, V_old[S], gammas, C, LY, rho)
#v2[which(v2==-Inf)] <- -740
#v2[which(v2==Inf)] <- exp(700)
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.F.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (Weibull and Exponential)
#
V.F.post = function(Sigma.v,
S,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.v[s,s])
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.F.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (log likelihood)
#
V.F.post2 = function(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.v[s,s])
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.F.MH.sampling (Cure Model with non-spatial Frailties)
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.F.MH.sampling = function(Sigma.v,
S,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.F.post(Sigma.v,S, Y,Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
v1[which(v1==-Inf)] <- -740
v2 = V.F.post(Sigma.v,S, Y, Y0,eXB, Z, V_old[S], gammas, C, LY, rho)
v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.F.MH.sampling2 (Cure Model with non-spatial Frailties)
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling (log likelihood)
#
V.F.MH.sampling2 = function(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.F.post2(Sigma.v, S, Y, Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
#v1[which(v1==-Inf)] <- -740
v2 = V.F.post2(Sigma.v, S, Y, Y0, eXB, Z, V_old[S], gammas, C, LY, rho)
#v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title lambda.gibbs.sampling2
# @description log-posterior distribution of rho
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param W spatial random effects
# @param V spatial random effects
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
lambda.gibbs.sampling2 <- function(S,
A,
W,
V,
a = 1, # prior
b = 1) { # prior
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
J = nrow(S_uniq)
sums = 0
for (j in 1:J) {
adj = which(A[j,]==1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
vj = S_uniq[which(S_uniq[,1] %in% adj),3]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
W_j = S_uniq[j, 2]
V_j = S_uniq[j, 3]
sums = sums + m_j/2 * ((W_j-W_j_bar)^2 + (V_j-V_j_bar)^2)
}
lambda = rgamma(1, J + a, sums + b)
return(lambda)
}
# @title mcmcSP
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian split population survival model with no frailties
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
#
# @return chain of the variables of interest
#
mcmcSP <- function(Y,
Y0,
C,
LY,
X,
Z,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
form) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(0, length(Y))
#V = rep(0, length(Y))
delta = exp(Z %*% gammas)/ (1 + exp(Z %*% gammas))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
# if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
betas = betas.slice.sampling(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas))
gammas = gammas.slice.sampling(Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
delta.samp[(iter - burn) / thin] = mean(delta)
}
}
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, delta = delta.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma)))
}
# @title mcmcSPlog
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return chain of the variables of interest
#
mcmcSPlog <- function(Y,
C,
Y0,
X,
LY,
Z,
N,
burn,
thin,
w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(0, length(Y))
#V = rep(0, length(Y))
delta = exp(Z %*% gammas)/ (1 + exp(Z %*% gammas))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #F #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp((X %*% betas))
gammas = gammas.slice.sampling3(Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
}
}
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma)))
}
# @title mcmcspatialSP
# @description Markov Chain Monte Carlo (MCMC) routine for Bayesian spatial split population survival model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param LY last observation year
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcspatialSP <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
A,
N,
burn,
thin, w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV,
prop.varW,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
#CAR model
lambda = lambda.gibbs.sampling2(S, A, W, V)
W = W.MH.sampling(S, A, lambda, Y, Y0,X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling(Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.MH.sampling(S, A, lambda, Y,Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling2(Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmcSpatialLog
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian spatial cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcSpatialLog <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
A,
N,
burn,
thin,
w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV = .00001,
prop.varW = .00001,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
#delta = 1/(1 + exp(-Z %*% gammas + V))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
#CAR model
lambda = lambda.gibbs.sampling2(S, A, W, V)
W = W.MH.sampling2(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp((X %*% betas) + W)
V = V.MH.sampling2(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling4(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
if (form == "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
# print(delta) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
# print(100) #### ***** #### ***** #### ***** #### ***** ####
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, delta= delta.samp, lambda = lambda.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmcfrailtySP
# @description Markov Chain Monte Carlo (MCMC) routine to run Bayesian non-spatial frailties split population survival model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param LY last observation year
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcfrailtySP <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
N,
burn,
thin, w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV,
prop.varW,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
p3 = length(unique(S))
p4 = length(unique(S))
# initial values
rho = 1
lambda = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
WS = rep(ini.W, p3)
VS = rep(ini.V, p4)
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
Sigma.w = 10 * p3 * diag(p3)
Sigma.v = 10 * p4 * diag(p4)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
Sigma.w = riwish(1 + p3, WS %*% t(WS) + p3 * diag(p3))
Sigma.v = riwish(1 + p4, VS %*% t(VS) + p4 * diag(p4))
}
#non-spatial Frailty model
W = W.F.MH.sampling(Sigma.w, S,Y, Y0,X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling(Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.F.MH.sampling(Sigma.v, S, Y,Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling2(Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmc Cure with Non-spatial frailties
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian spatial cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcfrailtySPlog <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV = .00001,
prop.varW = .00001,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
p3 = length(unique(S))
p4 = length(unique(S))
# initial values
rho = 1
lambda = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
WS = rep(ini.W, p3)
VS = rep(ini.V, p4)
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
prop.varV = prop.varV
prop.varW = prop.varW
#delta = 1/(1 + exp(-Z %*% gammas + V))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
Sigma.w = 5 * p3 * diag(p3)
Sigma.v = 5 * p4 * diag(p4)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
Sigma.w = riwish(1 + p3, WS %*% t(WS) + p3 * diag(p3))
Sigma.v = riwish(1 + p4, VS %*% t(VS) + p4 * diag(p4))
}
#non-spatial Frailty model.
