Predictiveness Curve Assessment under Competing Risks for Risk Prediction Models

The predictiveness curve is a valuable tool for predictive evaluation, risk stratification, and threshold selection in a target population, given a single biomarker or a prediction model. In the presence of competing risks, regression models are often used to generate predictive risk scores or probabilistic predictions targeting the cumulative incidence function–distinct from the cumulative distribution function used in conventional predictiveness curve analyses. We propose estimation and inference procedures for the predictiveness curve with a competing risks regression model, to display the relationship between the cumulative incidence probability and the quantiles of model-based predictions. The estimation procedure combines cross-validation with a flexible regression model for tau-year event risk given the model-based risk score, with corresponding inference procedures via perturbation resampling. The proposed methods perform satisfactorily in simulation studies and are implemented through an R package. We apply the proposed methods to a cirrhosis study to depict the predictiveness curve with model-based predictions for liver-related mortality.