Choice of Prognostic Estimators in Joint Models by Estimating Differences of Expected Conditional Kullback–Leibler Risks

Prognostic estimators for a clinical event may use repeated measurements of markers in addition to fixed covariates. These measurements can be linked to the clinical event by joint models that involve latent features. When the objective is to choose between different prognosis estimators based on joint models, the conventional Akaike information criterion is not well adapted and decision should be based on predictive accuracy. We define an adapted risk function called expected prognostic cross-entropy. We define another risk function for the case of right-censored observations, the expected prognostic observed cross-entropy (EPOCE). These risks can be estimated by leave-one-out cross-validation, for which we give approximate formulas and asymptotic distributions. The approximated cross-validated estimator CVPOL (a) of EPOCE is studied in simulation and applied to the comparison of several joint latent class models for prognosis of recurrence of prostate cancer using prostate-specific antigen measurements.