Individual Prediction in Prostate Cancer Studies Using a Joint Longitudinal Survival-Cure Model - Yu, Menggang; Taylor, Jeremy M. G; Sandler, Howard M (Journal of the American Statistical Association, 2008)
Patients treated for prostate cancer are monitored by periodically measuring prostate-specific antigen (PSA) after treatment. Increases in PSA are suggestive of cancer recurrence 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 on modeling and estimation. We analyze data from a prostate cancer study in which the patients are treated with radiation therapy, using a joint model extended by adding a mixture structure to the model. Here we focus on using this model to make individualized predictions 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 nonlinear hierarchical mixed model, with different models for the cured and susceptible groups. To accommodate the heavy tail manifested by the data and possible outliers, a t distribution is used 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 the of posttreatment PSA profile. The baseline hazard is assumed to have a generalized Weibull form. Estimates of the parameters in the model are obtained using a Markov chain Monte Carlo method. The model is used to give individual predictions of both future PSA values and the predicted probability of recurrence up to four years in the future. These predictions 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.