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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 ..."
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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
Improving Cox survival analysis with a neuralBayesian approach
, 2001
"... this article we show that traditional Cox survival analysis can be improved upon when supplemented with sensible priors and analysed within a neural Bayesian framework. We demonstrate that the Bayesian method gives more reliable predictions, in particular for relatively small data sets ..."
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Cited by 1 (0 self)
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this article we show that traditional Cox survival analysis can be improved upon when supplemented with sensible priors and analysed within a neural Bayesian framework. We demonstrate that the Bayesian method gives more reliable predictions, in particular for relatively small data sets
Regression Modeling and Validation Strategies
, 1997
"... through the use of predicted responses, to separate subjects with low observed responses from those with high responses Perils of Overfitting 4 # # Perils of Overfitting q Fitting a model with 20 patients and 20 variables (counting the intercept) will result in 5 # #no matter what the variabl ..."
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through the use of predicted responses, to separate subjects with low observed responses from those with high responses Perils of Overfitting 4 # # Perils of Overfitting q Fitting a model with 20 patients and 20 variables (counting the intercept) will result in 5 # #no matter what the variables are q Analyzing too many variables for the available sample size will not cause a problem with apparent predictive accuracy q Calibration or discrimination accuracy assessed on a new sample will suffer q Caused by multiple comparison problems and trying to estimate too many parameters (regression coefficients) from the sample q To use standard statistical methods, need to have a certain number of subjects per candidate predictor a a The term candidate is used because one needs to count all varia
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...
SPECIAL EDITORIAL SERIES STATISTICAL ISSUE IN CANCER RESEARCH Statistical aspects of prognostic factor studies in oncology
"... Studies of new prognostic factors form an extensive part of the literature of oncology. Recent examples published in this journal include studies of patients with primary cerebral lymphoma (Blay et al., 1993), head and neck sarcomas (Eeles et al., 1993) and testicular cancer (Steyerberg et al., 1993 ..."
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Studies of new prognostic factors form an extensive part of the literature of oncology. Recent examples published in this journal include studies of patients with primary cerebral lymphoma (Blay et al., 1993), head and neck sarcomas (Eeles et al., 1993) and testicular cancer (Steyerberg et al., 1993). In some cases such studies may offer insight into the molecular pathogenesis of the disease. In others they may help in medical decision making; for example, in identifying which patients are at sufficiently high risk of recurrence to warrant a toxic or expensive treatment. Identification of major prognostic determinants can facilitate the design of further clinical trials, aid in intertrial comparisons and guide the counselling of individual patients. Unfortunately, however, the results of different prognostic factor studies are often inconsistent or contradictory.