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Biostatistics Advance Access originally published online on November 19, 2007
Biostatistics 2008 9(3):400-410; doi:10.1093/biostatistics/kxm038
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

The separation of timescales in Bayesian survival modeling of the time-varying effect of a time-dependent exposure

Sebastien J.-P. A. Haneuse*

Center for Health Studies, 1730 Minor Avenue, Suite 1600, Seattle, WA 98101-1448, USA
haneuse.s{at}ghc.org

Kyle D. Rudser

Department of Biostatistics, University of Washington, Seattle, WA, USA

Daniel L. Gillen

Department of Statistics, University of California, Irvine, Irvine, CA, USA

* To whom correspondence should be addressed.

In this paper, we apply flexible Bayesian survival analysis methods to investigate the risk of lymphoma associated with kidney transplantation among patients with end-stage renal disease. Of key interest is the potentially time-varying effect of a time-dependent exposure: transplant status. Bayesian modeling of the baseline hazard and the effect of transplant requires consideration of 2 timescales: time since study start and time since transplantation, respectively. Previous related work has not dealt with the separation of multiple timescales. Using a hierarchical model for the hazard function, both timescales are incorporated via conditionally independent stochastic processes; smoothing of each process is specified via intrinsic conditional Gaussian autoregressions. Features of the corresponding posterior distribution are evaluated from draws obtained via a Metropolis–Hastings–Green algorithm.

Keywords: Bayesian survival analysis; Conditional autoregression; Nonproportional hazards; Reversible jump Markov chain Monte Carlo

Received November 13, 2006; revised April 27, 2007; revised July 3, 2007; revised August 6, 2007; accepted for publication October 12, 2007.


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