Joint longitudinal-survival-cure model with application in prostate cancer studies.

Abstract

Many medical investigations generate both longitudinal and survival data. Methods for the combined analysis of both kinds of data have been developed in recent years. In prostate cancer studies, patients are usually monitored and PSA are measured periodically after they received treatment. It is also common for there to be long term survivors or cured patients. This dissertation extends the joint modeling method to analyze data from prostate cancer studies, by adding a mixture structure to the survival model component of the joint model. There are 3 components in our model: an incidence model for cure status of a patient, a longitudinal model for a biomarker, and a survival model for susceptibles or not cured patients. A Markov chain Monte Carlo estimation method is developed. Two different versions of the same data are analyzed in this dissertation. The version with shorter followup (till March 1995) is analyzed with results compared to those obtained from a Monte Carlo EM algorithm. The version with longer followup (till February 2001) is analyzed using a more flexible model. In this version, we utilize the actual survival information for patients who received hormonal therapy (HT) as a salvage therapy and treat HT as a time-dependent covariate. We include the slope of the longitudinal profile as a time-dependent covariate. We also consider additional baseline covariates in the joint model. To accommodate the heavier tail manifested by the data, we use a t distribution for the measurement error term in the longitudinal model. We use our model to predict cancer recurrence for censored (alive) patients under the assumptions that they either do or do not receive HT right after the censoring time. The reconstruction of marginal survival distributions is carried out using multiple imputations. We assess the fit of the model using a validation data set. We investigate whether incorporating a cure component in the survival model provides a better fit to the data, by using Bayesian approaches for model selection. Our simulation study found that the CPO statistic performs better than BIC and Bayes factors. We apply CPO to a model selection problem for the prostate cancer data set. We find that joint modeling with a cure model component provides a better fit than without the cure model component.