Following previous posts on longitudinal models (see posts) and interviews where mentions have been made to survival analysis (read one of these interviews), we will focus today on models incorporating both methodologies, the so-called Joint Models.
Often problems pose more than a single approach. For example, when HIV data are analyzed, we can on the one hand focus on studying the evolution of CD4 cell counts (longitudinal model) and on the other hand, we can also study the time to death (survival analysis model). Joint modeling will allow both models to share information and will achieve better results.
From a practical point of view, in R, we can use two packages called JM and JMbayes to fit these models, under either the frequentist or the Bayesian paradigm, respectively. The use of these packages is not difficult because they are based on the use of packages nlme and survival with which you might already be familiar.
Here I show you how to use them:
- We loaded packages JM and JMbayes
- We fit the longitudinal and survival models independently, saving the results in objects
# Fit the longitudinal model lmeFit.aids <- lme(CD4 ~ obstime * drug, random = ~obstime | patient, data = aids) # Fit the survival model survFit.aids <- coxph(Surv(Time, death) ~ drug, data = aids.id, x = TRUE)
- We use the objects lmeObject and survObject with the functions in the packages JM and JMbayes
# Fit the joint model (Frequentist) jointFit.aidsFREQ <- jointModel(lmeFit.aids, survFit.aids, timeVar = "obstime") # Fit the joint model (Bayesian) jointFit.aidsBAYES <- jointModelBayes(lmeFit.aids, survFit.aids, timeVar = "obstime")
It’s possible to specify different characteristics about the joint model. With JM package various options for the survival model are available. With JMbayes it is possible to choose the type of association structure between the longitudinal and survival processes.
Finally, if you are interested in these models and are thinking about using them in your research, a good reference is the book Joint Models for Longitudinal and Time-to-Event Data: With Applications in R of Dimitris Rizopoulos, author of JM and JMbayes.
Note: The databank to fit the longitudinal model must have as many rows as observations per patient have (aids). On the other hand, the survival model requires a database that has only one observation for each patient over time to death and censoring indicator (aids.id).