###########################################################################
############## FUNCTIONS FOR REFERENCE BY MAIN - NOT FOR USER #############
###########################################################################
# m.dat.chang, all RE, v.est and sd.estpar FUNCTIONS #
#_______________________________________________________________________________
# Original by Chihyun Lee (August, 2017) #
# Last Modified by Sandra Castro-Pearson (June, 2018) #
# Received from Chihyun Lee (January, 2018) #
#_______________________________________________________________________________
######################
##-----reformat dataset
m.dat.chang=function(dat,beta) {
n=length(unique(dat$id))
mc=max(dat$epi)-1
p=length(beta)/2
beta1=beta[1:p]
beta2=beta[(p+1):(2*p)]
maxb=apply(cbind(beta1,beta2),1,max)
#amat=cbind(dat$a1,dat$a2,dat$a3) changed below
amat_indexes <- c(9:ncol(dat))
amat <- as.matrix(dat[,amat_indexes])
dat$txij=dat$xij*exp(-amat%*%beta1)
dat$tzij=dat$txij+dat$yij*exp(-amat%*%beta2)
dat$tci=dat$ci*exp(-amat%*%maxb)
all.t.xij=all.t.zij=all.t.d1=all.t.d2=all.mstar=all.a=NULL
for (i in unique(dat$id)) {
tmp=dat[dat$id==i,]
t.xij=min(tmp$txij[1],tmp$tci[1])
t.zij=min(tmp$tzij[1],tmp$tci[1])
t.d1=(t.xij<tmp$tci[1])
t.d2=(t.zij<tmp$tci[1])
if (nrow(tmp)>1) {
td1=t.d1
td2=t.d2
j=2
while (td1==1 & td2==1 & j<=nrow(tmp)) {
tsum=sum(t.zij[1:(j-1)])
txij=min(tmp$txij[j],tmp$tci[j]-tsum)
tzij=min(tmp$tzij[j],tmp$tci[j]-tsum)
td1=(txij+tsum)<tmp$tci[j]
td2=(tzij+tsum)<tmp$tci[j]
if (td1==1 & td2==1) {
t.xij=c(t.xij,txij)
t.zij=c(t.zij,tzij)
t.d1=c(t.d1,td1)
t.d2=c(t.d2,td2)
}
j=j+1
}
}
all.t.xij=c(all.t.xij,t.xij)
all.t.zij=c(all.t.zij,t.zij)
all.t.d1=c(all.t.d1,t.d1)
all.t.d2=c(all.t.d2,t.d2)
all.mstar=c(all.mstar,rep(length(t.xij),length(t.xij)))
all.a=rbind(all.a, tmp[1:length(t.xij), amat_indexes])
}
ugap1 = cbind(tgtime = all.t.xij, delta = as.integer(all.t.d1), all.a, mstar=all.mstar)
ugap2 = cbind(tgtime = all.t.zij, delta = as.integer(all.t.d2), all.a, mstar=all.mstar)
#order
ugap1=ugap1[order(ugap1$tgtime,decreasing=TRUE),]
ugap2=ugap2[order(ugap2$tgtime,decreasing=TRUE),]
out=list(n=n,ugap1=ugap1,ugap2=ugap2)
return(out)
}
##-----point estimation
##rev-biv
RE.biv=function(beta,dat) {
mdat=m.dat.chang(dat,beta)
n=mdat$n
ugap1=mdat$ugap1
ugap2=mdat$ugap2
ncov = length(c(9:ncol(dat)))
a_indexes1 = a_indexes2 = seq(3, 2+ncov, 1)
ss10=cumsum(1/ugap1$mstar/n)
#ss11=apply(cbind(ugap1$a1,ugap1$a2,ugap1$a3)/ugap1$mstar/n,2,cumsum)
#sub1=ugap1$delta*(cbind(ugap1$a1,ugap1$a2,ugap1$a3)-ss11/ss10)/ugap1$mstar/sqrt(n)
#changed below
ss11=apply(ugap1[, a_indexes1]/ugap1$mstar/n,2,cumsum)
sub1=ugap1$delta*(ugap1[, a_indexes1]-ss11/ss10)/ugap1$mstar/sqrt(n)
ss20=cumsum(1/ugap2$mstar/n)
#ss21=apply(cbind(ugap2$a1,ugap2$a2,ugap2$a3)/ugap2$mstar/n,2,cumsum)
#sub2=ugap2$delta*(cbind(ugap2$a1,ugap2$a2,ugap2$a3)-ss21/ss20)/ugap2$mstar/sqrt(n)
#changed below
ss21=apply(ugap2[, a_indexes2]/ugap2$mstar/n,2,cumsum)
sub2=ugap2$delta*(ugap2[, a_indexes2]-ss21/ss20)/ugap2$mstar/sqrt(n)
out1=apply(sub1,2,sum)
out2=apply(sub2,2,sum)
out=c(out1,out2)
return(out)
}
RE.uf=function(beta,dat) {
tmp.out=RE.biv(beta,dat)
out=tmp.out%*%tmp.out
return(out)
}
RE.uest=function(init,dat) {
res=optim(init, RE.uf, dat=dat, control=list(maxit=20000))
return(list(par=res$par,value=res$value,conv=res$convergence))
}
##-----variance estimation
############################################
#Zeng
############################################
v.est=function(beta,dat,R)
#----------------------------------------------------------------------------------------------------------------------------
# first step of variance estimate: estimate V by bootstrap, only need to evaluate the estimating function, no need to solve it
#----------------------------------------------------------------------------------------------------------------------------
{
id=dat$id
ids=unique(dat$id)
n=length(ids)
freq=table(dat$id)
index=cumsum( c(0, freq[-n]) )
p=length(beta)
A=matrix(rep(NA,R*p),ncol=p)
for (i in 1:R)
{
w=table(sample(ids,n,replace=TRUE))
s=as.numeric(names(w)) # because of this line, id must be 1:n
w=as.numeric(w)
location=NULL
newid=NULL
for(ss in 1:length(s))
{
location=c(location, rep(index[s[ss]]+(1:freq[s[ss]]),times=w[ss]))
