Construction of Parsimonious Event Risk Scores by an Ensemble Method. An Illustration for Short-Term Predictions in Chronic Heart Failure Patients from the GISSI-HF Trial

Selecting which explanatory variables to include in a given score is a common difficulty, as a balance must be found between statistical fit and practical application. This article presents a methodology for constructing parsimonious event risk scores combining a stepwise selection of variables with ensemble scores obtained by aggregation of several scores, using several classifiers, bootstrap samples and various modalities of random selection of variables. Selection methods based on a probabilistic model can be used to achieve a stepwise selection for a given classifier such as logistic regression, but not directly for an ensemble classifier constructed by aggregation of several classifiers. Three selection methods are proposed in this framework, two involving a backward selection of the variables based on their coefficients in an ensemble score and the third involving a forward selection of the variables maximizing the AUC. The stepwise selection allows constructing a succession of scores, with the practitioner able to choose which score best fits his needs. These three methods are compared in an application to construct parsimonious short-term event risk scores in chronic HF patients, using as event the composite endpoint of death or hospitalization for worsening HF within 180 days of a visit. Focusing on the fastest method, four scores are constructed, yielding out-of-bag AUCs ranging from 0.81 (26 variables) to 0.76 (2 variables).