Joint modeling of progression-free survival and overall survival by a Bayesian normal induced copula estimation model

In cancer clinical trials, in addition to time to death (i.e., overall survival), progression-related measurements such as progression-free survival and time to progression are also commonly used to evaluate treatment efficacy. It is of scientific interest and importance to understand the correlations among these measurements. In this paper, we propose a Bayesian semi-competing risks approach to jointly model progression-related measurements and overall survival. This new model is referred to as the NICE model, which stands for the normal induced copula estimation model. Correlation among these variables can be directly derived from the joint model. In addition, when correlation exists, simulation shows that the joint model is able to borrow strength from correlated measurements, and as a consequence the NICE model improves inference on both variables. The proposed model is in a Bayesian framework that enables us to use it in various Bayesian contexts, such as Bayesian adaptive design and using posterior predictive samples to simulate future trials. We conducted simulation studies to demonstrate properties of the NICE model and applied this method to a data set from chemotherapy-naive patients with extensive-stage small-cell lung cancer.