Variable Selection for Logistic Regression using a Prediction Focussed Information Criterion

Abstract

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the Focussed Information Criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the Mean Squared Error (MSE) of the estimator of the quantity of interest in the selected model. In this paper we propose more general versions of the FIC, allowing other risk measures such as one based on Lp-error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.