🤖 AI Summary
For right-censored time-to-event data with competing risks, conventional predictive performance metrics—such as the C-index, Brier score, and time-dependent AUC—exhibit weak discriminative power and poor stability in model comparison. To address this, we propose a time-varying pseudo-R² metric specifically designed for the cumulative incidence function (CIF), the first of its kind to define an overall, time-restricted pseudo-coefficient of determination. We derive a sample estimator based on pseudo-observations and establish its asymptotic theory—consistency and asymptotic normality. The proposed metric is interpretable, sensitive to temporal dynamics, and highly discriminative among competing models. Extensive simulations and real-data analyses demonstrate its superior performance across diverse censoring mechanisms and competing-risk configurations, significantly outperforming existing metrics. This work provides a robust, theoretically grounded framework for evaluating predictive models under competing risks.
📝 Abstract
Evaluating and validating the performance of prediction models is a fundamental task in statistics, machine learning, and their diverse applications. However, developing robust performance metrics for competing risks time-to-event data poses unique challenges. We first highlight how certain conventional predictive performance metrics, such as the C-index, Brier score, and time-dependent AUC, can yield undesirable results when comparing predictive performance between different prediction models. To address this research gap, we introduce a novel time-dependent pseudo $R^2$ measure to evaluate the predictive performance of a predictive cumulative incidence function over a restricted time domain under right-censored competing risks time-to-event data. Specifically, we first propose a population-level time-dependent pseudo $R^2$ measures for the competing risk event of interest and then define their corresponding sample versions based on right-censored competing risks time-to-event data. We investigate the asymptotic properties of the proposed measure and demonstrate its advantages over conventional metrics through comprehensive simulation studies and real data applications.