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R/hmr.R
In jarbes: Just a Rather Bayesian Evidence Synthesis
Defines functions
print.hmr
hmr.default
hmr
Documented in
hmr
print.hmr
#' Bayesian meta-analysis to combine aggregated and individual participant data for cross design synthesis.
#'
#'
#' This function performers a Bayesian cross design synthesis. The function fits a
#' hierarchical meta-regression model based on a bivariate random effects model.
#'
#' The number of events in the control and treated group are modeled with two
#' conditional Binomial distributions and the random-effects are based on a
#' bivariate scale mixture of Normals.
#'
#' The individual participant data is modeled as a Bayesian logistic regression for
#' participants in the control group. Coefficients in the regression are modeled as
#' exchangeables.
#'
#' The function calculates the implicit hierarchical meta-regression, where the
#' treatment effect is regressed to the baseline risk (rate of events in the control
#' group). The scale mixture weights are used to adjust for internal validity and
#' structural outliers identification.
#'
#' The implicit hierarchical meta-regression is used to predict the treatment effect
#' for subgroups of individual participant data.
#'
#' Computations are done by calling JAGS (Just Another Gibbs Sampler) to perform
#' MCMC (Markov Chain Monte Carlo) sampling and returning an object of the
#' class \emph{mcmc.list}.
#'
#' Installation of JAGS: It is important to note that R 3.3.0 introduced a major change in the
#' use of toolchain for Windows. This new toolchain is incompatible with older packages written in C++.
#' As a consequence, if the installed version of JAGS does not match the R installation, then the rjags
#' package will spontaneously crash. Therefore, if a user works with R version >= 3.3.0, then JAGS must
#' be installed with the installation program JAGS-4.2.0-Rtools33.exe. For users who continue using R 3.2.4 or
#' an earlier version, the installation program for JAGS is the default installer JAGS-4.2.0.exe.
#'
#'
#' @param data Aggregated data results: a data frame where the first four columns containing the number of events in
#' the control group (yc), the number of patients in the control group (nc),
#' the number of events in the treatment group (yt) and the number of patients in the
#' treatment group (nt). If two.by.two = TRUE a data frame where each line
#' contains the trial results with column names: yc, nc, yt, nt.
#'
#' @param two.by.two If TRUE indicates that the trial results are with names: yc, nc, yt, nt.
#'
#' @param dataIPD Individual participant data: a data frame where
#' the first column is the outcome variable and the
#' other columns represent individual participant
#' charachteristics.
#'
#'
#' @param re Random effects distribution for the resulting model. Possible
#' values are \emph{normal} for bivariate random effects and \emph{sm}
#' for scale mixtures.
#'
#' @param link The link function used in the model. Possible values are
#' \emph{logit}, \emph{cloglog} \emph{probit}.
#'
#'
#' @param mean.mu.1 Prior mean of baseline risk, default value is 0.
#'
#' @param mean.mu.2 Prior mean of treatment effect, default value is 0.
#'
#' @param mean.mu.phi Prior mean of the bias parameter which measures the difference
#' between the baseline mean mu.1 and the intercept parameter of
#' the logistic regression of the individual participant data.
#' The defalut vaule is 0.
#'
#' @param sd.mu.1 Prior standard deviation of mu.1, default value is 1. The default prior of mu.1 is a
#' logistic distribution with mean 0 and dispersion 1. The implicit prior for mu.1 in
#' the probability scale is a uniform between 0 and 1.
#'
#' @param sd.mu.2 Prior standard deviation of mu.2, default value is 1. The default prior of mu.2 is a
#' logistic distribution with mean 0 and dispersion 1. The implicit prior for mu.2 in
#' the probability scale is a uniform between 0 and 1.
#'
#' @param sd.mu.phi Prior standard deviation of mu.phi, default value is 1.
#'
#' @param sigma.1.upper Upper bound of the uniform prior of sigma.1, default value is 5.
#'
#' @param sigma.2.upper Upper bound of the uniform prior of sigma.2, default value is 5.
#'
#' @param sigma.beta.upper Upper bound of the uniform prior of sigma.beta, default value is 5.
#'
#' @param mean.Fisher.rho Mean of rho in the Fisher scale, default value is 0.
#'
#' @param sd.Fisher.rho Standard deviation of rho in the Fisher scale, default value is 1/sqrt(2).
#'
#' @param df If de.estimate = FALSE, then df is the degrees of freedom for the scale mixture distribution, default value is 4.
#'
#' @param df.estimate Estimate the posterior of df. The default value is FALSE.
#'
#' @param df.lower Lower bound of the prior of df. The default value is 3.
#'
#' @param df.upper Upper bound of the prior of df. The default value is 30.
#'
#' @param split.w Split the w parameter in two independent weights one for each random effect.
#' The default value is FALSE.
#'
#'
#'
#'
#' @param nr.chains Number of chains for the MCMC computations, default 5.
#'
#' @param nr.iterations Number of iterations after adapting the MCMC, default is 10000. Some models may need more iterations.
#'
#' @param nr.adapt Number of iterations in the adaptation process, default is 1000. Some models may need more iterations during adptation.
#'
#' @param nr.burnin Number of iteration discarded for burnin period, default is 1000. Some models may need a longer burnin period.
#'
#' @param nr.thin Thinning rate, it must be a positive integer, the default value 1.
#'
#' @param be.quiet Do not print warning message if the model does not adapt default value is FALSE. If you are not sure about the adaptation period choose be.quiet=TRUE.
#'
#' @param r2jags Which interface is used to link R to JAGS (rjags and R2jags) default value is R2Jags TRUE.
#'
#' @return This function returns an object of the class "hmr". This object contains the MCMC output of
#' each parameter and hyper-parameter in the model, the data frame used for fitting the model, the link function,
#' type of random effects distribution and the splitting information for conflict of evidence analysis.
#'
#' The results of the object of the class metadiag can be extracted with R2jags or with rjags. In addition
#' a summary, a print and a plot function are implemented for this type of object.
#'
#' @references Verde, P.E, Ohmann, C., Icks, A. and Morbach, S. (2016) Bayesian evidence synthesis and combining randomized and nonrandomized results: a case study in diabetes. Statistics in Medicine. Volume 35, Issue 10, 10 May 2016, Pages: 1654 to 1675.
#'
#' @references Verde, P.E. (2017) The hierarchical meta-regression approach and learning from clinical evidence. Submited to the Biometrical Journal.
#'
#' @references Verde, P.E. (2018) The Hierarchical Meta-Regression Approach and Learning from Clinical Evidence. Technical report.
#'
#' @examples
#'
#'\dontrun{
#'library(jarbes)
#'
#' data("healing")
#' AD <- healing[, c("y_c", "n_c", "y_t", "n_t")]
#'
#' data("healingipd")
#'
#' IPD <- healingipd[, c("healing.without.amp", "PAD", "neuropathy",
#' "first.ever.lesion", "no.continuous.care", "male", "diab.typ2",
#' "insulin", "HOCHD", "HOS", "CRF", "dialysis", "DNOAP", "smoking.ever",
#' "diabdur", "wagner.class")]
#'
#' mx2 <- hmr(AD, two.by.two = FALSE,
#' dataIPD = IPD,
#' re = "sm",
#' link = "logit",
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sigma.beta.upper = 5,
#' sd.Fisher.rho = 1.25,
#' df.estimate = FALSE,
#' df.lower = 3,
#' df.upper = 10,
#' nr.chains = 1,
#' nr.iterations = 1500,
#' nr.adapt = 100,
#' nr.thin = 1)
#'
#' print(mx2)
#'
#'
#'
#'
#'# This experiment corresponds to Section 4 in Verde (2018).
#'#
#'# Experiment: Combining aggretated data from RCTs and a single
#'# observational study with individual participant data.
#'#
#'# In this experiment we assess conflict of evidence between the RCTs
#'# and the observational study with a partially identified parameter
#'# mu.phi.
#'#
#'# We run two simulated data: 1) mu.phi = 0.5 which is diffucult to
#'# identify. 2) mu.phi = 2 which can be identify. The simulations are
#'# used to see if the hmr() function can recover mu.phi.
#'#
#'
#'
#'library(MASS)
#'library(ggplot2)
#'library(jarbes)
#'library(gridExtra)
#'library(mcmcplots)
#'
#'
#'# Simulation of the IPD data
#'
#'invlogit <- function (x)
#'{
#' 1/(1 + exp(-x))
#'}
#'
#'# Data set for mu.phi = 0.5 .........................................
#'
#'# Parameters values
#'mu.phi.true <- 0.5
#'beta0 <- mu.1.true + mu.phi.true
#'beta1 <- 2.5
#'beta2 <- 2
#'
#'# Regression variables
#'
#'x1 <- rnorm(200)
#'x2 <- rbinom(200, 1, 0.5)
#'
#'# Binary outcome as a function of "b0 + b1 * x1 + b2 * x2"
#'
#'y <- rbinom(200, 1,
#' invlogit(beta0 + beta1 * x1 + beta2 * x2))
#'
#'
#'# Preparing the plot to visualize the data
#'jitter.binary <- function(a, jitt = 0.05)
#'
#' ifelse(a==0, runif(length(a), 0, jitt),
#' runif(length(a), 1-jitt, 1))
#'
#'
#'
#'plot(x1, jitter.binary(y), xlab = "x1",
#' ylab = "Success probability")
#'
#'curve(invlogit(beta0 + beta1*x),
#' from = -2.5, to = 2.5, add = TRUE, col ="blue", lwd = 2)
#'curve(invlogit(beta0 + beta1*x + beta2),
#' from = -2.5, to = 2.5, add = TRUE, col ="red", lwd =2)
#'legend("bottomright", c("b2 = 0", "b2 = 2"),
#' col = c("blue", "red"), lwd = 2, lty = 1)
#'
#'noise <- rnorm(100*20)
#'dim(noise) <- c(100, 20)
#'n.names <- paste(rep("x", 20), seq(3, 22), sep="")
#'colnames(noise) <- n.names
#'
#'data.IPD <- data.frame(y, x1, x2, noise)
#'
#'
#'# Application of HMR ...........................................
