Bayesian Information Criterion for Censored Survival Models

We investigate 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 defined in terms of the number of uncensored events instead of the number of observations. For a simple censored data model, 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 defining 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. Key words: Bayes factor; Cox ..

Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance

Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the model-building process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a double-blinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis..

Bayesian Model Averaging

Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples. In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software. KEYWORDS: Bayesian model averaging; Bayesian graphical models; Learning; Model uncertainty; Markov chain Monte Carlo Research supported in part by the U.S. National Science Foundation and the U.S. Office of Naval Research (N00014-91-J-1014). The authors are grateful to David Lewis and Ro..

Bayesian model averaging

Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-con dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue o

Bayesian Model Averaging in Proportional Hazard Models: Assessing Stroke Risk

Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for stroke. We introduce a technique based on the leaps and bounds algorithm which efficiently locates and fits the best models in the very large model space and thereby extends all subsets regression to Cox models. For each independent variable considered, the method provides the posterior probability that it belongs in the model. This is more directly interpretable than the corresponding P-values, and also more valid in that it takes account of model uncertainty. P-values from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable. In our data Bayesian model averaging predictively outperforms standard model selection methods for assessing st..

Bayesian Model Averaging: A Tutorial

Abstract. Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident in-ferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for ac-counting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples. In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software. Key words and phrases: Bayesian model averaging, Bayesian graphica