Bayesian proportional hazards model for current status data with monotone splines

The proportional hazards model is widely used to deal with time to event data in many fields. However, its popularity is limited to right-censored data, for which the partial likelihood is available and the partial likelihood method allows one to estimate the regression coefficients directly without estimating the baseline hazard function. In this paper, we focus on current status data and propose an efficient and easy-to-implement Bayesian approach under the proportional hazards model. Specifically, we model the baseline cumulative hazard function with monotone splines leading to only a finite number of parameters to estimate while maintaining great modeling flexibility. An efficient Gibbs sampler is proposed for posterior computation relying on a data augmentation through Poisson latent variables. The proposed method is evaluated and compared to a constrained maximum likelihood method and three other existing approaches in a simulation study. Uterine fibroid data from an epidemiological study are analyzed as an illustration.