#'
#'res.s2 <- hmr(AD.s1, two.by.two = FALSE,
#' dataIPD = data.IPD,
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sd.Fisher.rho = 1.5)
#'
#'
#'print(res.s2)
#'
#'# Data set for mu.phi = 2 ......................................
#'# Parameters values
#'
#'mu.phi.true <- 2
#'beta0 <- mu.1.true + mu.phi.true
#'beta1 <- 2.5
#'beta2 <- 2
#'
#'# Regression variables
#'x1 <- rnorm(200)
#'x2 <- rbinom(200, 1, 0.5)
#'# Binary outcome as a function of "b0 + b1 * x1 + b2 * x2"
#'y <- rbinom(200, 1,
#' invlogit(beta0 + beta1 * x1 + beta2 * x2))
#'
#'# Preparing the plot to visualize the data
#'jitter.binary <- function(a, jitt = 0.05)
#'
#' ifelse(a==0, runif(length(a), 0, jitt),
#' runif(length(a), 1-jitt, 1))
#'
#'plot(x1, jitter.binary(y), xlab = "x1",
#' ylab = "Success probability")
#'
#'curve(invlogit(beta0 + beta1*x),
#' from = -2.5, to = 2.5, add = TRUE, col ="blue", lwd = 2)
#'curve(invlogit(beta0 + beta1*x + beta2),
#' from = -2.5, to = 2.5, add = TRUE, col ="red", lwd =2)
#'legend("bottomright", c("b2 = 0", "b2 = 2"),
#' col = c("blue", "red"), lwd = 2, lty = 1)
#'
#'noise <- rnorm(100*20)
#'dim(noise) <- c(100, 20)
#'n.names <- paste(rep("x", 20), seq(3, 22), sep="")
#'colnames(noise) <- n.names
#'
#'data.IPD <- data.frame(y, x1, x2, noise)
#'
#'# Application of HMR ................................................
#'
#'
#'res.s3 <- hmr(AD.s1, two.by.two = FALSE,
#' dataIPD = data.IPD,
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sd.Fisher.rho = 1.5
#')
#'
#'print(res.s3)
#'
#'# Posteriors for mu.phi ............................
#'attach.jags(res.s2)
#'mu.phi.0.5 <- mu.phi
#'df.phi.05 <- data.frame(x = mu.phi.0.5)
#'
#'attach.jags(res.s3)
#'mu.phi.1 <- mu.phi
#'df.phi.1 <- data.frame(x = mu.phi.1)
#'
#'
#'p1 <- ggplot(df.phi.05, aes(x=x))+
#' xlab(expression(mu[phi])) +
#' ylab("Posterior distribution")+
#' xlim(c(-7,7))+
#' geom_histogram(aes(y=..density..),fill = "royalblue",
#' colour = "black", alpha= 0.4, bins=60) +
#' geom_vline(xintercept = 0.64, colour = "black", size = 1.7, lty = 2)+
#' geom_vline(xintercept = 0.5, colour = "black", size = 1.7, lty = 1)+
#' stat_function(fun = dlogis,
#' n = 101,
#' args = list(location = 0, scale = 1), size = 1.5) + theme_bw()
#'
#'p2 <- ggplot(df.phi.1, aes(x=x))+
#' xlab(expression(mu[phi])) +
#' ylab("Posterior distribution")+
#' xlim(c(-7,7))+
#' geom_histogram(aes(y=..density..),fill = "royalblue",
#' colour = "black", alpha= 0.4, bins=60) +
#' geom_vline(xintercept = 2.2, colour = "black", size = 1.7, lty = 2)+
#' geom_vline(xintercept = 2, colour = "black", size = 1.7, lty = 1)+
#' stat_function(fun = dlogis,
#' n = 101,
#' args = list(location = 0, scale = 1), size = 1.5) + theme_bw()
#'
#'grid.arrange(p1, p2, ncol = 2, nrow = 1)
#'
#'
#' # Cater plots for regression coefficients ...........................
#'
#' var.names <- names(data.IPD[-1])
#' v <- paste("beta", names(data.IPD[-1]), sep = ".")
#' mcmc.x <- as.rjags.mcmc(res.s2$BUGSoutput$sims.matrix)
#' mcmc.x.2 <- as.mcmc.rjags(res.s2)
#' mcmc.x.3 <- as.mcmc.rjags(res.s3)
#'
#' greek.names <- paste(paste("beta[",1:22, sep=""),"]", sep="")
#' par.names <- paste(paste("beta.IPD[",1:22, sep=""),"]", sep="")
#'
#' caterplot(mcmc.x.2,
#' parms = par.names,
#' col = "black", lty = 1,
#' labels = greek.names,
#' greek = T,
#' labels.loc="axis", cex =0.7,
#' style = "plain",reorder = F, denstrip = F)
#'
#'caterplot(mcmc.x.3,
#' parms = par.names,
#' col = "grey", lty = 2,
#' labels = greek.names,
#' greek = T,
#' labels.loc="axis", cex =0.7,
#' style = "plain",reorder = F, denstrip = F,
#' add = TRUE,
#' collapse=TRUE, cat.shift=-0.5)
#'
#'
#'
#'abline(v=0, lty = 2, lwd = 2)
#'abline(v =2, lty = 2, lwd = 2)
#'abline(v =2.5, lty = 2, lwd = 2)
#'
#' # End of the examples.
#'
#' }
#'
#'
#' @import R2jags
#' @import rjags
#' @import graphics
#' @import stats
#' @import graphics
#'
#' @export
#'
hmr <- function(data,
two.by.two = TRUE,
dataIPD,
# Arguments for the model:
re = "normal",
link = "logit",
# Hyperpriors parameters............................................
mean.mu.1 = 0,
mean.mu.2 = 0,
mean.mu.phi = 0,
sd.mu.1 = 1,
sd.mu.2 = 1,
sd.mu.phi = 1,
sigma.1.upper = 5,
sigma.2.upper = 5,
sigma.beta.upper = 5,
mean.Fisher.rho = 0,
sd.Fisher.rho = 1/sqrt(2),
df = 4,
df.estimate = FALSE,
df.lower = 3,
df.upper = 20,
# Split weights
split.w = FALSE,
# MCMC setup........................................................
nr.chains = 2,
nr.iterations = 10000,
nr.adapt = 1000,
nr.burnin = 1000,
nr.thin = 1,
# Further options to link jags and R ...............................
be.quiet = FALSE,
r2jags = TRUE
)UseMethod("hmr")
#' @export
#'
hmr.default <- function(
data,
two.by.two = TRUE,
dataIPD,
# Arguments for the model:
re = "normal",
link = "logit",
# Hyperpriors parameters............................................
mean.mu.1 = 0,
mean.mu.2 = 0,
mean.mu.phi = 0,
sd.mu.1 = 1,
sd.mu.2 = 1,
sd.mu.phi = 1,
sigma.1.upper = 5,
sigma.2.upper = 5,
sigma.beta.upper = 5,
mean.Fisher.rho = 0,
sd.Fisher.rho = 1/sqrt(2),
df = 4,
df.estimate = FALSE,
df.lower = 3,
df.upper = 20,
# Split weights
split.w = FALSE,
# MCMC setup........................................................
nr.chains = 2,
nr.iterations = 10000,
nr.adapt = 1000,
nr.burnin = 1000,
nr.thin = 1,
# Further options to link jags and R ...............................
be.quiet = FALSE,
r2jags = TRUE
)
{
# Model errors checking-----
if(re=="normal" & split.w==TRUE)stop("Normal random effects and splitting weights are not compatible options")
re.test <- re %in% c("normal", "sm")
if(!re.test)stop("This random effects distribution is not implemented")
link.test <- link %in% c("logit", "cloglog", "probit")
if(!link.test)stop("This link function is not implemented")
# Setting up hyperparameters ...
pre.mu.1 <- 1/(sd.mu.1*sd.mu.1)
pre.mu.2 <- 1/(sd.mu.2*sd.mu.2)
pre.mu.phi <- 1/ (sd.mu.phi * sd.mu.phi)
pre.Fisher.rho <- 1/(sd.Fisher.rho * sd.Fisher.rho)
# Setting up data nodes ...
if(two.by.two == FALSE)
{
yc <- data[,1]
nc <- data[,2]
yt <- data[,3]
nt <- data[,4]
} else
{
yc <- data$yc
nc <- data$nc
yt <- data$yt
nt <- data$nt
}
N <- length(nc)
# Increase N for one observacional study
N <- N + 1
# Data errors
#if(yc>nc || yt>nt)stop("the data is inconsistent")
#if(missing(data))stop("NAs are not allowed in this function")
# Setup IPD data for regression ................................................
dataIPD$y <- dataIPD[,1]
dataIPD <- dataIPD[,-1] # <- corregido! Se generó un bug version > 1.7.0
model.1 <- model.frame(y ~ ., data = dataIPD)
X.IPD <- model.matrix(model.1, data = dataIPD)
X.IPD <- X.IPD[ , dimnames(X.IPD)[[2]] != "(Intercept)", drop=FALSE]
y.0.IPD <- model.response(model.1)
if(is.factor(y.0.IPD)){y.0.IPD <- unclass(y.0.IPD) - 1}
K <- dim(X.IPD)[2]
M <- dim(X.IPD)[1]
#.............................................................................
