Clustered partly interval-censored survival data naturally arise from many medical and epidemiological studies. We propose a Bayesian semiparametric approach for fitting a mixed effects proportional hazards (PH) model to clustered partly interval-censored data. The proposed method allows for not only a random intercept as most frailty models do for clustered survival data, but also random effects of covariates. We assume a normal prior for each random intercept/random effect, seeing the instability of a gamma prior for a frailty in this situation. Simulation studies with data generated from both mixed effects PH model and mixed effects accelerated failure times model are conducted, to evaluate the performance of the proposed method and compare it with the three methods currently available in the literature. The application of the proposed approach is illustrated through analyzing the progression-free survival data derived from a phase III metastatic colorectal cancer clinical trial.

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