Statistica Sinica 14(2004), 835-862

JOINT LONGITUDINAL-SURVIVAL-CURE MODELS AND

THEIR APPLICATION TO PROSTATE CANCER

Menggang Yu$^1$, Ngayee J. Law$^2$, Jeremy M. G. Taylor$^{1,3}$

and Howard M. Sandler$^3$

$^1$Indiana University, $^2$Roche Molecular Systems, Inc.

and $^3$University of Michigan

Abstract: Many scientific investigations generate both longitudinal data and survival data. Methods for the combined analysis of both kinds of data have been developed in recent years, with the main emphasis being on modeling and estimation. In cancer research it is common for there to be long term survivors or cured patients and methods have been developed to analyze such data. In this article, we review both joint models for the analysis of longitudinal and survival data and cure models. We then present a joint longitudinal-survival-cure model to analyze data from a study of prostate cancer patients treated with radiation therapy. In this model each patient is assumed to be either cured or susceptible to clinical recurrence. The cured fraction is modeled as a logistic function of baseline covariates. The longitudinal PSA data is modeled as a non-linear hierarchical mixed model, with different models for the cured and susceptible groups. The clinical recurrences are modeled as a time-dependent proportional hazards model for those in the susceptible group. The baseline variables are covariates in both the failure time and longitudinal models. We use both a Monte Carlo EM algorithm and Markov chain Monte Carlo techniques to fit the model. The results from the two estimation methods are compared. We focus on both selected parameters of the model and derived interpretable quantities.

Key words and phrases: Cure models, joint longitudinal-survival models, prostate cancer.