# Data, initial values and parameters .......................................
data.model <-
list(M = M,
K = K,
X.IPD = X.IPD,
y.0.IPD = y.0.IPD,
N = N,
yc = yc,
nc = nc,
yt = yt,
nt = nt,
mean.mu.1 = mean.mu.1,
mean.mu.2 = mean.mu.2,
mean.mu.phi = mean.mu.phi,
pre.mu.1 = pre.mu.1,
pre.mu.2 = pre.mu.2,
pre.mu.phi = pre.mu.phi,
sigma.1.upper = sigma.1.upper,
sigma.2.upper = sigma.2.upper,
sigma.beta.upper = sigma.beta.upper,
mean.Fisher.rho = mean.Fisher.rho,
pre.Fisher.rho = pre.Fisher.rho
)
if(re == "sm" & df.estimate == TRUE){data.model$df.lower <- df.lower
data.model$df.upper <- df.upper}
if(re == "sm" & df.estimate == FALSE){data.model$df <- df}
# Parameters to monitor ....................................................................
parameters.model <-
c("mu.1",
"mu.2",
"mu.phi",
"sigma.1",
"sigma.2",
"rho",
"Odds.pool",
# "Odds.new",
"P_control.pool",
# "P_control.new",
"alpha.0",
"alpha.1",
"beta.IPD",
"sigma.beta",
"x.subgroup",
"eta.subgroup" # Verde's formula ....
)
# This take the weights for the scale mixture random effects model, etc...
if(re == "sm" & split.w == TRUE & df.estimate == TRUE)
parameters.model <- c(parameters.model, "w1", "w2", "p.w1", "p.w2", "df")
else
if(re == "sm" & split.w == TRUE & df.estimate == FALSE)
parameters.model <- c(parameters.model, "w1", "w2", "p.w1", "p.w2")
else
if(re=="sm" & split.w == FALSE & df.estimate == TRUE)
parameters.model <- c(parameters.model, "w", "p.w", "df")
else
if(re=="sm" & split.w == FALSE & df.estimate == FALSE)
parameters.model <- c(parameters.model, "w", "p.w")
# Model BUGS script
#----
blueprint <- function(link = "logit", re = "normal", split.w = FALSE, df.estimate = FALSE)
{
if(split.w == FALSE & df.estimate == TRUE ) re <- "sm.df"
if(split.w == TRUE & df.estimate == FALSE) re <- "sm.split"
if(split.w == TRUE & df.estimate == TRUE ) re <- "sm.split.df"
#----
# Block for data model ......................................................................
dm <-
"
model
{
for(i in 1:(N-1))
{
yc[i] ~ dbin(pc[i], nc[i])
yt[i] ~ dbin(pt[i], nt[i])
"
#----
# Block for the link function................................................................
link.logit <-
"
# Random effects model
logit(pc[i]) <- theta.1[i]
logit(pt[i]) <- theta.2[i] + logit(pc[i])
"
link.cloglog <-
"
# Random effects model
cloglog(pc[i]) <- theta.1[i]
cloglog(pt[i]) <- theta.2[i] + cloglog(pc[i])
"
link.probit <-
"
# Random effects model
probit(pc[i]) <- theta.1[i]
probit(pt[i]) <- theta.2[i] + probit(pc[i])
"
# Block for structural distribution .........................................................
re.normal <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1)
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1)
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.theta.1 <- 1/(sigma.1*sigma.1)
pre.theta.2 <- 1/(sigma.2*sigma.2)
# Conditional precision
pre.theta.2.1 <- pre.theta.2 / (1 - rho*rho)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
Sigma.new[1, 1] <- pow(sigma.1, 2)
Sigma.new[2, 2] <- pow(sigma.2, 2)
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2
Sigma.new[2, 1] <- Sigma.new[1, 2]
Omega.new[1:2, 1:2] <- inverse(Sigma.new[1:2, 1:2])
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Block for: link = logistic, re = normal and split.w = FALSE
# Model for individual data ..................................................
# Random effect for the observational study ..................................
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1)
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1)
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#----
re.sm <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1[i])
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1[i])
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
# Conditional precision
pre.theta.2.1[i] <- pre.theta.2[i] / (1 - rho * rho)
lambda[i] ~ dchisqr(df)
w[i] <- df/lambda[i]
pre.theta.1[i] <- pre.1 / w[i]
pre.theta.2[i] <- pre.2 / w[i]
# Probability of outlier
p.w[i] <- step(w[i]-0.99)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.1 <- 1/(sigma.1*sigma.1)
pre.2 <- 1/(sigma.2*sigma.2)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
Sigma.new[1, 1] <- pow(sigma.1, 2)
Sigma.new[2, 2] <- pow(sigma.2, 2)
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2
Sigma.new[2, 1] <- Sigma.new[1, 2]
lambda.new ~ dchisqr(df)
w.new <- df/lambda.new
Omega.new[1:2,1:2] <- inverse(Sigma.new[1:2, 1:2]) / w.new
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Block for: link = logistic, re = sm and split.w = FALSE
# Model for individual data ..................................................
# Random effect for the observational study ..................................
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Structure of w[N]...........................................................
# Case: random weight same as RCTs
lambda[N] ~ dchisqr(df)
w[N] <- df/lambda[N]
pre.theta.1[N] <- pre.1 / w[N]
pre.theta.2[N] <- pre.2 / w[N]
pre.theta.2.1[N] <- pre.theta.2[N] / (1-rho*rho)
# Probability of outlier.......................................................
p.w[N] <- step(w[N]-0.99)
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1[N])
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1[N])
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#--------------------------------------------------
re.sm.split <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1[i])
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1[i])
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
# Conditional precision
pre.theta.2.1[i] <- pre.theta.2[i] / (1 - rho * rho)
pre.theta.1[i] <- pre.1 / w1[i]
pre.theta.2[i] <- pre.2 / w2[i]
lambda1[i] ~ dchisqr(df)
w1[i] <- df/lambda1[i]
lambda2[i] ~ dchisqr(df)
w2[i] <- df/lambda2[i]
# Probability of outlier
p.w1[i] <- step(w1[i]-0.99)
p.w2[i] <- step(w2[i]-0.99)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.1 <- 1/(sigma.1*sigma.1)
pre.2 <- 1/(sigma.2*sigma.2)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
lambda1.new ~ dchisqr(df)
lambda2.new ~ dchisqr(df)
w1.new <- df/lambda1.new
w2.new <- df/lambda2.new
Sigma.new[1, 1] <- pow(sigma.1, 2)/w1.new
Sigma.new[2, 2] <- pow(sigma.2, 2)/w2.new
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2 / sqrt(w1.new*w2.new)
Sigma.new[2, 1] <- Sigma.new[1, 2]
Omega.new[1:2,1:2] <- inverse(Sigma.new[1:2, 1:2])
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Structure of w[N]...........................................................
# Case: random weight same as RCTs
lambda1[N] ~ dchisqr(df)
w1[N] <- df/lambda1[N]
lambda2[N] ~ dchisqr(df)
w2[N] <- df/lambda2[N]
pre.theta.1[N] <- pre.1 / w1[N]
pre.theta.2[N] <- pre.2 / w2[N]
pre.theta.2.1[N] <- pre.theta.2[N] / (1-rho*rho)
# Probability of outlier.......................................................
p.w1[N] <- step(w1[N]-0.99)
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1[N])
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1[N])
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#------------------------------------------------------------------------
prior.of.df <- "
# Degrees of freedom
a <- 1/df.upper
b <- 1/df.lower
df <- 1/U
U ~ dunif(a, b)
"
re.sm.df <- paste(re.sm, prior.of.df)
#------------------------------------------------------------------------
re.sm.split.df <- paste(re.sm.split, prior.of.df)
#...........................................................................
# Block of parameters of interest depending on the links ......................
par.logit <- "
#..............................................................................
for(i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
logit(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
Odds.pool <- exp(alpha.0) # Here was a bug in version < 2.0.0
P_control.pool <- ilogit(mu.1)
# Predictive summaries ...
# Odds.new <- exp(theta.new[2]) # Here was a bug in version < 2.0.0
# P_control.new <- ilogit(theta.new[1])
}"
par.cloglog <- "
#..............................................................................
for( i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
cloglog(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
# F(x) = exp(-exp(x)) this is the quantile function of the Gumbel distribution
# F(mu.1) = p.0
# F(alpha.0 + alpha.1) = p.1
# OR = p.1/(1-p.1) / p.0/(1-p.1)
p.0 = icloglog(mu.1)
p.1 = icloglog(mu.1 + alpha.0)
Odds.pool = p.1/(1-p.1)/(p.0/(1-p.0))
P_control.pool = p.1
# Predictive summaries ...
# p.new.0 = icloglog(theta.new[1])
# p.new.1 = icloglog(theta.new[1]+theta.new[2])
#
# Odds.new = p.new.1/(1-p.new.1)/(p.new.0/(1-p.new.0))
# P_control.new = p.new.0
}"
par.probit <-
"
#..............................................................................
for( i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
probit(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
# F(x) = phi(x) this is the quantile function of Standized Normal
# F(mu.1) = p.0
# F(alpha.0 + alpha.1) = p.1
# OR = p.1/(1-p.1) / p.0/(1-p.1)
p.0 = phi(mu.1)
p.1 = phi(mu. 1 + alpha.0)
Odds.pool = p.1/(1-p.1)/(p.0/(1-p.0))
P_control.pool = p.1
# Predictive summaries ...
# p.new.0 = phi(theta.new[1])
# p.new.1 = phi(theta.new[1]+theta.new[2])
#
# Odds.new = p.new.1/(1-p.new.1)/(p.new.0/(1-p.new.0))
# P_control.new = p.new.0
}
"
#...........................................................................
