For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure to the survival model component of the model. Here we focus on utilizing the model to make individualized prediction of disease progression for censored and alive patients.
In this model each patient is assumed to be either cured by the treatment or susceptible to clinical recurrence. The cured fraction is modeled as a logistic function of baseline covariates, measured before the end of the radiation therapy period. The longitudinal PSA data is modeled as a non-linear hierarchical mixed model, with different models for the cured and susceptible groups. To accommodate the heavy tail manifested by the data and possible outliers, we use a t-distribution for the measurement error. The clinical recurrences are modeled using a time-dependent proportional hazards model for those in the susceptible group where the time dependent covariates include both the current value and the slope of post-treatment PSA profile. Estimates of the parameters in the model are obtained by the Markov chain Monte Carlo (MCMC) technique. Residuals from the longitudinal model are plotted for model checking. The model is used to give individual predictors for both future PSA values and the predicted probability of recurrence up to four years in the future. These predictors are compared with observed data from a validation data set consisting of further follow-up of the subjects in the study. There is good correspondence between the predictions and the validation data.
Disease Modeling | Longitudinal Data Analysis and Time Series | Statistical Models | Survival Analysis
Yu, Menggang; Taylor, Jeremy; and Sandler, Howard M., "Individual Prediction in Prostate Cancer Studies Using a Joint Longitudinal-Survival-Cure Model" (February 2004). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 24.