Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects

Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.