chapter11.qmd

---
title: "Chapter 11 - Joint Analysis of Longitudinal and Survival Data"
---

## Slides

Lecture slides [here](chap11.html){target="_blank"}. (To convert html to pdf, press E $\to$ Print $\to$ Destination: Save to pdf)

## Base R Code

```{r}
#| code-fold: true
#| code-summary: "Show the code"
#| eval: false

##################################################################
# This code generates all numerical results in chapter 11.      ##
##################################################################


############################################################
# Analysis of the anti-retroviral drug trial
############################################################

#load required packages
library(nlme) # for linear mixed effects model
library(survival)

# read in the study dataset
data <- read.table("Data//Anti-retroviral Trial//aids.txt")
head(data)

#load the JM package
install.packages("JM")
library(JM)

#####################################################
# Figure 11.2 Histograms of CD4 count and square-root
#       transformation
#####################################################
par(mfrow=c(1,2))
hist(data$CD4,xlab="CD4 count", main = "", lwd=2)
hist(sqrt(data$CD4),xlab="Square root of CD4 count",main="",lwd=2)

# taking square root of CD4 count
data$y <- sqrt(data$CD4)

# create a de-duplicated data for survival sub-model
data.surv <- data[!duplicated(data$id),]

# Joint model fit for the HIV/AIDS dataset
# longitudinal sub-model
longit.sub <- lme(y ~ obsmo + obsmo:drug + sex + hist,
                   random = ~ obsmo|id, data = data)

# survival sub-model
surv.sub <- coxph(Surv(time, status) ~ drug + sex + hist,
                     data = data.surv, x = TRUE)

# combine the two models
# piecewise linear baseline with six internal knots
joint.model <- jointModel(longit.sub, surv.sub,
                            timeVar = "obsmo",
                            method = "piecewise-PH-aGH")


joint.model$coefficients

# print out the summary
summary(joint.model)



######################################
# Figure 11.3
######################################

# compute the mean trajectories based on the longitudinal
# sub-model results

t <- (0:180)/10

g0 <- 2.2123
g1 <- -0.0414
g3 <- 0.9153
g4 <- 0.0061


ddC.nonhist <- (g0+g3+g1*t)^2
ddC.hist <- (g0+g1*t)^2


ddI.nonhist <- (g0+g3+(g1+g4)*t)^2
ddI.hist <- (g0+(g1+g4)*t)^2


#######################################################
# Figure 11.3
# Model-based estimates of the mean trajectories
#  of CD4 count for female patients by treatment
#  group and previous infection status. Solid, ddC;
#  dotted, ddI
######################################################
par(mfrow=c(1,2))

plot(t, ddC.nonhist,type='l',frame.plot=F,
     main="No previous infection",xlim=c(0,20),ylim=c(0,10),
     xlab="Time (months)", ylab="Mean CD4 cell count", lwd=2, cex.main = 1)
lines(t,ddI.nonhist,lty=3,lwd=2)

plot(t, ddC.hist,type='l',frame.plot=F,
     main="Previous infection",xlim=c(0,20),ylim=c(0,10),
     xlab="Time (months)", ylab="Mean CD4 cell count", lwd=2, cex.main = 1)
lines(t,ddI.hist,lty=3,lwd=2)

```