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

Presently, there are few options with readily available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated nonparametrically. 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 nonparametric alternative to the piecewise exponential model which assumes continuity of the hazard, and to develop easily modifiable software thereby allowing the use of these methods in a variety of settings. To accomplish this aim, we construct a piecewise linear log-hazard model using a low-rank thin plate spline formulation for the loghazard function. We discuss extensions that facilitate nonparametric adjustment for covariates with time-dependent effects and nonlinear time-independent effects possibly subject to shape restrictions. We investigate the properties of these modeling choices via simulation. We then apply our methods to colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care with respect to overall survival. In particular, we characterize the hazard ratio as a function of time between each novel regime and 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.