Bayesian Analysis

Flexible Bayesian Survival Modeling with Semiparametric Time-Dependent and Shape-Restricted Covariate Effects

Thomas A. Murray, Brian P. Hobbs, Daniel J. Sargent, and Bradley P. Carlin

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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.

Article information

Bayesian Anal. Volume 11, Number 2 (2016), 381-402.

First available in Project Euclid: 14 May 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference 62N86: Fuzziness, and survival analysis and censored data
Secondary: 62F30: Inference under constraints

Bayesian methods survival analysis semiparametric methods penalized splines shape-restricted effects time-dependent effects colorectal cancer


Murray, Thomas A.; Hobbs, Brian P.; Sargent, Daniel J.; Carlin, Bradley P. Flexible Bayesian Survival Modeling with Semiparametric Time-Dependent and Shape-Restricted Covariate Effects. Bayesian Anal. 11 (2016), no. 2, 381--402. doi:10.1214/15-BA954.

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