# List of possible models ...
# normal random effects
m1 <- paste(dm, link.logit, re.normal, par.logit)
m2 <- paste(dm, link.cloglog, re.normal, par.cloglog)
m3 <- paste(dm, link.probit, re.normal, par.probit)
# sm random effects
m4 <- paste(dm, link.logit, re.sm, par.logit)
m5 <- paste(dm, link.cloglog, re.sm, par.cloglog)
m6 <- paste(dm, link.probit, re.sm, par.probit)
# sm random effects with two t-distributions one for each random effect
m7 <- paste(dm, link.logit, re.sm.split, par.logit)
m8 <- paste(dm, link.cloglog, re.sm.split, par.cloglog)
m9 <- paste(dm, link.probit, re.sm.split, par.probit)
# sm random effects
m10 <- paste(dm, link.logit, re.sm.df, par.logit)
m11 <- paste(dm, link.cloglog, re.sm.df, par.cloglog)
m12 <- paste(dm, link.probit, re.sm.df, par.probit)
# sm random effects with two t-distributions one for each random effect
m13 <- paste(dm, link.logit, re.sm.split.df, par.logit)
m14 <- paste(dm, link.cloglog, re.sm.split.df, par.cloglog)
m15 <- paste(dm, link.probit, re.sm.split.df, par.probit)
#...
switch(re,
normal = switch(link,
logit = return(m1),
cloglog = return(m2),
probit = return(m3),
stop("The model you requested is not implemented.")
),
sm = switch(link,
logit = return(m4),
cloglog = return(m5),
probit = return(m6),
stop("The model you requested is not implemented.")
),
sm.split = switch(link,
logit = return(m7),
cloglog = return(m8),
probit = return(m9),
stop("The model you requested is not implemented.")
),
sm.df = switch(link,
logit = return(m10),
cloglog = return(m11),
probit = return(m12),
stop("The model you requested is not implemented.")
),
sm.split.df = switch(link,
logit = return(m13),
cloglog = return(m14),
probit = return(m15),
stop("The model you requested is not implemented.")
),
stop("The model you requested is not implemented.")
)
}
#----
model.bugs <- blueprint(link, re, split.w, df.estimate)
model.bugs.connection <- textConnection(model.bugs)
if(r2jags == TRUE){
# Use R2jags as interface for JAGS ...
results <- jags( data = data.model,
parameters.to.save = parameters.model,
model.file = model.bugs.connection,
n.chains = nr.chains,
n.iter = nr.iterations,
n.burnin = nr.burnin,
n.thin = nr.thin)
}
else {
# Use rjags as interface for JAGS ...
# Send the model to JAGS, check syntax, run ...
jm <- jags.model(file = model.bugs.connection,
data = data.model,
# inits = inits.model,
n.chains = nr.chains,
n.adapt = nr.adapt,
quiet = be.quiet)
results <- coda.samples(jm,
variable.names = parameters.model,
n.iter = nr.iterations)
}
if(r2jags == FALSE)
{cat("You are using the package rjags as interface to JAGS.", "\n")
cat("The plot functions for output analysis are not implemented in this jarbes version", "\n")
}
# Close text conecction
close(model.bugs.connection)
# Extra outputs that are linked with other functions ...
IPD.names <- names(dataIPD)
IPD.names <- IPD.names[IPD.names!="y"]
results$beta.names <- paste("beta.", IPD.names, sep = "")
results$link <- link
results$re <- re
results$data <- data
results$two.by.two <- two.by.two
results$r2jags <- r2jags
results$split.w <- split.w
results$df.estimate <- df.estimate
# Priors ...
results$prior$mean.mu.1 = mean.mu.1
results$prior$mean.mu.1 = mean.mu.1
results$prior$mean.mu.phi = mean.mu.phi
results$prior$sd.mu.1 = sd.mu.1
results$prior$sd.mu.2 = sd.mu.2
results$prior$sd.mu.phi = sd.mu.phi
results$prior$sigma.1.upper = sigma.1.upper
results$prior$sigma.2.upper = sigma.2.upper
results$prior$mean.Fisher.rho = mean.Fisher.rho
results$prior$sd.Fisher.rho = sd.Fisher.rho
results$prior$df = df
results$prior$df.estimate = df.estimate
results$prior$df.lower = df.lower
results$prior$df.upper = df.upper
class(results) <- c("hmr")
return(results)
}
#' Generic print function for hmr object in jarbes.
#' @param x The object generated by the function hmr.
#'
#' @param digits The number of significant digits printed. The default value is 3.
#'
#' @param intervals A numeric vector of probabilities with values in [0,1]. The default value is
#' intervals = c(0.025, 0.5, 0.975).
#' @param ... \dots
#'
#' @export
print.hmr <- function(x, digits = 3,
intervals = c(0.025, 0.25, 0.5, 0.75, 0.975), ...)
{
m <- x
x <- x$BUGSoutput
sims.matrix <- x$sims.matrix
mu.vect <- apply(sims.matrix, 2, mean)
sd.vect <- apply(sims.matrix, 2, sd)
int.matrix <- apply(sims.matrix, 2, quantile, intervals)
if (x$n.chains>1) {
n.eff <- x$summary[,"n.eff"]
Rhat <- x$summary[,"Rhat"]
} else {
n.eff <- Rhat <- NULL
}
summaryMatrix <- t(rbind(mu.vect, sd.vect, int.matrix, Rhat, n.eff))
rownameMatrix <- rownames(summaryMatrix)
# Names of the regression coefficients ...
ind.names <- grep("beta.IPD", rownameMatrix)
rownameMatrix[ind.names] <- m$beta.names
rownames(summaryMatrix) <- rownameMatrix
dev.idx <- match("deviance", rownameMatrix)
if(any(!is.na(dev.idx))){
summaryMatrix <- rbind(summaryMatrix[-dev.idx,], summaryMatrix[dev.idx,])
rownames(summaryMatrix) <- c(rownameMatrix[-dev.idx], rownameMatrix[dev.idx])
}
if (!is.null(m$model.file))
cat("Inference for Bugs model at \"", m$model.file, "\", ",
sep = "")
if (!is.null(m$program))
cat("fit using ", m$program, ",", sep = "")
cat("\n ", m$n.chains, " chains, each with ", m$n.iter, " iterations (first ",
x$n.burnin, " discarded)", sep = "")
if (x$n.thin > 1)
cat(", n.thin =", x$n.thin)
cat("\n n.sims =", x$n.sims, "iterations saved\n")
print(round(summaryMatrix, digits), ...)
if (x$n.chains > 1) {
cat("\nFor each parameter, n.eff is a crude measure of effective sample size,")
cat("\nand Rhat is the potential scale reduction factor (at convergence, Rhat=1).\n")
}
if (x$isDIC) {
msgDICRule <- ifelse(x$DICbyR, "(using the rule, pD = var(deviance)/2)",
"(using the rule, pD = Dbar-Dhat)")
cat(paste("\nDIC info ", msgDICRule, "\n", sep = ""))
if (length(x$DIC) == 1) {
cat("pD =", fround(x$pD, 1), "and DIC =", fround(x$DIC,
1))
}
else if (length(x$DIC) > 1) {
print(round(x$DIC, 1))
}
cat("\nDIC is an estimate of expected predictive error (lower deviance is better).\n")
}
invisible(x)
}
fround <- function (x, digits) {
format (round (x, digits), nsmall=digits)
}
pfround <- function (x, digits) {
print (fround (x, digits), quote=FALSE)
}
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Defines functions print.hmr hmr.default hmr
Documented in hmr print.hmr
#' Bayesian meta-analysis to combine aggregated and individual participant data for cross design synthesis.
#'
#'
#' This function performers a Bayesian cross design synthesis. The function fits a
#' hierarchical meta-regression model based on a bivariate random effects model.
#'
#' The number of events in the control and treated group are modeled with two
#' conditional Binomial distributions and the random-effects are based on a
#' bivariate scale mixture of Normals.
#'
#' The individual participant data is modeled as a Bayesian logistic regression for
#' participants in the control group. Coefficients in the regression are modeled as
#' exchangeables.
#'
#' The function calculates the implicit hierarchical meta-regression, where the
#' treatment effect is regressed to the baseline risk (rate of events in the control
#' group). The scale mixture weights are used to adjust for internal validity and
#' structural outliers identification.
#'
#' The implicit hierarchical meta-regression is used to predict the treatment effect
#' for subgroups of individual participant data.
#'
#' Computations are done by calling JAGS (Just Another Gibbs Sampler) to perform
#' MCMC (Markov Chain Monte Carlo) sampling and returning an object of the
#' class \emph{mcmc.list}.
#'
#' Installation of JAGS: It is important to note that R 3.3.0 introduced a major change in the
#' use of toolchain for Windows. This new toolchain is incompatible with older packages written in C++.