W = W.F.MH.sampling2(Sigma.w, S,Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.F.MH.sampling2(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling4(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form == "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title llFun
# @description Log-likelihood function for exchnageable and spatial frailty split population models
#
# @param est parameter estimates from the model
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C immunity indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param W survival stage (spatial) frailty parameter estimates
# @param V split stage (spatial) frailty parameter estimates
# @param data data that contains the variables of interest
#
# @return Log-likelihood of the exchangeable or the spatial split population survial model
#
llFun <- function(est,
Y,
Y0,
C,
X,
Z,
W,
V,
data,
form){ #Note the extra variable Y0 passed to the time varying MF Weibull
n <- nrow(data)
llik <- matrix(0, nrow = n, ncol = 1)
gamma <- est[1:ncol(Z)]
beta <- est[(ncol(Z)+1):(ncol(Z)+ncol(X))]
p <- est[length(est)]
XB <- X %*% beta
ZG <- Z %*% gamma
phi <- exp(-ZG + V)/(1+exp(-ZG + V))
eXB <- exp(-XB + W)
if(form == "loglog"){
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*(1+((eXB*Y0)^(p)))/(1+exp(-(eXB*Y)^(p)))^2)+(1-C)*(log(phi+(1-phi)*(1+((eXB*Y0)^p)))^2/(1+((eXB*Y)^p)))^2)
} else {
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*exp(-(eXB*Y))^p/exp(-(eXB*Y0))^p))+(1-C)*(log(phi+(1-phi)*((exp(-eXB*Y))^p)/((exp(-eXB*Y0))^p)))
}
one <- nrow(llik)
llik <- subset(llik, is.finite(llik))
two <- nrow(llik)
llik <- subset(llik, llik[,1] > -1000)
three <- nrow(llik)
llik <- -1*sum(llik)
list(llik = llik, one = one, two = two, three = three)
}
# @title rllFun
# @description Log-likelihood function for pooled split population models
#
# @param est parameter estimates from the model
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C immunity indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param data data that contains the variables of interest
#
# @return Log-likelihood of the poold slit population survival model
#
rllFun <- function(est,
Y,
Y0,
C,
X,
Z,
data,
form){ #Note the extra variable Y0 passed to the time varying MF Weibull
n <- nrow(data)
llik <- matrix(0, nrow = n, ncol = 1)
gamma <- est[1:ncol(Z)]
beta <- est[(ncol(Z)+1):(ncol(Z)+ncol(X))]
p <- est[length(est)]
XB <- X %*% beta
ZG <- Z %*% gamma
phi <- exp(-ZG )/(1+exp(-ZG ))
eXB <- exp(-XB )
if(form == "loglog"){
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*(1+((eXB*Y0)^(p)))/(1+exp(-(eXB*Y)^(p)))^2)+(1-C)*(log(phi+(1-phi)*(1+((eXB*Y0)^p)))^2/(1+((eXB*Y)^p)))^2)
} else {
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*exp(-(eXB*Y))^p/exp(-(eXB*Y0))^p))+(1-C)*(log(phi+(1-phi)*((exp(-eXB*Y))^p)/((exp(-eXB*Y0))^p)))
}
one <- nrow(llik)
llik <- subset(llik, is.finite(llik))
two <- nrow(llik)
llik <- subset(llik, llik[,1] > -1000)
three <- nrow(llik)
llik <- -1*sum(llik)
list(llik = llik, one = one, two = two, three = three)
}
JointCount<- function(X, W) {
PB<- mean (X)
PW<- 1- mean(X)
PBB<- PB*PB
PWW<- PW*PW
PBW<- 2*PB*(1-PB)
n<-length(X)
nB<-sum(X)
EBB<- 0.5*sum(W)*PBB
EWW<- 0.5*sum(W)*PWW
EBW<- 0.5*sum(W)*PBW
s.2j<-rep(NA,ncol(W))
s.2i<-rep(NA,nrow(W))
s.3j<-rep(NA,ncol(W))
s.3i<-rep(NA,nrow(W))
s_2<-matrix(NA,nrow(W),ncol(W))
bb<-matrix(NA,nrow(W),ncol(W))
ww<-matrix(NA,nrow(W),ncol(W))
bw<-matrix(NA,nrow(W),ncol(W))
for (i in 1:nrow(W)){
for (j in 1:ncol(W)){
s_2[i,j]<-(W[i,j]+W[j,i])^2
bb[i,j]<-W[i,j]*X[i]*X[j]
ww[i,j]<-W[i,j]*(1-X[i])*(1-X[j])
bw[i,j]<-W[i,j]*((X[i]-X[j])^2)
}
s.3j[i]<-(sum(W[i,])+ sum(W[,i]))^2
}
BB<-0.5*sum(bb)
WW<-0.5*sum(ww)
BW<-0.5*sum(bw)
s2<-sum(s_2)*0.5
s3<-sum(s.3j)
s1<-sum(W)
varBW<-0.25*(((2*s2*nB*(n-nB))/(n*(n-1)))+(((s3-s1)*nB*(n-nB))/(n*(n-1)))+((4*(s1^2+s2-s3)*nB*(nB-1)*(n-nB)*(n-nB-1))/(n*(n-1)*(n-2)*(n-3)) ))-(EBW^2)
ZBW<-(BW-EBW)/sqrt(varBW)
out<-data.frame(BW,EBW,sqrt(varBW),ZBW)
colnames(out)<-c("Obs","Exp","sd","Z")
return(out)
}
data_plots <- function(data, var_id = character(), var_time = character(), n = 0, threshold){
dat <- lapply(split(data, data[,var_time]), function(x){x[!duplicated(x[, var_id]), ]})
dat <- dat[sapply(dat, nrow) >= n]
mats <- lapply(dat, function(x){BayesSPsurv::spatial_SA(x, var_ccode = var_id, threshold = threshold)$matrixA})
w2 <- list()
for(i in 1:length(dat)){w2[[i]] <- dat[[i]][order(dat[[i]][, var_id]),]}
list(mats = mats, w2 = w2)
}
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Defines functions data_plots JointCount rllFun llFun mcmcfrailtySPlog mcmcfrailtySP mcmcSpatialLog mcmcspatialSP mcmcSPlog mcmcSP lambda.gibbs.sampling2 V.F.MH.sampling2 V.F.MH.sampling V.F.post2 V.F.post V.MH.sampling2 V.MH.sampling V.post2 V.post W.F.MH.sampling2 W.F.MH.sampling W.F.post2 W.F.post W.MH.sampling2 W.MH.sampling W.post2 W.post rho.post2 rho.post gammas.post4 gammas.post3 gammas.post2 gammas.post betas.post2 betas.post rho.slice.sampling2 rho.slice.sampling univ.gammas.slice.sampling4 univ.gammas.slice.sampling3 univ.gammas.slice.sampling univ.gammas.slice.sampling2 gammas.slice.sampling4 gammas.slice.sampling3 gammas.slice.sampling2 gammas.slice.sampling univ.betas.slice.sampling2 univ.betas.slice.sampling betas.slice.sampling2 betas.slice.sampling formcall
#' @useDynLib BayesSPsurv
#' @importFrom stats dgamma runif rgamma dnorm model.frame as.formula model.matrix model.response na.omit
#' @importFrom MCMCpack riwish
#' @importFrom coda mcmc
#' @import grDevices
#' @import graphics
#' @importFrom FastGP rcpp_rmvnorm rcpp_log_dmvnorm
#' @importFrom dplyr distinct
#' @importFrom reshape2 acast
#' @export
.onUnload <- function (libpath) {
library.dynam.unload("BayesSPsurv", libpath)
}
nameob <- c('capdist', 'numa', 'numb', 'kmdist', 'midist')
if(getRversion() >= "2.15.1"){
utils::globalVariables(c(nameob))
utils::suppressForeignCheck(c(nameob))
}
formcall <- function(duration,
immune,
Y0,
LY,
S = NULL,
A = NULL,
data,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
form,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
prop.varV = NULL,
prop.varW = NULL,
model = character())
{
formula1 <- as.formula(duration)
formula2 <- as.formula(immune)
variable <- unique(c(all.vars(formula1), all.vars(formula2)))
mf1 <- model.frame(formula = duration, data = data)
mf2 <- model.frame(formula = immune, data = data)
X <- model.matrix(attr(mf1, "terms"), data = mf1)
Z <- model.matrix(attr(mf2, "terms"), data = mf2)
Y <- as.matrix(model.response(mf1))
C <- as.matrix(model.response(mf2))
Y0 <- data[,Y0]
LY <- data[,LY]
burn <- burn
if (is.null(w)) w <- c(1,1,1) else w <- w
if (is.null(m)) m <- 10 else m <- m
if (is.null(ini.beta)) ini.beta <- 0 else ini.beta <- ini.beta
