Methodology for Constructing a Short-Term Event Risk Score in Heart Failure Patients

We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.

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).

Construction and Update of an Online Ensemble Score Involving Linear Discriminant Analysis and Logistic Regression

The present aim is to update, upon arrival of new learning data, the parameters of a score constructed with an ensemble method involving linear discriminant analysis and logistic regression in an online setting, without the need to store all of the previously obtained data. Poisson bootstrap and stochastic approximation processes were used with online standardized data to avoid numerical explosions, the convergence of which has been established theoretically. This empirical convergence of online ensemble scores to a reference “batch” score was studied on five different datasets from which data streams were simulated, comparing six different processes to construct the online scores. For each score, 50 replications using a total of 10N observations (N being the size of the dataset) were performed to assess the convergence and the stability of the method, computing the mean and standard deviation of a convergence criterion. A complementary study using 100N observations was also performed. All tested processes on all datasets converged after N iterations, except for one process on one dataset. The best processes were averaged processes using online standardized data and a piecewise constant step-size.