# since the same subject may be drawn multiple times, new id need to be created to distinguish different duplicates
# e.g., the first duplicate's id will be original id+1000, the next will be id+2000, etc.
newid=c(newid,rep(id[index[s[ss]]+(1:freq[s[ss]])],times=w[ss])+rep(((1:w[ss])-1)*1000,each=freq[s[ss]]))
}
dat.boot=dat[location,]
#cbind(dat.boot,newid=newid)
dat.boot$id=newid
A[i,]=RE.biv(beta,dat.boot)
}
v=cov(A)
return(v)
}
############################################
#parzen
############################################
#should do v.est first
############################################
RE.bivR=function(beta,dat,R) {
mdat=m.dat.chang(dat,beta)
n=mdat$n
p=length(beta)
ugap1=mdat$ugap1
ugap2=mdat$ugap2
ncov = length(c(9:ncol(dat))) #added line
a_indexes1 = a_indexes2 = seq(3, 2+ncov, 1) #added line
ss10=cumsum(1/ugap1$mstar/n)
#ss11=apply(cbind(ugap1$a1,ugap1$a2,ugap1$a3)/ugap1$mstar/n,2,cumsum)
#sub1=ugap1$delta*(cbind(ugap1$a1,ugap1$a2,ugap1$a3)-ss11/ss10)/ugap1$mstar/sqrt(n)
ss11=apply(ugap1[, a_indexes1]/ugap1$mstar/n,2,cumsum)
sub1=ugap1$delta*(ugap1[, a_indexes1]-ss11/ss10)/ugap1$mstar/sqrt(n)
ss20=cumsum(1/ugap2$mstar/n)
#ss21=apply(cbind(ugap2$a1,ugap2$a2,ugap2$a3)/ugap2$mstar/n,2,cumsum)
#sub2=ugap2$delta*(cbind(ugap2$a1,ugap2$a2,ugap2$a3)-ss21/ss20)/ugap2$mstar/sqrt(n)
#changed below
ss21=apply(ugap2[, a_indexes2]/ugap2$mstar/n,2,cumsum)
sub2=ugap2$delta*(ugap2[, a_indexes2]-ss21/ss20)/ugap2$mstar/sqrt(n)
out1=apply(sub1,2,sum)-R[1:(p/2)]
out2=apply(sub2,2,sum)-R[(p/2+1):p]
out=c(out1,out2)
return(out)
}
RE.ufR=function(beta,dat,R) {
tmp.out=RE.bivR(beta,dat,R)
out=tmp.out%*%tmp.out
return(out)
}
RE.uestR=function(init,dat,R) {
res=optim(init,RE.ufR,dat=dat,R=R, control=list(maxit=20000))
return(list(par=res$par,value=res$value,conv=res$convergence))
}
sd.estpar=function(init, dat, v, B) {
p=length(init)
A=matrix(rep(NA,B*p),ncol=p)
i=0
while (i < B)
{
R=MASS::mvrnorm(1,rep(0,p),v)
est.R=RE.uestR(init,dat,R)
if (est.R$conv!=0) next
i=i+1
A[i,]=est.R$par
}
var_est=cov(A,A) #cov compute the cov between columns
out=sqrt(diag(var_est))
return(list(sd=out, covmat=var_est))
}
###################################################################
#################### FUNCTION NOT FOR USER ########################
###################################################################
#' A Function for multivariate fits using semiparametric regression method on a biv.rec object
#'
#' @description
#' This function fits the model using Chang's Method given multiple covariates. Called from biv.rec.fit(). No user interface.
#' @param new_data An object that has been reformatted for fit using the biv.rec.reformat() function. Passed from biv.rec.fit().
#' @param cov_names A vector with the names of the covariates. Passed from biv.rec.fit().
#' @param SE Passed from biv.rec.fit().
#'
#' @return A list with estimates, SE and variance-covariance matrix.
#'
#' @importFrom stats na.omit
#' @importFrom stats optim
#' @importFrom stats optimize
#' @importFrom stats qnorm
#' @importFrom stats cov
#' @importFrom MASS mvrnorm
#' @importFrom survival Surv
#'
#' @noRd
#' @keywords internal
#multivariable regression analysis-Chang's method
chang_multivariate <- function(new_data, cov_names, SE) {
print(paste("Fitting model with covariates:", stringr::str_c(cov_names, collapse = ", "), sep=" "))
beta <- rep(0, length(cov_names)*2)
#solve to get all estimates
chang <- RE.uest(init = beta, dat=new_data)
if (chang$conv!=0) {
stop("Max iterations reached. Did not converge.")
}
if (is.null(SE)==TRUE) {
#return only point estimates
changfit <- data.frame(chang$par)
colnames(changfit) <- c("Estimate")
rownames(changfit) <- c(paste("xij", cov_names), paste("yij", cov_names))
return(list(fit = as.matrix(changfit)))
} else {
print("Estimating standard errors")
#estimate covariance matrix / std. errors using Parzen's method
changv <- v.est(chang$par,new_data,R=50)
changsd <- sd.estpar(init = beta, dat = new_data, v = changv, B=30)
#Join all info, put in nice table
changfit <- data.frame(chang$par, changsd$sd)
colnames(changfit) <- c("Estimate", "SE")
rownames(changfit) <- c(paste("xij", cov_names), paste("yij", cov_names))
return(list(fit = as.matrix(changfit), vcovmat = changsd$covmat))
}
}
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