if (is.null(ini.gamma)) ini.gamma <- 0 else ini.gamma <- ini.gamma
if (is.null(ini.W)) ini.W <- 0 else ini.W <- ini.W
if (is.null(ini.V)) ini.V <- 0 else ini.V <- ini.V
form <- form
cnx <- colnames(X)
cnz <- colnames(Z)
if(model == "SPsurv"){
dataset <- data.frame(cbind(Y, Y0, C, LY, X, Z))
dataset <- na.omit(dataset)
Y <- as.matrix(dataset[,1])
Y0 <- as.matrix(dataset[,2])
C <- as.matrix(dataset[,3])
LY <- as.matrix(dataset[,4])
X <- as.matrix(dataset[,5:(4+ncol(X))])
Z <- as.matrix(dataset[,(5+ncol(X)):ncol(dataset)])
colnames(X) <- cnx
colnames(Z) <- cnz
fm <- list(Y = Y, Y0 = Y0, C = C, LY = LY, X = X, Z = Z, N = N, burn = burn,
thin = thin, w = w, m = m, ini.beta = ini.beta, ini.gamma = ini.gamma, form = form)
} else {
prop.varV <- prop.varV
prop.varW <- prop.varW
S <- data[, S]
dataset <- data.frame(cbind(Y, Y0, C, LY, S, X, Z))
dataset <- na.omit(dataset)
Y <- as.matrix(dataset[,1])
Y0 <- as.matrix(dataset[,2])
C <- as.matrix(dataset[,3])
LY <- as.matrix(dataset[,4])
S <- as.matrix(dataset[,5])
X <- as.matrix(dataset[,6:(5+ncol(X))])
Z <- as.matrix(dataset[,(6+ncol(X)):ncol(dataset)])
colnames(X) <- cnx
colnames(Z) <- cnz
fm <- list(Y = Y, Y0 = Y0, C = C, LY = LY, X = X, Z = Z, S = S, N = N, burn = burn,
thin = thin, w = w, m = m, ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V,
form = form, prop.varV = prop.varV, prop.varW = prop.varW)
}
if(!is.null(A)) fm$A <- as.matrix(A)
return(fm)
}
# @title betas.slice.sampling
# @description slice sampling for betas
#
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
betas.slice.sampling = function(Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
w,
m,
form) {
p1 = length(betas)
for (p in sample(1:p1, p1, replace = FALSE)) {
betas[p] = univ.betas.slice.sampling(betas[p], p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w, m, form = form)
}
return(betas)
}
# @title betas.slice.sampling2
# @description slice sampling for betas
#
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
betas.slice.sampling2 = function(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, form) {
p1 = length(betas)
for (p in sample(1:p1, p1, replace = FALSE)) {
betas[p] = univ.betas.slice.sampling2(betas[p], p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, form = form)
}
return(betas)
}
# @title univ.betas.slice.sampling
# @description univariate slice sampling for betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.betas.slice.sampling = function(betas.p,
p,
Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
b0 = betas.p
b.post0 = betas.post(b0, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
e.b.post0 = exp(b.post0)
if (is.infinite(e.b.post0)){e.b.post0 = exp(700)}
if (exp(b.post0) > 0) { b.post0 = log(runif(1, 0, e.b.post0))}
u = runif(1, 0, w)
L = b0 - u
R = b0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (betas.post(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (betas.post(R, p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (betas.post(L, p, Sigma.b, Y,Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (betas.post(R, p, Sigma.b, Y,Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
b1 = runif(1, L, R)
b.post1 = betas.post(b1, p, Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, form)
if (b.post1 >= b.post0) break
if (b1 > b0) {
R = b1
} else {
L = b1
}
}
return(b1)
}
# @title univ.betas.slice.sampling2
# @description univariate slice sampling for betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.betas.slice.sampling2 = function(betas.p, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
b0 = betas.p
b.post0 = betas.post2(b0, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
e.b.post0 = exp(b.post0)
if (is.infinite(e.b.post0)){e.b.post0 = exp(700)}
if (exp(b.post0) > 0) { b.post0 = log(runif(1, 0, e.b.post0))}
u = runif(1, 0, w)
L = b0 - u
R = b0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (betas.post2(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (betas.post2(R, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, is.numeric(m)))
K = (is.numeric(m) - 1) - J
while (J > 0) {
if (L <= lower) break
if (betas.post2(L, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (betas.post2(R, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) <= b.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
b1 = runif(1, L, R)
b.post1 = betas.post2(b1, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form)
if (b.post1 >= b.post0) break
if (b1 > b0) {
R = b1
} else {
L = b1
}
}
return(b1)
}
# @title gammas.slice.sampling
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling = function(Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
w,
m,
form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling(gammas[p], p, Sigma.g, Y,Y0, eXB, Z, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling2
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling2 = function(Sigma.g,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
w,
m,
form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling2(gammas[p], p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling3
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling3 = function(Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling3(gammas[p], p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title gammas.slice.sampling4
# @description slice sampling for gammas
#
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
gammas.slice.sampling4 = function(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form) {
p2 = length(gammas)
for (p in sample(1:p2, p2, replace = FALSE)) {
gammas[p] = univ.gammas.slice.sampling4(gammas[p], p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, form = form)
}
return(gammas)
}
# @title univ.gammas.slice.sampling2
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling2 = function(gammas.p,
p, Sigma.g,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
g0 = gammas.p
g.post0 = gammas.post2(g0, p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post2(L, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post2(R, p, Sigma.g, Y,Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post2(L, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post2(R, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post2(g1, p, Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
w,
m,
lower = -Inf,
upper = +Inf,
form) {
g0 = gammas.p
g.post0 = gammas.post(g0, p, Sigma.g, Y, Y0,eXB, Z,gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post(L, p, Sigma.g, Y,Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post(R, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post(L, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post(R, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post(g1, p, Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling3
