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Research Article Received 12 May 2011, Accepted 3 April 2012 Published online in Wiley Online Library () DOI: 10.1002/sim.5487 Joint modeling of progression-free survival and overall survival by a Bayesian normal induced copula estimation model Haoda Fu,*† Yanping Wang, Jingyi Liu, Pandurang M. Kulkarni and Allen S. Melemed 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 effi- cacy. 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 corre- lated 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 adap- tive 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. Copyright © 2012 John Wiley Sons, Ltd. Keywords: Bayesian method; cancer clinical trials; Gaussian copula; joint modeling; overall survival; progression-free survival; semi-competing risks; time to progression 1. Introduction In cancer patients, progression of disease is usually a significant event acting as a prelude to f