#' As a consequence, if the installed version of JAGS does not match the R installation, then the rjags
#' package will spontaneously crash. Therefore, if a user works with R version >= 3.3.0, then JAGS must
#' be installed with the installation program JAGS-4.2.0-Rtools33.exe. For users who continue using R 3.2.4 or
#' an earlier version, the installation program for JAGS is the default installer JAGS-4.2.0.exe.
#'
#'
#' @param data Aggregated data results: a data frame where the first four columns containing the number of events in
#' the control group (yc), the number of patients in the control group (nc),
#' the number of events in the treatment group (yt) and the number of patients in the
#' treatment group (nt). If two.by.two = TRUE a data frame where each line
#' contains the trial results with column names: yc, nc, yt, nt.
#'
#' @param two.by.two If TRUE indicates that the trial results are with names: yc, nc, yt, nt.
#'
#' @param dataIPD Individual participant data: a data frame where
#' the first column is the outcome variable and the
#' other columns represent individual participant
#' charachteristics.
#'
#'
#' @param re Random effects distribution for the resulting model. Possible
#' values are \emph{normal} for bivariate random effects and \emph{sm}
#' for scale mixtures.
#'
#' @param link The link function used in the model. Possible values are
#' \emph{logit}, \emph{cloglog} \emph{probit}.
#'
#'
#' @param mean.mu.1 Prior mean of baseline risk, default value is 0.
#'
#' @param mean.mu.2 Prior mean of treatment effect, default value is 0.
#'
#' @param mean.mu.phi Prior mean of the bias parameter which measures the difference
#' between the baseline mean mu.1 and the intercept parameter of
#' the logistic regression of the individual participant data.
#' The defalut vaule is 0.
#'
#' @param sd.mu.1 Prior standard deviation of mu.1, default value is 1. The default prior of mu.1 is a
#' logistic distribution with mean 0 and dispersion 1. The implicit prior for mu.1 in
#' the probability scale is a uniform between 0 and 1.
#'
#' @param sd.mu.2 Prior standard deviation of mu.2, default value is 1. The default prior of mu.2 is a
#' logistic distribution with mean 0 and dispersion 1. The implicit prior for mu.2 in
#' the probability scale is a uniform between 0 and 1.
#'
#' @param sd.mu.phi Prior standard deviation of mu.phi, default value is 1.
#'
#' @param sigma.1.upper Upper bound of the uniform prior of sigma.1, default value is 5.
#'
#' @param sigma.2.upper Upper bound of the uniform prior of sigma.2, default value is 5.
#'
#' @param sigma.beta.upper Upper bound of the uniform prior of sigma.beta, default value is 5.
#'
#' @param mean.Fisher.rho Mean of rho in the Fisher scale, default value is 0.
#'
#' @param sd.Fisher.rho Standard deviation of rho in the Fisher scale, default value is 1/sqrt(2).
#'
#' @param df If de.estimate = FALSE, then df is the degrees of freedom for the scale mixture distribution, default value is 4.
#'
#' @param df.estimate Estimate the posterior of df. The default value is FALSE.
#'
#' @param df.lower Lower bound of the prior of df. The default value is 3.
#'
#' @param df.upper Upper bound of the prior of df. The default value is 30.
#'
#' @param split.w Split the w parameter in two independent weights one for each random effect.
#' The default value is FALSE.
#'
#'
#'
#'
#' @param nr.chains Number of chains for the MCMC computations, default 5.
#'
#' @param nr.iterations Number of iterations after adapting the MCMC, default is 10000. Some models may need more iterations.
#'
#' @param nr.adapt Number of iterations in the adaptation process, default is 1000. Some models may need more iterations during adptation.
#'
#' @param nr.burnin Number of iteration discarded for burnin period, default is 1000. Some models may need a longer burnin period.
#'
#' @param nr.thin Thinning rate, it must be a positive integer, the default value 1.
#'
#' @param be.quiet Do not print warning message if the model does not adapt default value is FALSE. If you are not sure about the adaptation period choose be.quiet=TRUE.
#'
#' @param r2jags Which interface is used to link R to JAGS (rjags and R2jags) default value is R2Jags TRUE.
#'
#' @return This function returns an object of the class "hmr". This object contains the MCMC output of
#' each parameter and hyper-parameter in the model, the data frame used for fitting the model, the link function,
#' type of random effects distribution and the splitting information for conflict of evidence analysis.
#'
#' The results of the object of the class metadiag can be extracted with R2jags or with rjags. In addition
#' a summary, a print and a plot function are implemented for this type of object.
#'
#' @references Verde, P.E, Ohmann, C., Icks, A. and Morbach, S. (2016) Bayesian evidence synthesis and combining randomized and nonrandomized results: a case study in diabetes. Statistics in Medicine. Volume 35, Issue 10, 10 May 2016, Pages: 1654 to 1675.
#'
#' @references Verde, P.E. (2017) The hierarchical meta-regression approach and learning from clinical evidence. Submited to the Biometrical Journal.
#'
#' @references Verde, P.E. (2018) The Hierarchical Meta-Regression Approach and Learning from Clinical Evidence. Technical report.
#'
#' @examples
#'
#'\dontrun{
#'library(jarbes)
#'
#' data("healing")
#' AD <- healing[, c("y_c", "n_c", "y_t", "n_t")]
#'
#' data("healingipd")
#'
#' IPD <- healingipd[, c("healing.without.amp", "PAD", "neuropathy",
#' "first.ever.lesion", "no.continuous.care", "male", "diab.typ2",
#' "insulin", "HOCHD", "HOS", "CRF", "dialysis", "DNOAP", "smoking.ever",
#' "diabdur", "wagner.class")]
#'
#' mx2 <- hmr(AD, two.by.two = FALSE,
#' dataIPD = IPD,
#' re = "sm",
#' link = "logit",
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sigma.beta.upper = 5,
#' sd.Fisher.rho = 1.25,
#' df.estimate = FALSE,
#' df.lower = 3,
#' df.upper = 10,
#' nr.chains = 1,
#' nr.iterations = 1500,
#' nr.adapt = 100,
#' nr.thin = 1)
#'
#' print(mx2)
#'
#'
#'
#'
#'# This experiment corresponds to Section 4 in Verde (2018).
#'#
#'# Experiment: Combining aggretated data from RCTs and a single
#'# observational study with individual participant data.
#'#
#'# In this experiment we assess conflict of evidence between the RCTs
#'# and the observational study with a partially identified parameter
#'# mu.phi.
#'#
#'# We run two simulated data: 1) mu.phi = 0.5 which is diffucult to
#'# identify. 2) mu.phi = 2 which can be identify. The simulations are
#'# used to see if the hmr() function can recover mu.phi.
#'#
#'
#'
#'library(MASS)
#'library(ggplot2)
#'library(jarbes)
#'library(gridExtra)
#'library(mcmcplots)
#'
#'
#'# Simulation of the IPD data
#'
#'invlogit <- function (x)
#'{
#' 1/(1 + exp(-x))
#'}
#'
#'# Data set for mu.phi = 0.5 .........................................
#'
#'# Parameters values
#'mu.phi.true <- 0.5
#'beta0 <- mu.1.true + mu.phi.true
#'beta1 <- 2.5
#'beta2 <- 2
#'
#'# Regression variables
#'
#'x1 <- rnorm(200)
#'x2 <- rbinom(200, 1, 0.5)
#'
#'# Binary outcome as a function of "b0 + b1 * x1 + b2 * x2"
#'
#'y <- rbinom(200, 1,
#' invlogit(beta0 + beta1 * x1 + beta2 * x2))
#'
#'
#'# Preparing the plot to visualize the data
#'jitter.binary <- function(a, jitt = 0.05)
#'
#' ifelse(a==0, runif(length(a), 0, jitt),
#' runif(length(a), 1-jitt, 1))
#'
#'
#'
#'plot(x1, jitter.binary(y), xlab = "x1",
#' ylab = "Success probability")
#'
#'curve(invlogit(beta0 + beta1*x),
#' from = -2.5, to = 2.5, add = TRUE, col ="blue", lwd = 2)
#'curve(invlogit(beta0 + beta1*x + beta2),
#' from = -2.5, to = 2.5, add = TRUE, col ="red", lwd =2)
#'legend("bottomright", c("b2 = 0", "b2 = 2"),
#' col = c("blue", "red"), lwd = 2, lty = 1)
#'
#'noise <- rnorm(100*20)
#'dim(noise) <- c(100, 20)
#'n.names <- paste(rep("x", 20), seq(3, 22), sep="")
#'colnames(noise) <- n.names
#'
#'data.IPD <- data.frame(y, x1, x2, noise)
#'
#'
#'# Application of HMR ...........................................
#'
#'res.s2 <- hmr(AD.s1, two.by.two = FALSE,
#' dataIPD = data.IPD,
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sd.Fisher.rho = 1.5)
#'
#'
#'print(res.s2)
#'
#'# Data set for mu.phi = 2 ......................................