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Exponential or Weibull)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling3 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
g0 = gammas.p
g.post0 = gammas.post3(g0, p, Sigma.g, Y, Y0, eXB, Z,gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post3(L, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post3(R, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post3(L, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post3(R, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post3(g1, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title univ.gammas.slice.sampling4
# @description univariate slice sampling for gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
# @param form type of parametric model (Log Likelihood)
#
# @return One sample update using slice sampling
#
univ.gammas.slice.sampling4 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w, m, lower = -Inf, upper = +Inf, form) {
g0 = gammas.p
g.post0 = gammas.post4(g0, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form)
e.g.post0 = exp(g.post0)
if (is.infinite(e.g.post0)){e.g.post0 = exp(700)}
if (exp(g.post0) > 0) { g.post0 = log(runif(1, 0, e.g.post0))}
u = runif(1, 0, w)
L = g0 - u
R = g0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (gammas.post4(L, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (gammas.post4(R, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, is.numeric(m)))
K = (is.numeric(m) - 1) - J
while (J > 0) {
if (L <= lower) break
if (gammas.post4(L, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (gammas.post4(R, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) <= g.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
g1 = runif(1, L, R)
g.post1 = gammas.post4(g1, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form)
if (g.post1 >= g.post0) break
if (g1 > g0) {
R = g1
} else {
L = g1
}
}
return(g1)
}
# @title rho.slice.sampling
# @description univariate slice sampling for rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling. A vector of values for beta, gamma, rho.
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
#
# @return One sample update using slice sampling
#
rho.slice.sampling = function(Y,
Y0,
eXB,
delta,
C,
LY,
rho,
w,
m,
lower = 0.01,
upper = +Inf) {
l0 = rho
l.post0 = rho.post(Y, Y0,eXB, delta, C, LY, l0)
e.l.post0 = exp(l.post0)
if (is.infinite(e.l.post0)){e.l.post0 = exp(700)}
if (exp(l.post0) > 0) { l.post0 = log(runif(1, 0, e.l.post0))}
u = runif(1, 0, w)
L = l0 - u
R = l0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (rho.post(Y, Y0,eXB, delta, C, LY, L) <= l.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (is.na(rho.post(Y, Y0,eXB, delta, C, LY, R))) #browser()
if (rho.post(Y, Y0,eXB, delta, C, LY, R) <= l.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (rho.post(Y, Y0,eXB, delta, C, LY, L) <= l.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (is.na(rho.post(Y, Y0,eXB, delta, C, LY, R))) #browser()
if (rho.post(Y, Y0,eXB, delta, C, LY, R) <= l.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
l1 = runif(1, L, R)
l.post1 = rho.post(Y, Y0,eXB, delta, C, LY, l1)
if (l.post1 >= l.post0) break
if (l1 > l0) {
R = l1
} else {
L = l1
}
}
return(l1)
}
# @title rho.slice.sampling2
# @description univariate slice sampling for rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param w size of the slice in the slice sampling
# @param m limit on steps in the slice sampling
# @param lower lower bound on support of the distribution
# @param upper upper bound on support of the distribution
#
# @return One sample update using slice sampling
#
rho.slice.sampling2 = function(Y, Y0, eXB, delta, C, LY, rho, w, m, lower = 0.01, upper = +Inf) {
l0 = rho
l.post0 = rho.post2(Y, Y0, eXB, delta, C, LY, l0)
e.l.post0 = exp(l.post0)
if (is.infinite(e.l.post0)){e.l.post0 = exp(700)}
if (exp(l.post0) > 0) { l.post0 = log(runif(1, 0, e.l.post0))}
u = runif(1, 0, w)
L = l0 - u
R = l0 + (w - u)
if (is.infinite(m)) {
repeat
{ if (L <= lower) break
if (rho.post2(Y, Y0, eXB, delta, C, LY, L) <= l.post0) break
L = L - w
}
repeat
{
if (R >= upper) break
if (is.na(rho.post2(Y, Y0, eXB, delta, C, LY, R))) #browser()
if (rho.post2(Y, Y0, eXB, delta, C, LY, R) <= l.post0) break
R = R + w
}
} else if (m > 1) {
J = floor(runif(1, 0, m))
K = (m - 1) - J
while (J > 0) {
if (L <= lower) break
if (rho.post2(Y, Y0, eXB, delta, C, LY, L) <= l.post0) break
L = L - w
J = J - 1
}
while (K > 0) {
if (R >= upper) break
if (is.na(rho.post2(Y, Y0, eXB, delta, C, LY, R))) #browser()
if (rho.post2(Y, Y0, eXB, delta, C, LY, R) <= l.post0) break
R = R + w
K = K - 1
}
}
if (L < lower) {
L = lower
}
if (R > upper) {
R = upper
}
repeat
{
l1 = runif(1, L, R)
l.post1 = rho.post2(Y, Y0, eXB, delta, C, LY, l1)
if (l.post1 >= l.post0) break
if (l1 > l0) {
R = l1
} else {
L = l1
}
}
return(l1)
}
# @title betas.post
# @description log-posterior distribution of betas with pth element fixed as betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
betas.post = function(betas.p,
p, Sigma.b,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
form) {
betas[p] = betas.p
eXB = exp(-(X %*% betas) + W)
lprior = rcpp_log_dmvnorm(Sigma.b, rep(0, length(betas)), betas, FALSE)
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title betas.post
# @description log-posterior distribution of betas with pth element fixed as betas.p
#
# @param betas.p current value of the pth element of betas
# @param p pth element
# @param Sigma.b variance estimate of betas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Log Lokelihood)
#
# @return log- posterior density of betas
#
betas.post2 = function(betas.p, p, Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, form) {
betas[p] = betas.p
eXB = exp(-(X %*% betas) + W)
lprior = rcpp_log_dmvnorm(Sigma.b, rep(0, length(betas)), betas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB,
Z,
gammas,
C,
LY,
rho,
form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikWeibull(Y, Y0,eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post2
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post2 = function(gammas.p,
p,
Sigma.g,
Y,
Y0,
eXB, Z, V, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikWeibull(Y, Y0,eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post3
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Log Likelihood)
#
# @return log- posterior density of betas
#
gammas.post3 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title gammas.post4
# @description log-posterior distribution of gammas with pth element fixed as gammas.p
#
# @param gammas.p current value of the pth element of gammas
# @param p pth element
# @param Sigma.g variance estimate of gammas
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param form type of parametric model (Exponential or Weibull)
