Bayesian Analysis of the Generalized Additive Proportional Hazards Model: Asymptotic Studies

Abstract

In this paper, we study Bayesian asymptotic properties of the proportional hazards model where the link function is modeled by the generalized additive model. As the standard generalized additive model is, the generalized additive proportional hazards model is a useful tool in finding the nonlinearity of covariate effects to survival times. We develop a data-dependent sieve prior for the generalized additive link function and use the Bayesian bootstrap prior for the baseline hazard function. We prove that the posterior contraction rate of the generalized additive link function is minimax optimal up to a $logn$ term when the prior is carefully selected. By analyzing simulated as well as real data, we verify our theoretical results and compare with exisiting algorithms for the generalized additive proportional hazards model to illustrate that the proposed Bayesian model is a useful inference tool.