A joint model of longitudinal data and time to event data with cured fraction

A joint model to analyze longitudinal prostate specific antigen (PSA) data and time to recurrence in prostate cancer patients after receiving radiation therapy is developed. We assume a fraction of patients to be cured, i.e., where the risk of recurrence is assumed to be zero. In the model, the probability of cure is modeled using a logistic model, and the log-transformed serial PSA measurements are modeled using a linear mixed effects model. In the uncured group the random effects of the longitudinal data and a suitable transformation of time to event is assumed to have a multivariate normal distribution. An EM algorithm is formulated to estimate the parameters of the model and the standard errors are obtained from bootstrapping and numerical methods available in SAS/IML. Estimation of parameters numerically using the Newton-Raphson method is also explored. Properties and performance of the model and estimates are examined using simulation studies.;As an extension to the above model a joint model for longitudinal data and time to event data with latent subclasses is developed. The applications of these models are presented on an example dataset. The BIC criterion is used for model selection.