#
# @return log- posterior density of betas
#
gammas.post4 = function(gammas.p, p, Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, form) {
gammas[p] = gammas.p
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
lprior = rcpp_log_dmvnorm(Sigma.g, rep(0, length(gammas)), gammas, FALSE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title rho.post
# @description log-posterior distribution of rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
rho.post = function(Y,
Y0,
eXB,
delta,
C,
LY,
rho,
a = 1,
b = 1) {
lprior = dgamma(rho, a, b, log = TRUE)
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title rho.post2
# @description log-posterior distribution of rho
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
rho.post2 = function(Y, Y0, eXB, delta, C, LY, rho, a = 1, b = 1) {
lprior = dgamma(rho, a, b, log = TRUE)
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W (Weibull or exponential)
#
W.post = function(S,
A,
lambda,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
lprior = lprior + dnorm(S_uniq[s, 2], W_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W (Log likelihood)
#
W.post2 = function(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
lprior = lprior + dnorm(S_uniq[s, 2], W_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.MH.sampling
# @description MH Sampling for W
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.MH.sampling = function(S,
A,
lambda,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.post(S, A, lambda, Y, Y0,X, W_new[S], betas, delta, C, LY, rho)
w1[which(w1==-Inf)] <- -740
w2 = W.post(S, A, lambda, Y,Y0, X, W_old[S], betas, delta, C, LY, rho)
w2[which(w2==-Inf)] <- -740
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.MH.sampling2
# @description slice sampling for W
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.MH.sampling2 = function(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.post2(S, A, lambda, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
#w1[which(w1==-Inf)] <- -740
#w1[which(w1==Inf)] <- exp(700)
w2 = W.post2(S, A, lambda, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
#w2[which(w2==Inf)] <- exp(700)
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.F.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W
#
W.F.post = function(Sigma.w,
S,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.w[s,s])
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.F.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of W
#
W.F.post2 = function(Sigma.w, S, Y, Y0, X, W, betas, delta, C, LY, rho) {
eXB = exp(-(X %*% betas) + W)
S_uniq = unique(cbind(S, W))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.w[s,s])
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title W.F.MH.sampling (Cure Model with Frailties)
# @description MH sampling for W
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.F.MH.sampling = function(Sigma.w,
S,
Y,
Y0,
X,
W,
betas,
delta,
C,
LY,
rho,
prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.F.post(Sigma.w, S, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
w2 = W.F.post(Sigma.w, S, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title W.F.MH.sampling2 (Cure Model with Frailties)
# @description MH sampling for W
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param X covariates for betas
# @param W spatial random effects
# @param betas current value of betas
# @param delta probability of true censoring
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
W.F.MH.sampling2 = function(Sigma.w, S, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW) {
S_uniq = unique(cbind(S, W))
W_old = S_uniq[order(S_uniq[,1]), 2]
W_new = rcpp_rmvnorm(1, prop.varW * diag(length(W_old)), W_old)
W_new = W_new - mean(W_new)
u = log(runif(1))
w1 = W.F.post2(Sigma.w, S, Y, Y0, X, W_new[S], betas, delta, C, LY, rho)
w1[which(w1==-Inf)] <- -740
w2 = W.F.post2(Sigma.w, S, Y, Y0, X, W_old[S], betas, delta, C, LY, rho)
w2[which(w2==-Inf)] <- -740
temp = w1- w2
alpha = min(0, temp)
if (u <= alpha) {
W = W_new[S]
} else {
W = W_old[S]
}
return(W)
}
# @title V.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas
#
V.post = function(S,
A,
lambda,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
vj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
lprior = lprior + dnorm(S_uniq[s, 2], V_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (log likelihood)
#
V.post2 = function(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:nrow(A)) {
adj = which(A[s,] == 1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
vj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
lprior = lprior + dnorm(S_uniq[s, 2], V_j_bar, sqrt(1/(lambda * m_j)), log = TRUE)
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.MH.sampling
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.MH.sampling = function(S,
A,
lambda,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.post(S, A, lambda, Y,Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
v1[which(v1==-Inf)] <- -740
v2 = V.post(S, A, lambda, Y, Y0,eXB, Z, V_old[S], gammas, C, LY, rho)
v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.MH.sampling2
# @description slice sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param lambda CAR parameter
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.MH.sampling2 = function(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.post2(S, A, lambda, Y, Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
#v1[which(v1==-Inf)] <- -740
#V1[which(V1==Inf)] <- exp(700)
v2 = V.post2(S, A, lambda, Y, Y0, eXB, Z, V_old[S], gammas, C, LY, rho)
#v2[which(v2==-Inf)] <- -740
#v2[which(v2==Inf)] <- exp(700)
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.F.post
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (Weibull and Exponential)
#
V.F.post = function(Sigma.v,
S,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.v[s,s])
}
lpost = llikWeibull(Y,Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.F.post2
# @description log-posterior distribution of W with sth element fixed as W.s
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
#
# @return log- posterior density of betas (log likelihood)
#
V.F.post2 = function(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho) {
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
S_uniq = unique(cbind(S, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
lprior = 0
for (s in 1:length(unique(S))){
lprior = lprior + dnorm(S_uniq[s, 2], 0, Sigma.v[s,s])
}
lpost = llikLoglog(Y, Y0, eXB, delta, C, LY, rho) + lprior
return(lpost)
}