#'# Parameters values
#'
#'mu.phi.true <- 2
#'beta0 <- mu.1.true + mu.phi.true
#'beta1 <- 2.5
#'beta2 <- 2
#'
#'# Regression variables
#'x1 <- rnorm(200)
#'x2 <- rbinom(200, 1, 0.5)
#'# Binary outcome as a function of "b0 + b1 * x1 + b2 * x2"
#'y <- rbinom(200, 1,
#' invlogit(beta0 + beta1 * x1 + beta2 * x2))
#'
#'# Preparing the plot to visualize the data
#'jitter.binary <- function(a, jitt = 0.05)
#'
#' ifelse(a==0, runif(length(a), 0, jitt),
#' runif(length(a), 1-jitt, 1))
#'
#'plot(x1, jitter.binary(y), xlab = "x1",
#' ylab = "Success probability")
#'
#'curve(invlogit(beta0 + beta1*x),
#' from = -2.5, to = 2.5, add = TRUE, col ="blue", lwd = 2)
#'curve(invlogit(beta0 + beta1*x + beta2),
#' from = -2.5, to = 2.5, add = TRUE, col ="red", lwd =2)
#'legend("bottomright", c("b2 = 0", "b2 = 2"),
#' col = c("blue", "red"), lwd = 2, lty = 1)
#'
#'noise <- rnorm(100*20)
#'dim(noise) <- c(100, 20)
#'n.names <- paste(rep("x", 20), seq(3, 22), sep="")
#'colnames(noise) <- n.names
#'
#'data.IPD <- data.frame(y, x1, x2, noise)
#'
#'# Application of HMR ................................................
#'
#'
#'res.s3 <- hmr(AD.s1, two.by.two = FALSE,
#' dataIPD = data.IPD,
#' sd.mu.1 = 2,
#' sd.mu.2 = 2,
#' sd.mu.phi = 2,
#' sigma.1.upper = 5,
#' sigma.2.upper = 5,
#' sd.Fisher.rho = 1.5
#')
#'
#'print(res.s3)
#'
#'# Posteriors for mu.phi ............................
#'attach.jags(res.s2)
#'mu.phi.0.5 <- mu.phi
#'df.phi.05 <- data.frame(x = mu.phi.0.5)
#'
#'attach.jags(res.s3)
#'mu.phi.1 <- mu.phi
#'df.phi.1 <- data.frame(x = mu.phi.1)
#'
#'
#'p1 <- ggplot(df.phi.05, aes(x=x))+
#' xlab(expression(mu[phi])) +
#' ylab("Posterior distribution")+
#' xlim(c(-7,7))+
#' geom_histogram(aes(y=..density..),fill = "royalblue",
#' colour = "black", alpha= 0.4, bins=60) +
#' geom_vline(xintercept = 0.64, colour = "black", size = 1.7, lty = 2)+
#' geom_vline(xintercept = 0.5, colour = "black", size = 1.7, lty = 1)+
#' stat_function(fun = dlogis,
#' n = 101,
#' args = list(location = 0, scale = 1), size = 1.5) + theme_bw()
#'
#'p2 <- ggplot(df.phi.1, aes(x=x))+
#' xlab(expression(mu[phi])) +
#' ylab("Posterior distribution")+
#' xlim(c(-7,7))+
#' geom_histogram(aes(y=..density..),fill = "royalblue",
#' colour = "black", alpha= 0.4, bins=60) +
#' geom_vline(xintercept = 2.2, colour = "black", size = 1.7, lty = 2)+
#' geom_vline(xintercept = 2, colour = "black", size = 1.7, lty = 1)+
#' stat_function(fun = dlogis,
#' n = 101,
#' args = list(location = 0, scale = 1), size = 1.5) + theme_bw()
#'
#'grid.arrange(p1, p2, ncol = 2, nrow = 1)
#'
#'
#' # Cater plots for regression coefficients ...........................
#'
#' var.names <- names(data.IPD[-1])
#' v <- paste("beta", names(data.IPD[-1]), sep = ".")
#' mcmc.x <- as.rjags.mcmc(res.s2$BUGSoutput$sims.matrix)
#' mcmc.x.2 <- as.mcmc.rjags(res.s2)
#' mcmc.x.3 <- as.mcmc.rjags(res.s3)
#'
#' greek.names <- paste(paste("beta[",1:22, sep=""),"]", sep="")
#' par.names <- paste(paste("beta.IPD[",1:22, sep=""),"]", sep="")
#'
#' caterplot(mcmc.x.2,
#' parms = par.names,
#' col = "black", lty = 1,
#' labels = greek.names,
#' greek = T,
#' labels.loc="axis", cex =0.7,
#' style = "plain",reorder = F, denstrip = F)
#'
#'caterplot(mcmc.x.3,
#' parms = par.names,
#' col = "grey", lty = 2,
#' labels = greek.names,
#' greek = T,
#' labels.loc="axis", cex =0.7,
#' style = "plain",reorder = F, denstrip = F,
#' add = TRUE,
#' collapse=TRUE, cat.shift=-0.5)
#'
#'
#'
#'abline(v=0, lty = 2, lwd = 2)
#'abline(v =2, lty = 2, lwd = 2)
#'abline(v =2.5, lty = 2, lwd = 2)
#'
#' # End of the examples.
#'
#' }
#'
#'
#' @import R2jags
#' @import rjags
#' @import graphics
#' @import stats
#' @import graphics
#'
#' @export
#'
hmr <- function(data,
two.by.two = TRUE,
dataIPD,
# Arguments for the model:
re = "normal",
link = "logit",
# Hyperpriors parameters............................................
mean.mu.1 = 0,
mean.mu.2 = 0,
mean.mu.phi = 0,
sd.mu.1 = 1,
sd.mu.2 = 1,
sd.mu.phi = 1,
sigma.1.upper = 5,
sigma.2.upper = 5,
sigma.beta.upper = 5,
mean.Fisher.rho = 0,
sd.Fisher.rho = 1/sqrt(2),
df = 4,
df.estimate = FALSE,
df.lower = 3,
df.upper = 20,
# Split weights
split.w = FALSE,
# MCMC setup........................................................
nr.chains = 2,
nr.iterations = 10000,
nr.adapt = 1000,
nr.burnin = 1000,
nr.thin = 1,
# Further options to link jags and R ...............................
be.quiet = FALSE,
r2jags = TRUE
)UseMethod("hmr")
#' @export
#'
hmr.default <- function(
data,
two.by.two = TRUE,
dataIPD,
# Arguments for the model:
re = "normal",
link = "logit",
# Hyperpriors parameters............................................
mean.mu.1 = 0,
mean.mu.2 = 0,
mean.mu.phi = 0,
sd.mu.1 = 1,
sd.mu.2 = 1,
sd.mu.phi = 1,
sigma.1.upper = 5,
sigma.2.upper = 5,
sigma.beta.upper = 5,
mean.Fisher.rho = 0,
sd.Fisher.rho = 1/sqrt(2),
df = 4,
df.estimate = FALSE,
df.lower = 3,
df.upper = 20,
# Split weights
split.w = FALSE,
# MCMC setup........................................................
nr.chains = 2,
nr.iterations = 10000,
nr.adapt = 1000,
nr.burnin = 1000,
nr.thin = 1,
# Further options to link jags and R ...............................
be.quiet = FALSE,
r2jags = TRUE
)
{
# Model errors checking-----
if(re=="normal" & split.w==TRUE)stop("Normal random effects and splitting weights are not compatible options")
re.test <- re %in% c("normal", "sm")
if(!re.test)stop("This random effects distribution is not implemented")
link.test <- link %in% c("logit", "cloglog", "probit")
if(!link.test)stop("This link function is not implemented")
# Setting up hyperparameters ...
pre.mu.1 <- 1/(sd.mu.1*sd.mu.1)
pre.mu.2 <- 1/(sd.mu.2*sd.mu.2)
pre.mu.phi <- 1/ (sd.mu.phi * sd.mu.phi)
pre.Fisher.rho <- 1/(sd.Fisher.rho * sd.Fisher.rho)
# Setting up data nodes ...
if(two.by.two == FALSE)
{
yc <- data[,1]
nc <- data[,2]
yt <- data[,3]
nt <- data[,4]
} else
{
yc <- data$yc
nc <- data$nc
yt <- data$yt
nt <- data$nt
}
N <- length(nc)
# Increase N for one observacional study
N <- N + 1
# Data errors
#if(yc>nc || yt>nt)stop("the data is inconsistent")
#if(missing(data))stop("NAs are not allowed in this function")
# Setup IPD data for regression ................................................
dataIPD$y <- dataIPD[,1]
dataIPD <- dataIPD[,-1] # <- corregido! Se generó un bug version > 1.7.0
model.1 <- model.frame(y ~ ., data = dataIPD)
X.IPD <- model.matrix(model.1, data = dataIPD)
X.IPD <- X.IPD[ , dimnames(X.IPD)[[2]] != "(Intercept)", drop=FALSE]
y.0.IPD <- model.response(model.1)
if(is.factor(y.0.IPD)){y.0.IPD <- unclass(y.0.IPD) - 1}
K <- dim(X.IPD)[2]
M <- dim(X.IPD)[1]
#.............................................................................
