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 of

Logic regression is an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates. In many regression problems a model is developed that relates the main effects (the predictors or transformations thereof) to the response, while interactions are usually kept simple (two- to three-way interactions at most). Often, especially when all predictors are binary, the interaction between many predictors may be what causes the differences in response. This issue arises, for example, in the analysis of SNP microarray data or in some data mining problems. In the proposed methodology, given a set of binary predictors we create new predictors such as “X1, X2, X3, and X4 are true, ” or “X5 or X6 but not X7 are true. ” In more speci � c terms: we try to � t regression models of the form g(E[Y]) = b0 + b1L1 + ¢ ¢ ¢ + bnLn, where Lj is any Boolean expression of the predictors. The Lj and bj are estimated simultaneously using a simulated annealing algorithm. This article discusses how to � t logic regression models, how to carry out model selection for these models, and gives some examples.

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 e ciently locates and ts 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

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 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.

Stroke is the third leading cause of death and the principal cause of serious long-term disability in the United States. Accurate prediction of stroke is highly valuable for early intervention and treatment. In this study, we compare the Cox proportional hazards model with a machine learning approach for stroke prediction on the Cardiovascular Health Study (CHS) dataset. Specifically, we consider the common problems of data imputation, feature selection, and prediction in medical datasets. We propose a novel automatic feature selection algorithm that selects robust features based on our proposed heuristic: conservative mean. Combined with Support Vector Machines (SVMs), our proposed feature selection algorithm achieves a greater area under the ROC curve (AUC) as compared to the Cox proportional hazards

Genome-wide association analysis identifies multiple loci related with resting heart rate Eijgelsheim et al.