# @title V.F.MH.sampling (Cure Model with non-spatial Frailties)
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling
#
V.F.MH.sampling = function(Sigma.v,
S,
Y,
Y0,
eXB,
Z,
V,
gammas,
C,
LY,
rho,
prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.F.post(Sigma.v,S, Y,Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
v1[which(v1==-Inf)] <- -740
v2 = V.F.post(Sigma.v,S, Y, Y0,eXB, Z, V_old[S], gammas, C, LY, rho)
v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title V.F.MH.sampling2 (Cure Model with non-spatial Frailties)
# @description MH sampling for rcpp_log_dmvnorm
#
# @param S spatial information (e.g. district)
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param eXB exponentiated vector of covariates times betas
# @param Z covariates for gammas
# @param V spatial random effects
# @param gammas current value of gammas
# @param C censoring indicator
# @param rho current value of rho
# @param prop.varV proposal variance for Metropolis-Hastings
#
# @return One sample update using slice sampling (log likelihood)
#
V.F.MH.sampling2 = function(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV) {
S_uniq = unique(cbind(S, V))
V_old = S_uniq[order(S_uniq[,1]), 2]
V_new = rcpp_rmvnorm(1, prop.varV * diag(length(V_old)), V_old)
V_new = V_new - mean(V_new)
u = log(runif(1))
v1 = V.F.post2(Sigma.v, S, Y, Y0, eXB, Z, V_new[S], gammas, C, LY, rho)
#v1[which(v1==-Inf)] <- -740
v2 = V.F.post2(Sigma.v, S, Y, Y0, eXB, Z, V_old[S], gammas, C, LY, rho)
#v2[which(v2==-Inf)] <- -740
temp = v1- v2
alpha = min(0, temp)
if (u <= alpha) {
V = V_new[S]
} else {
V = V_old[S]
}
return(V)
}
# @title lambda.gibbs.sampling2
# @description log-posterior distribution of rho
#
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param W spatial random effects
# @param V spatial random effects
# @param a shape parameter of gammas prior
# @param b scale parameter of gammas prior
#
# @return log- posterior density of betas
#
lambda.gibbs.sampling2 <- function(S,
A,
W,
V,
a = 1, # prior
b = 1) { # prior
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
J = nrow(S_uniq)
sums = 0
for (j in 1:J) {
adj = which(A[j,]==1)
m_j = length(adj)
if(m_j == 0){
m_j <- exp(-700)
} else {
m_j <- m_j
}
wj = S_uniq[which(S_uniq[,1] %in% adj),2]
if (length(wj) == 0){
W_j_bar = 0
} else {
W_j_bar = mean(wj)
}
vj = S_uniq[which(S_uniq[,1] %in% adj),3]
if (length(vj) == 0){
V_j_bar = 0
} else {
V_j_bar = mean(vj)
}
W_j = S_uniq[j, 2]
V_j = S_uniq[j, 3]
sums = sums + m_j/2 * ((W_j-W_j_bar)^2 + (V_j-V_j_bar)^2)
}
lambda = rgamma(1, J + a, sums + b)
return(lambda)
}
# @title mcmcSP
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian split population survival model with no frailties
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
#
# @return chain of the variables of interest
#
mcmcSP <- function(Y,
Y0,
C,
LY,
X,
Z,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
form) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(0, length(Y))
#V = rep(0, length(Y))
delta = exp(Z %*% gammas)/ (1 + exp(Z %*% gammas))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
# if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
betas = betas.slice.sampling(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas))
gammas = gammas.slice.sampling(Sigma.g, Y, Y0,eXB, Z, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
delta.samp[(iter - burn) / thin] = mean(delta)
}
}
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, delta = delta.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma)))
}
# @title mcmcSPlog
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Log Likelihood)
#
# @return chain of the variables of interest
#
mcmcSPlog <- function(Y,
C,
Y0,
X,
LY,
Z,
N,
burn,
thin,
w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(0, length(Y))
#V = rep(0, length(Y))
delta = exp(Z %*% gammas)/ (1 + exp(Z %*% gammas))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #F #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp((X %*% betas))
gammas = gammas.slice.sampling3(Sigma.g, Y, Y0, eXB, Z, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
}
}
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma)))
}
# @title mcmcspatialSP
# @description Markov Chain Monte Carlo (MCMC) routine for Bayesian spatial split population survival model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param LY last observation year
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcspatialSP <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
A,
N,
burn,
thin, w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV,
prop.varW,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
#CAR model
lambda = lambda.gibbs.sampling2(S, A, W, V)
W = W.MH.sampling(S, A, lambda, Y, Y0,X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling(Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.MH.sampling(S, A, lambda, Y,Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling2(Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmcSpatialLog
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian spatial cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcSpatialLog <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
A,
N,
burn,
thin,
w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV = .00001,
prop.varW = .00001,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
# initial values
rho = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
#delta = 1/(1 + exp(-Z %*% gammas + V))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = nrow(A))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
}
#CAR model
lambda = lambda.gibbs.sampling2(S, A, W, V)
W = W.MH.sampling2(S, A, lambda, Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp((X %*% betas) + W)
V = V.MH.sampling2(S, A, lambda, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling4(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
#delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
if (form == "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
# print(delta) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
# print(100) #### ***** #### ***** #### ***** #### ***** ####
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, delta= delta.samp, lambda = lambda.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmcfrailtySP
# @description Markov Chain Monte Carlo (MCMC) routine to run Bayesian non-spatial frailties split population survival model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C censoring indicator
# @param LY last observation year
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param A adjacency information corresponding to spatial information
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling. A vector of values for beta, gamma, rho.
