Bayesian Information Criterion for Censored Survival Models

Abstract

We i n vestigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unit-information prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is de ned in terms of the number of uncensored events instead of the number of observations. For the simplest censored data model, that of exponential distributions of survival times (i.e. a constant hazard rate), this revision results in a better approximation to the exact Bayes factor based on a conjugate unit-information prior. In the Cox proportional hazards regression model, we propose de ning BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space, and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.

Construction of regulatory networks using expression time-series data of a genotyped population

“…BMA takes model uncertainty into account by averaging over the posterior distributions of a quantity of interest based on multiple models, weighted by their posterior model probabilities. BMA has been shown to be effective in many different applications (19)(20)(21)(22).…”

Antidepressant use and 10-year incident fracture risk: the population-based Canadian Multicentre Osteoporosis Study (CaMoS)

“…Main analyses relied on the multivariable Cox proportional hazards regression models, with timedependent covariates representing the history of SSRI/SNRI exposure (see section on "Drug use assessment and modeling") [21,22]. The final multivariable Cox model was identified through a combination of a stepwise forward selection of covariates and the Bayesian information criterion (BIC) [23] adopted for censored time-to-event data [24]. Specifically, starting from the initial model that included only indicators of SSRI/SNRI exposure, at each step of forward selection we added the most "significant" of the remaining covariates, i.e., the covariate with the lowest p value for its effect adjusted for all covariates included at the earlier steps, and the resulting change in BIC was computed.…”

“…Specifically, starting from the initial model that included only indicators of SSRI/SNRI exposure, at each step of forward selection we added the most "significant" of the remaining covariates, i.e., the covariate with the lowest p value for its effect adjusted for all covariates included at the earlier steps, and the resulting change in BIC was computed. The selection process ended when BIC no longer decreased, suggesting the best-fitting multivariable model [24]. Based on the corresponding BIC-optimal multivariable Cox model, we reported the adjusted hazard ratio (HR) and 95 % confidence intervals (CIs) for the relevant measure of SSRI/SNRI exposure.…”

CLIPI: a new prognostic index for indolent cutaneous B cell lymphoma proposed by the International Extranodal Lymphoma Study Group (IELSG 11)

“…In the next step a prognostic model was built to fit a Cox proportional hazard model [22] using all the covariates affecting PFS at p<0.1 in the univariate analysis and the final model was selected based on the Bayes Information Criteria proposed by Raftery-Volinsky (BIC'), as a measure of overall fit. We chosen the model with the more negative BIC [23]. The proportionality of the risks and overall model fit were graphically checked using scaled Schoenfeld [24] and Cox-Snell residuals; overfitting (shrinkage factor) and the performance of the model were checked using Harrell's method [25].…”