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Bayesian model averaging
 STAT.SCI
, 1999
"... 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 overcon dent inferences and decisions tha ..."
Abstract

Cited by 42 (0 self)
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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 overcon 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 outofsample predictive performance. We also provide a catalogue of
Bayesian Model Averaging in proportional hazard models: Assessing the risk of a stroke
 Applied Statistics
, 1997
"... 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 ..."
Abstract

Cited by 28 (5 self)
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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 Pvalues, and also more valid in that it takes account of model uncertainty. Pvalues 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
The Practical Utility of Incorporating Model Selection Uncertainty
, 2004
"... Predictions of disease outcome in prognostic factor models are usually based on one selected model. However, often several models fit the data equally well, but these models might di#er substantially in terms of included explanatory variables and might lead to di#erent predictions for individual pat ..."
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Predictions of disease outcome in prognostic factor models are usually based on one selected model. However, often several models fit the data equally well, but these models might di#er substantially in terms of included explanatory variables and might lead to di#erent predictions for individual patients. For survival data we discuss two approaches for accounting for model selection uncertainty in two data examples with the main emphasis on variable selection in a proportional hazard Cox model. The main aim of our investigation is to establish in which ways either of the two approaches are useful in such prognostic models. The first approach is Bayesian model averaging (BMA) adapted for the proportional hazard model (Volinsky et al., 1997). As a new approach we propose a method which averages over a set of possible models using weights estimated from bootstrap resampling as proposed by Buckland et al. (1997), but in addition we perform an initial screening of variables based on the inclusion frequency of each variable to reduce the set of variables and corresponding models. The main objective of prognostic models is prediction, but the interpretation of single e#ects is also important and models should be general enough to ensure transportability to other clinical centres. In the data examples we compare predictions of the two approaches with "conventional" predictions from one selected model and with predictions from the full model. Confidence intervals are compared in one example. Comparisons are based on the partial predictive score and the Brier score. We conclude that the two model averaging methods yield similar results and are especially useful when there is a high number of potential prognostic factors, most likely some of them without influence in a multivariab...