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcfrailtySP <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
N,
burn,
thin, w = c(1, 1, 1),
m,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV,
prop.varW,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
p3 = length(unique(S))
p4 = length(unique(S))
# initial values
rho = 1
lambda = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
WS = rep(ini.W, p3)
VS = rep(ini.V, p4)
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
Sigma.b = 10 * p1 * diag(p1)
Sigma.g = 10 * p2 * diag(p2)
Sigma.w = 10 * p3 * diag(p3)
Sigma.v = 10 * p4 * diag(p4)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
Sigma.w = riwish(1 + p3, WS %*% t(WS) + p3 * diag(p3))
Sigma.v = riwish(1 + p4, VS %*% t(VS) + p4 * diag(p4))
}
#non-spatial Frailty model
W = W.F.MH.sampling(Sigma.w, S,Y, Y0,X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling(Sigma.b, Y, Y0,X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.F.MH.sampling(Sigma.v, S, Y,Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling2(Sigma.g, Y, Y0,eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form %in% "Weibull") {
rho = rho.slice.sampling(Y, Y0,eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title mcmc Cure with Non-spatial frailties
# @description Markov Chain Monte Carlo (MCMC) to run Bayesian spatial cure model
#
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param C censoring indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param S spatial information (e.g. district)
# @param N number of MCMC iterations
# @param burn burn-in to be discarded
# @param thin thinning to prevent from autocorrelation
# @param w size of the slice in the slice sampling for (betas, gammas, rho)
# @param m limit on steps in the slice sampling
# @param form type of parametric model (Exponential or Weibull)
# @param prop.varV proposal variance for Metropolis-Hastings
# @param prop.varW proposal variance for Metropolis-Hastings
#
# @return chain of the variables of interest
#
mcmcfrailtySPlog <- function(Y,
Y0,
C,
LY,
X,
Z,
S,
N,
burn,
thin,
w = c(1, 1, 1),
m = 10,
ini.beta = 0,
ini.gamma = 0,
ini.W = 0,
ini.V= 0,
form,
prop.varV = .00001,
prop.varW = .00001,
id_WV) {
p1 = dim(X)[2]
p2 = dim(Z)[2]
p3 = length(unique(S))
p4 = length(unique(S))
# initial values
rho = 1
lambda = 1
betas = rep(ini.beta, p1)
gammas = rep(ini.gamma, p2)
W = rep(ini.W, length(Y))
V = rep(ini.V, length(Y))
WS = rep(ini.W, p3)
VS = rep(ini.V, p4)
delta = exp(Z %*% gammas + V)/ (1 + exp(Z %*% gammas + V))
prop.varV = prop.varV
prop.varW = prop.varW
#delta = 1/(1 + exp(-Z %*% gammas + V))
Sigma.b = 5 * p1 * diag(p1)
Sigma.g = 5 * p2 * diag(p2)
Sigma.w = 5 * p3 * diag(p3)
Sigma.v = 5 * p4 * diag(p4)
betas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p1)
gammas.samp = matrix(NA, nrow = (N - burn) / thin, ncol = p2)
rho.samp = rep(NA, (N - burn) / thin)
lambda.samp = rep(NA, (N - burn) / thin)
delta.samp = rep(NA, (N - burn) / thin)
W.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
V.samp = matrix(NA, nrow = (N - burn) / thin, ncol = length(unique(S)))
pb <- progress::progress_bar$new(total = N)
for (iter in 1:N) {
pb$tick()
Sys.sleep(1/N)
#if (iter %% 1000 == 0) print(iter) #### ***** #### ***** #### ***** #### ***** ####
if (iter > burn) {
Sigma.b = riwish(1 + p1, betas %*% t(betas) + p1 * diag(p1))
Sigma.g = riwish(1 + p2, gammas %*% t(gammas) + p2 * diag(p2))
Sigma.w = riwish(1 + p3, WS %*% t(WS) + p3 * diag(p3))
Sigma.v = riwish(1 + p4, VS %*% t(VS) + p4 * diag(p4))
}
#non-spatial Frailty model.
W = W.F.MH.sampling2(Sigma.w, S,Y, Y0, X, W, betas, delta, C, LY, rho, prop.varW)
betas = betas.slice.sampling2(Sigma.b, Y, Y0, X, W, betas, delta, C, LY, rho, w[1], m, form = form)
eXB = exp(-(X %*% betas) + W)
V = V.F.MH.sampling2(Sigma.v, S, Y, Y0, eXB, Z, V, gammas, C, LY, rho, prop.varV)
gammas = gammas.slice.sampling4(Sigma.g, Y, Y0, eXB, Z, V, gammas, C, LY, rho, w[2], m, form = form)
num = exp(Z %*% gammas + V)
num[which(is.infinite(num))] <- exp(700)
denom = (1 + exp(Z %*% gammas + V))
num[which(is.infinite(denom))] <- exp(700)
delta = num/denom
if (form == "loglog") {
rho = rho.slice.sampling2(Y, Y0, eXB, delta, C, LY, rho, w[3], m)
}
if (iter > burn & (iter - burn) %% thin == 0) {
betas.samp[(iter - burn) / thin, ] = betas
gammas.samp[(iter - burn) / thin, ] = gammas
rho.samp[(iter - burn) / thin] = rho
lambda.samp[(iter - burn) / thin] = lambda
delta.samp[(iter - burn) / thin] = mean(delta)
S_uniq = unique(cbind(S, W, V))
S_uniq = S_uniq[order(S_uniq[,1]),]
W.samp[(iter - burn) / thin, ] = S_uniq[,2]
V.samp[(iter - burn) / thin, ] = S_uniq[,3]
}
}
colnames(V.samp) <- id_WV #colnames(A) #ADC
colnames(W.samp) <- id_WV #colnames(A) #ADC
