Bayesian analysis of Cox-type regression model with partly linear covariate effects via reversible jump Markov chain Monte Carlo

Abstract The partly linear Cox-type regression model provides a robust and flexible framework for exploring the potential nonlinear effects of a continuous variable on a censored outcome within the context of complex diseases. Most contemporary research studies the estimation methods of such a model based on the Frequentist paradigm, necessitating the selection of bandwidth and/or the number of spline basis functions for smoothing. We propose a Bayesian estimation approach that eliminates this requirement by employing the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. The proposed method can inherently estimate both the number and location of knots in the unknown function in a data-adaptive manner during the posterior inference process, thereby enhancing its applicability and predictive accuracy. We evaluate the finite-sample performance of the proposed method through a simulation study. The effectiveness of the proposed method is illustrated through the analysis of two medical datasets. The codes of the proposed algorithms and numerical studies can be found via https://github.com/BobZhangHT/RJMCMC_NonLinear .