Bayesian estimation and stochastic model specification search for dynamic survival models

Dynamic survival models are a useful extension of the popular Cox model as the effects of explanatory variables are allowed to change over time. In this paper a new auxiliary mixture sampler for Bayesian estimation of the model parameters is introduced. This sampler forms the basis of a model space MCMC method for stochastic model specification search in dynamic survival models, which involves selection of covariates to include in the model as well as specification of effects as time-varying or constant. The method is applied to two well-known data sets from the literature.

[1]  R. Kohn,et al.  Parsimonious Covariance Matrix Estimation for Longitudinal Data , 2002 .

[2]  D Sinha,et al.  Bayesian Analysis and Model Selection for Interval‐Censored Survival Data , 1999, Biometrics.

[3]  Mark F. J. Steel,et al.  On the effect of prior assumptions in Bayesian model averaging with applications to growth regression , 2009 .

[4]  H C van Houwelingen,et al.  Time-dependent effects of fixed covariates in Cox regression. , 1995, Biometrics.

[5]  Sylvia Frühwirth-Schnatter,et al.  Auxiliary mixture sampling with applications to logistic models , 2007, Comput. Stat. Data Anal..

[6]  L. Fahrmeir,et al.  Bayesian Regularisation in Structured Additive Regression Models for Survival Data , 2008 .

[7]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[8]  Benjamin Hofner,et al.  Building Cox-type structured hazard regression models with time-varying effects , 2011 .

[9]  Eduardo Ley,et al.  On the Effect of Prior Assumptions in Bayesian Model Averaging With Applications to Growth Regression , 2007 .

[10]  David W. Hosmer,et al.  Applied Survival Analysis: Regression Modeling of Time-to-Event Data , 2008 .

[11]  R. Tüchler.  Bayesian Variable Selection for Logistic Models Using Auxiliary Mixture Sampling , 2008 .

[12]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[13]  K. Hemming,et al.  A Class of Parametric Dynamic Survival Models , 2005, Lifetime data analysis.

[14]  J. E. H. Shaw,et al.  A parametric dynamic survival model applied to breast cancer survival times , 2002 .

[15]  E. George,et al.  Journal of the American Statistical Association is currently published by American Statistical Association. , 2007 .

[16]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[17]  N. Shephard,et al.  Markov chain Monte Carlo methods for stochastic volatility models , 2002 .

[18]  S. Frühwirth-Schnatter.  Data Augmentation and Dynamic Linear Models , 1994 .

[19]  Joseph G. Ibrahim,et al.  A Bayesian justification of Cox's partial likelihood , 2003 .

[20]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[21]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[22]  S. Frühwirth-Schnatter,et al.  Stochastic model specification search for Gaussian and partial non-Gaussian state space models , 2010 .

[23]  N. Shephard,et al.  Stochastic volatility with leverage: Fast and efficient likelihood inference , 2007 .

[24]  N. Shephard.  Partial non-Gaussian state space , 1994 .

[25]  Siddhartha Chib,et al.  Stochastic Volatility with Leverage: Fast Likelihood Inference , 2004 .

[26]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[27]  L. Fahrmeir,et al.  Geoadditive Survival Models , 2006 .

[28]  P. V. Rao,et al.  Applied Survival Analysis: Regression Modeling of Time to Event Data , 2000 .

[29]  D. Dey,et al.  Semiparametric Bayesian analysis of survival data , 1997 .

[30]  R. Kohn,et al.  Nonparametric regression using Bayesian variable selection , 1996 .

[31]  Sylvia Frühwirth-Schnatter,et al.  Bayesian parsimonious covariance estimation for hierarchical linear mixed models , 2008, Stat. Comput..

[32]  E. George,et al.  APPROACHES FOR BAYESIAN VARIABLE SELECTION , 1997 .

[33]  N. Shephard,et al.  The simulation smoother for time series models , 1995 .

[34]  D. Gamerman.  Dynamic Bayesian Models for Survival Data , 1991 .

[35]  S. Frühwirth-Schnatter,et al.  Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling , 2006 .