colnames(betas.samp) <- colnames(X) #adc
colnames(gammas.samp) <- colnames(Z) #adc
return(list(betas = betas.samp, gammas = gammas.samp, rho = rho.samp, lambda = lambda.samp, delta = delta.samp, W = W.samp, V = V.samp,
spstats = list(X = X, Z = Z, Y = Y, Y0 = Y0, C = C, S = S, form = form),
initial = list(ini.beta = ini.beta, ini.gamma = ini.gamma, ini.W = ini.W, ini.V = ini.V)))
}
# @title llFun
# @description Log-likelihood function for exchnageable and spatial frailty split population models
#
# @param est parameter estimates from the model
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C immunity indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param W survival stage (spatial) frailty parameter estimates
# @param V split stage (spatial) frailty parameter estimates
# @param data data that contains the variables of interest
#
# @return Log-likelihood of the exchangeable or the spatial split population survial model
#
llFun <- function(est,
Y,
Y0,
C,
X,
Z,
W,
V,
data,
form){ #Note the extra variable Y0 passed to the time varying MF Weibull
n <- nrow(data)
llik <- matrix(0, nrow = n, ncol = 1)
gamma <- est[1:ncol(Z)]
beta <- est[(ncol(Z)+1):(ncol(Z)+ncol(X))]
p <- est[length(est)]
XB <- X %*% beta
ZG <- Z %*% gamma
phi <- exp(-ZG + V)/(1+exp(-ZG + V))
eXB <- exp(-XB + W)
if(form == "loglog"){
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*(1+((eXB*Y0)^(p)))/(1+exp(-(eXB*Y)^(p)))^2)+(1-C)*(log(phi+(1-phi)*(1+((eXB*Y0)^p)))^2/(1+((eXB*Y)^p)))^2)
} else {
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*exp(-(eXB*Y))^p/exp(-(eXB*Y0))^p))+(1-C)*(log(phi+(1-phi)*((exp(-eXB*Y))^p)/((exp(-eXB*Y0))^p)))
}
one <- nrow(llik)
llik <- subset(llik, is.finite(llik))
two <- nrow(llik)
llik <- subset(llik, llik[,1] > -1000)
three <- nrow(llik)
llik <- -1*sum(llik)
list(llik = llik, one = one, two = two, three = three)
}
# @title rllFun
# @description Log-likelihood function for pooled split population models
#
# @param est parameter estimates from the model
# @param Y the time (duration) dependent variable for the survival stage (t)
# @param Y0 the elapsed time since inception until the beginning of time period (t-1)
# @param C immunity indicator
# @param X covariates for betas
# @param Z covariates for gammas
# @param data data that contains the variables of interest
#
# @return Log-likelihood of the poold slit population survival model
#
rllFun <- function(est,
Y,
Y0,
C,
X,
Z,
data,
form){ #Note the extra variable Y0 passed to the time varying MF Weibull
n <- nrow(data)
llik <- matrix(0, nrow = n, ncol = 1)
gamma <- est[1:ncol(Z)]
beta <- est[(ncol(Z)+1):(ncol(Z)+ncol(X))]
p <- est[length(est)]
XB <- X %*% beta
ZG <- Z %*% gamma
phi <- exp(-ZG )/(1+exp(-ZG ))
eXB <- exp(-XB )
if(form == "loglog"){
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*(1+((eXB*Y0)^(p)))/(1+exp(-(eXB*Y)^(p)))^2)+(1-C)*(log(phi+(1-phi)*(1+((eXB*Y0)^p)))^2/(1+((eXB*Y)^p)))^2)
} else {
llik <- C*(log((1-phi)*eXB*p*((eXB*Y)^(p-1))*exp(-(eXB*Y))^p/exp(-(eXB*Y0))^p))+(1-C)*(log(phi+(1-phi)*((exp(-eXB*Y))^p)/((exp(-eXB*Y0))^p)))
}
one <- nrow(llik)
llik <- subset(llik, is.finite(llik))
two <- nrow(llik)
llik <- subset(llik, llik[,1] > -1000)
three <- nrow(llik)
llik <- -1*sum(llik)
list(llik = llik, one = one, two = two, three = three)
}
JointCount<- function(X, W) {
PB<- mean (X)
PW<- 1- mean(X)
PBB<- PB*PB
PWW<- PW*PW
PBW<- 2*PB*(1-PB)
n<-length(X)
nB<-sum(X)
EBB<- 0.5*sum(W)*PBB
EWW<- 0.5*sum(W)*PWW
EBW<- 0.5*sum(W)*PBW
s.2j<-rep(NA,ncol(W))
s.2i<-rep(NA,nrow(W))
s.3j<-rep(NA,ncol(W))
s.3i<-rep(NA,nrow(W))
s_2<-matrix(NA,nrow(W),ncol(W))
bb<-matrix(NA,nrow(W),ncol(W))
ww<-matrix(NA,nrow(W),ncol(W))
bw<-matrix(NA,nrow(W),ncol(W))
for (i in 1:nrow(W)){
for (j in 1:ncol(W)){
s_2[i,j]<-(W[i,j]+W[j,i])^2
bb[i,j]<-W[i,j]*X[i]*X[j]
ww[i,j]<-W[i,j]*(1-X[i])*(1-X[j])
bw[i,j]<-W[i,j]*((X[i]-X[j])^2)
}
s.3j[i]<-(sum(W[i,])+ sum(W[,i]))^2
}
BB<-0.5*sum(bb)
WW<-0.5*sum(ww)
BW<-0.5*sum(bw)
s2<-sum(s_2)*0.5
s3<-sum(s.3j)
s1<-sum(W)
varBW<-0.25*(((2*s2*nB*(n-nB))/(n*(n-1)))+(((s3-s1)*nB*(n-nB))/(n*(n-1)))+((4*(s1^2+s2-s3)*nB*(nB-1)*(n-nB)*(n-nB-1))/(n*(n-1)*(n-2)*(n-3)) ))-(EBW^2)
ZBW<-(BW-EBW)/sqrt(varBW)
out<-data.frame(BW,EBW,sqrt(varBW),ZBW)
colnames(out)<-c("Obs","Exp","sd","Z")
return(out)
}
data_plots <- function(data, var_id = character(), var_time = character(), n = 0, threshold){
dat <- lapply(split(data, data[,var_time]), function(x){x[!duplicated(x[, var_id]), ]})
dat <- dat[sapply(dat, nrow) >= n]
mats <- lapply(dat, function(x){BayesSPsurv::spatial_SA(x, var_ccode = var_id, threshold = threshold)$matrixA})
w2 <- list()
for(i in 1:length(dat)){w2[[i]] <- dat[[i]][order(dat[[i]][, var_id]),]}
list(mats = mats, w2 = w2)
}
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