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Estimation of prediction error for survival models

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Abstract

When statistical models are used to predict the values of unobserved random variables, loss functions are often used to quantify the accuracy of a prediction. The expected loss over some specified set of occasions is called the prediction error. This paper considers the estimation of prediction error when regression models are used to predict survival times and discusses the use of these estimates. Extending the previous work, we consider both point and confidence interval estimations of prediction error, and allow for variable selection and model misspecification. Different estimators are compared in a simulation study for an absolute relative error loss function, and results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are sensitive to model misspecification. Links between performance measures for point predictors and for predictive distributions of survival times are also discussed. The methodology is illustrated in a medical setting involving survival after treatment for disease. Copyright © 2009 John Wiley & Sons, Ltd.

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