# Data, initial values and parameters .......................................
data.model <-
list(M = M,
K = K,
X.IPD = X.IPD,
y.0.IPD = y.0.IPD,
N = N,
yc = yc,
nc = nc,
yt = yt,
nt = nt,
mean.mu.1 = mean.mu.1,
mean.mu.2 = mean.mu.2,
mean.mu.phi = mean.mu.phi,
pre.mu.1 = pre.mu.1,
pre.mu.2 = pre.mu.2,
pre.mu.phi = pre.mu.phi,
sigma.1.upper = sigma.1.upper,
sigma.2.upper = sigma.2.upper,
sigma.beta.upper = sigma.beta.upper,
mean.Fisher.rho = mean.Fisher.rho,
pre.Fisher.rho = pre.Fisher.rho
)
if(re == "sm" & df.estimate == TRUE){data.model$df.lower <- df.lower
data.model$df.upper <- df.upper}
if(re == "sm" & df.estimate == FALSE){data.model$df <- df}
# Parameters to monitor ....................................................................
parameters.model <-
c("mu.1",
"mu.2",
"mu.phi",
"sigma.1",
"sigma.2",
"rho",
"Odds.pool",
# "Odds.new",
"P_control.pool",
# "P_control.new",
"alpha.0",
"alpha.1",
"beta.IPD",
"sigma.beta",
"x.subgroup",
"eta.subgroup" # Verde's formula ....
)
# This take the weights for the scale mixture random effects model, etc...
if(re == "sm" & split.w == TRUE & df.estimate == TRUE)
parameters.model <- c(parameters.model, "w1", "w2", "p.w1", "p.w2", "df")
else
if(re == "sm" & split.w == TRUE & df.estimate == FALSE)
parameters.model <- c(parameters.model, "w1", "w2", "p.w1", "p.w2")
else
if(re=="sm" & split.w == FALSE & df.estimate == TRUE)
parameters.model <- c(parameters.model, "w", "p.w", "df")
else
if(re=="sm" & split.w == FALSE & df.estimate == FALSE)
parameters.model <- c(parameters.model, "w", "p.w")
# Model BUGS script
#----
blueprint <- function(link = "logit", re = "normal", split.w = FALSE, df.estimate = FALSE)
{
if(split.w == FALSE & df.estimate == TRUE ) re <- "sm.df"
if(split.w == TRUE & df.estimate == FALSE) re <- "sm.split"
if(split.w == TRUE & df.estimate == TRUE ) re <- "sm.split.df"
#----
# Block for data model ......................................................................
dm <-
"
model
{
for(i in 1:(N-1))
{
yc[i] ~ dbin(pc[i], nc[i])
yt[i] ~ dbin(pt[i], nt[i])
"
#----
# Block for the link function................................................................
link.logit <-
"
# Random effects model
logit(pc[i]) <- theta.1[i]
logit(pt[i]) <- theta.2[i] + logit(pc[i])
"
link.cloglog <-
"
# Random effects model
cloglog(pc[i]) <- theta.1[i]
cloglog(pt[i]) <- theta.2[i] + cloglog(pc[i])
"
link.probit <-
"
# Random effects model
probit(pc[i]) <- theta.1[i]
probit(pt[i]) <- theta.2[i] + probit(pc[i])
"
# Block for structural distribution .........................................................
re.normal <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1)
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1)
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.theta.1 <- 1/(sigma.1*sigma.1)
pre.theta.2 <- 1/(sigma.2*sigma.2)
# Conditional precision
pre.theta.2.1 <- pre.theta.2 / (1 - rho*rho)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
Sigma.new[1, 1] <- pow(sigma.1, 2)
Sigma.new[2, 2] <- pow(sigma.2, 2)
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2
Sigma.new[2, 1] <- Sigma.new[1, 2]
Omega.new[1:2, 1:2] <- inverse(Sigma.new[1:2, 1:2])
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Block for: link = logistic, re = normal and split.w = FALSE
# Model for individual data ..................................................
# Random effect for the observational study ..................................
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1)
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1)
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#----
re.sm <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1[i])
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1[i])
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
# Conditional precision
pre.theta.2.1[i] <- pre.theta.2[i] / (1 - rho * rho)
lambda[i] ~ dchisqr(df)
w[i] <- df/lambda[i]
pre.theta.1[i] <- pre.1 / w[i]
pre.theta.2[i] <- pre.2 / w[i]
# Probability of outlier
p.w[i] <- step(w[i]-0.99)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.1 <- 1/(sigma.1*sigma.1)
pre.2 <- 1/(sigma.2*sigma.2)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
Sigma.new[1, 1] <- pow(sigma.1, 2)
Sigma.new[2, 2] <- pow(sigma.2, 2)
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2
Sigma.new[2, 1] <- Sigma.new[1, 2]
lambda.new ~ dchisqr(df)
w.new <- df/lambda.new
Omega.new[1:2,1:2] <- inverse(Sigma.new[1:2, 1:2]) / w.new
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Block for: link = logistic, re = sm and split.w = FALSE
# Model for individual data ..................................................
# Random effect for the observational study ..................................
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Structure of w[N]...........................................................
# Case: random weight same as RCTs
lambda[N] ~ dchisqr(df)
w[N] <- df/lambda[N]
pre.theta.1[N] <- pre.1 / w[N]
pre.theta.2[N] <- pre.2 / w[N]
pre.theta.2.1[N] <- pre.theta.2[N] / (1-rho*rho)
# Probability of outlier.......................................................
p.w[N] <- step(w[N]-0.99)
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1[N])
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1[N])
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#--------------------------------------------------
re.sm.split <-
"
theta.1[i] ~ dnorm(mu.1, pre.theta.1[i])
theta.2[i] ~ dnorm(mu.2.1[i], pre.theta.2.1[i])
#Conditional mean
mu.2.1[i] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[i] - mu.1)
# Conditional precision
pre.theta.2.1[i] <- pre.theta.2[i] / (1 - rho * rho)
pre.theta.1[i] <- pre.1 / w1[i]
pre.theta.2[i] <- pre.2 / w2[i]
lambda1[i] ~ dchisqr(df)
w1[i] <- df/lambda1[i]
lambda2[i] ~ dchisqr(df)
w2[i] <- df/lambda2[i]
# Probability of outlier
p.w1[i] <- step(w1[i]-0.99)
p.w2[i] <- step(w2[i]-0.99)
}
# Hyper priors
mu.1 ~ dlogis(mean.mu.1, pre.mu.1)
mu.2 ~ dlogis(mean.mu.2, pre.mu.2)
# Dispersion parameters
sigma.1 ~ dunif(0, sigma.1.upper)
sigma.2 ~ dunif(0, sigma.2.upper)
pre.1 <- 1/(sigma.1*sigma.1)
pre.2 <- 1/(sigma.2*sigma.2)
# Correlation
z ~ dnorm(mean.Fisher.rho, pre.Fisher.rho)
rho <- 2*exp(z)/(1+exp(z)) - 1
# Predictions ...
mu.new[1] <- mu.1
mu.new[2] <- mu.2
lambda1.new ~ dchisqr(df)
lambda2.new ~ dchisqr(df)
w1.new <- df/lambda1.new
w2.new <- df/lambda2.new
Sigma.new[1, 1] <- pow(sigma.1, 2)/w1.new
Sigma.new[2, 2] <- pow(sigma.2, 2)/w2.new
Sigma.new[1, 2] <- rho * sigma.1 * sigma.2 / sqrt(w1.new*w2.new)
Sigma.new[2, 1] <- Sigma.new[1, 2]
Omega.new[1:2,1:2] <- inverse(Sigma.new[1:2, 1:2])
theta.new[1:2] ~ dmnorm(mu.new[1:2], Omega.new[1:2 ,1:2])
# Functional parameters
alpha.0 <- (mu.2 - alpha.1 * mu.1)
alpha.1 <- rho * sigma.2/sigma.1
# Introduced mu.phi...........................................................
mu.phi ~ dlogis(mean.mu.phi, pre.mu.phi) # non-informative
mu.obs <- mu.1 + mu.phi
# Structure of w[N]...........................................................
# Case: random weight same as RCTs
lambda1[N] ~ dchisqr(df)
w1[N] <- df/lambda1[N]
lambda2[N] ~ dchisqr(df)
w2[N] <- df/lambda2[N]
pre.theta.1[N] <- pre.1 / w1[N]
pre.theta.2[N] <- pre.2 / w2[N]
pre.theta.2.1[N] <- pre.theta.2[N] / (1-rho*rho)
# Probability of outlier.......................................................
p.w1[N] <- step(w1[N]-0.99)
# Change mu.1 to mu.obs = mu.1 + mu.phi .......................................
mu.2.1[N] <- mu.2 + rho * sigma.2 / sigma.1 * (theta.1[N] - mu.obs)
theta.1[N] ~ dnorm(mu.obs, pre.theta.1[N])
theta.2[N] ~ dnorm(mu.2.1[N], pre.theta.2.1[N])
# Priors for beta.IPD .........................................................
for( i in 1:K)
{
beta.IPD[i] ~ dnorm(0, pre.beta.IPD)
}
pre.beta.IPD <- 1/(sigma.beta*sigma.beta)
sigma.beta ~ dunif(0, sigma.beta.upper)
"
#------------------------------------------------------------------------
prior.of.df <- "
# Degrees of freedom
a <- 1/df.upper
b <- 1/df.lower
df <- 1/U
U ~ dunif(a, b)
"
re.sm.df <- paste(re.sm, prior.of.df)
#------------------------------------------------------------------------
re.sm.split.df <- paste(re.sm.split, prior.of.df)
#...........................................................................
