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The development of risk prediction models is of increasing importance in medical research - their use in practice, however, is rare. Among other reasons this might be due to the fact that thorough validation is often lacking. This study focuses on two Bayesian approaches of how to validate a prediction rule for the diagnosis of pneumonia, and compares them with established validation methods.
Expert knowledge was used to derive a risk prediction model for pneumonia. Data on more than 600 patients presenting with cough and fever at a general practitioner’s practice in Switzerland were collected in order to validate the expert model and to examine the predictive performance of it. Additionally, four modifications of the original model including shrinkage of the regression coefficients, and two Bayesian approaches with the expert model used as prior mean and different weights for the prior covariance matrix were fitted. We quantify the predictive performance of the different methods with respect to calibration and discrimination, using cross-validation.
The predictive performance of the unshrinked regression coefficients was poor when applied to the Swiss cohort. Shrinkage improved the results, but a Bayesian model formulation with unspecified weight of the informative prior lead to large AUC and small Brier score, naïve and after cross-validation. The advantage of this approach is the flexibility in case of a prior-data conflict.
Published risk prediction rules in clinical research need to be validated externally before they can be used in new settings. We propose to use a Bayesian model formulation with the original risk prediction rule as prior. The posterior means of the coefficients, given the validation data showed best predictive performance with respect to cross-validated calibration and discriminative ability.