# Block of parameters of interest depending on the links ......................
par.logit <- "
#..............................................................................
for(i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
logit(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
Odds.pool <- exp(alpha.0) # Here was a bug in version < 2.0.0
P_control.pool <- ilogit(mu.1)
# Predictive summaries ...
# Odds.new <- exp(theta.new[2]) # Here was a bug in version < 2.0.0
# P_control.new <- ilogit(theta.new[1])
}"
par.cloglog <- "
#..............................................................................
for( i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
cloglog(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
# F(x) = exp(-exp(x)) this is the quantile function of the Gumbel distribution
# F(mu.1) = p.0
# F(alpha.0 + alpha.1) = p.1
# OR = p.1/(1-p.1) / p.0/(1-p.1)
p.0 = icloglog(mu.1)
p.1 = icloglog(mu.1 + alpha.0)
Odds.pool = p.1/(1-p.1)/(p.0/(1-p.0))
P_control.pool = p.1
# Predictive summaries ...
# p.new.0 = icloglog(theta.new[1])
# p.new.1 = icloglog(theta.new[1]+theta.new[2])
#
# Odds.new = p.new.1/(1-p.new.1)/(p.new.0/(1-p.new.0))
# P_control.new = p.new.0
}"
par.probit <-
"
#..............................................................................
for( i in 1:M){
y.0.IPD[i] ~ dbern(p0.IPD[i])
probit(p0.IPD[i]) <- theta.1[N] + inprod(beta.IPD[1:K], X.IPD[i,1:K])
}
# Verde's formula to estimate relative treatment effect in a subgroup .........
for(i in 1:K){
x.subgroup[i] = mean(mu.phi + beta.IPD[i])
eta.subgroup[i] = alpha.0 + alpha.1*(x.subgroup[i] - mu.1)
}
# Parameters of interest
# Pooled summaries ...
# F(x) = phi(x) this is the quantile function of Standized Normal
# F(mu.1) = p.0
# F(alpha.0 + alpha.1) = p.1
# OR = p.1/(1-p.1) / p.0/(1-p.1)
p.0 = phi(mu.1)
p.1 = phi(mu. 1 + alpha.0)
Odds.pool = p.1/(1-p.1)/(p.0/(1-p.0))
P_control.pool = p.1
# Predictive summaries ...
# p.new.0 = phi(theta.new[1])
# p.new.1 = phi(theta.new[1]+theta.new[2])
#
# Odds.new = p.new.1/(1-p.new.1)/(p.new.0/(1-p.new.0))
# P_control.new = p.new.0
}
"
#...........................................................................
# List of possible models ...
# normal random effects
m1 <- paste(dm, link.logit, re.normal, par.logit)
m2 <- paste(dm, link.cloglog, re.normal, par.cloglog)
m3 <- paste(dm, link.probit, re.normal, par.probit)
# sm random effects
m4 <- paste(dm, link.logit, re.sm, par.logit)
m5 <- paste(dm, link.cloglog, re.sm, par.cloglog)
m6 <- paste(dm, link.probit, re.sm, par.probit)
# sm random effects with two t-distributions one for each random effect
m7 <- paste(dm, link.logit, re.sm.split, par.logit)
m8 <- paste(dm, link.cloglog, re.sm.split, par.cloglog)
m9 <- paste(dm, link.probit, re.sm.split, par.probit)
# sm random effects
m10 <- paste(dm, link.logit, re.sm.df, par.logit)
m11 <- paste(dm, link.cloglog, re.sm.df, par.cloglog)
m12 <- paste(dm, link.probit, re.sm.df, par.probit)
# sm random effects with two t-distributions one for each random effect
m13 <- paste(dm, link.logit, re.sm.split.df, par.logit)
m14 <- paste(dm, link.cloglog, re.sm.split.df, par.cloglog)
m15 <- paste(dm, link.probit, re.sm.split.df, par.probit)
#...
switch(re,
normal = switch(link,
logit = return(m1),
cloglog = return(m2),
probit = return(m3),
stop("The model you requested is not implemented.")
),
sm = switch(link,
logit = return(m4),
cloglog = return(m5),
probit = return(m6),
stop("The model you requested is not implemented.")
),
sm.split = switch(link,
logit = return(m7),
cloglog = return(m8),
probit = return(m9),
stop("The model you requested is not implemented.")
),
sm.df = switch(link,
logit = return(m10),
cloglog = return(m11),
probit = return(m12),
stop("The model you requested is not implemented.")
),
sm.split.df = switch(link,
logit = return(m13),
cloglog = return(m14),
probit = return(m15),
stop("The model you requested is not implemented.")
),
stop("The model you requested is not implemented.")
)
}
#----
model.bugs <- blueprint(link, re, split.w, df.estimate)
model.bugs.connection <- textConnection(model.bugs)
if(r2jags == TRUE){
# Use R2jags as interface for JAGS ...
results <- jags( data = data.model,
parameters.to.save = parameters.model,
model.file = model.bugs.connection,
n.chains = nr.chains,
n.iter = nr.iterations,
n.burnin = nr.burnin,
n.thin = nr.thin)
}
else {
# Use rjags as interface for JAGS ...
# Send the model to JAGS, check syntax, run ...
jm <- jags.model(file = model.bugs.connection,
data = data.model,
# inits = inits.model,
n.chains = nr.chains,
n.adapt = nr.adapt,
quiet = be.quiet)
results <- coda.samples(jm,
variable.names = parameters.model,
n.iter = nr.iterations)
}
if(r2jags == FALSE)
{cat("You are using the package rjags as interface to JAGS.", "\n")
cat("The plot functions for output analysis are not implemented in this jarbes version", "\n")
}
# Close text conecction
close(model.bugs.connection)
# Extra outputs that are linked with other functions ...
IPD.names <- names(dataIPD)
IPD.names <- IPD.names[IPD.names!="y"]
results$beta.names <- paste("beta.", IPD.names, sep = "")
results$link <- link
results$re <- re
results$data <- data
results$two.by.two <- two.by.two
results$r2jags <- r2jags
results$split.w <- split.w
results$df.estimate <- df.estimate
# Priors ...
results$prior$mean.mu.1 = mean.mu.1
results$prior$mean.mu.1 = mean.mu.1
results$prior$mean.mu.phi = mean.mu.phi
results$prior$sd.mu.1 = sd.mu.1
results$prior$sd.mu.2 = sd.mu.2
results$prior$sd.mu.phi = sd.mu.phi
results$prior$sigma.1.upper = sigma.1.upper
results$prior$sigma.2.upper = sigma.2.upper
results$prior$mean.Fisher.rho = mean.Fisher.rho
results$prior$sd.Fisher.rho = sd.Fisher.rho
results$prior$df = df
results$prior$df.estimate = df.estimate
results$prior$df.lower = df.lower
results$prior$df.upper = df.upper
class(results) <- c("hmr")
return(results)
}
#' Generic print function for hmr object in jarbes.
#' @param x The object generated by the function hmr.
#'
#' @param digits The number of significant digits printed. The default value is 3.
#'
#' @param intervals A numeric vector of probabilities with values in [0,1]. The default value is
#' intervals = c(0.025, 0.5, 0.975).
#' @param ... \dots
#'
#' @export
print.hmr <- function(x, digits = 3,
intervals = c(0.025, 0.25, 0.5, 0.75, 0.975), ...)
{
m <- x
x <- x$BUGSoutput
sims.matrix <- x$sims.matrix
mu.vect <- apply(sims.matrix, 2, mean)
sd.vect <- apply(sims.matrix, 2, sd)
int.matrix <- apply(sims.matrix, 2, quantile, intervals)
if (x$n.chains>1) {
n.eff <- x$summary[,"n.eff"]
Rhat <- x$summary[,"Rhat"]
} else {
n.eff <- Rhat <- NULL
}
summaryMatrix <- t(rbind(mu.vect, sd.vect, int.matrix, Rhat, n.eff))
rownameMatrix <- rownames(summaryMatrix)
# Names of the regression coefficients ...
ind.names <- grep("beta.IPD", rownameMatrix)
rownameMatrix[ind.names] <- m$beta.names
rownames(summaryMatrix) <- rownameMatrix
dev.idx <- match("deviance", rownameMatrix)
if(any(!is.na(dev.idx))){
summaryMatrix <- rbind(summaryMatrix[-dev.idx,], summaryMatrix[dev.idx,])
rownames(summaryMatrix) <- c(rownameMatrix[-dev.idx], rownameMatrix[dev.idx])
}
if (!is.null(m$model.file))
cat("Inference for Bugs model at \"", m$model.file, "\", ",
sep = "")
if (!is.null(m$program))
cat("fit using ", m$program, ",", sep = "")
cat("\n ", m$n.chains, " chains, each with ", m$n.iter, " iterations (first ",
x$n.burnin, " discarded)", sep = "")
if (x$n.thin > 1)
cat(", n.thin =", x$n.thin)
cat("\n n.sims =", x$n.sims, "iterations saved\n")
print(round(summaryMatrix, digits), ...)
if (x$n.chains > 1) {
cat("\nFor each parameter, n.eff is a crude measure of effective sample size,")
cat("\nand Rhat is the potential scale reduction factor (at convergence, Rhat=1).\n")
}
if (x$isDIC) {
msgDICRule <- ifelse(x$DICbyR, "(using the rule, pD = var(deviance)/2)",
"(using the rule, pD = Dbar-Dhat)")
cat(paste("\nDIC info ", msgDICRule, "\n", sep = ""))
if (length(x$DIC) == 1) {
cat("pD =", fround(x$pD, 1), "and DIC =", fround(x$DIC,
1))
}
else if (length(x$DIC) > 1) {
print(round(x$DIC, 1))
}
cat("\nDIC is an estimate of expected predictive error (lower deviance is better).\n")
}
invisible(x)
}
fround <- function (x, digits) {
format (round (x, digits), nsmall=digits)
}
pfround <- function (x, digits) {
print (fround (x, digits), quote=FALSE)
}
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