Time-dependent Predictive Accuracy Metrics in the Context of Interval Censoring and Competing Risks

TL;DR

This paper introduces two methods for calculating time-dependent accuracy metrics in the presence of interval censoring and competing risks, validated through simulation, to improve model evaluation in complex medical time-to-event data.

Contribution

It proposes a model-based and an IPCW approach for evaluating predictive accuracy metrics under interval censoring and competing risks in time-varying settings.

Findings

The model-based approach includes all subjects in risk set analysis.

The IPCW approach considers only subjects known to be event-free or with events within the interval.

Simulation results compare the performance of both methods across metrics.

Abstract

Evaluating the performance of a prediction model is a common task in medical statistics. Standard accuracy metrics require the observation of the true outcomes. This is typically not possible in the setting with time-to-event outcomes due to censoring. Interval censoring, the presence of time-varying covariates, and competing risks present additional challenges in obtaining those accuracy metrics. In this study, we propose two methods to deal with interval censoring in a time-varying competing risk setting: a model-based approach and the inverse probability of censoring weighting (IPCW) approach, focusing on three key time-dependent metrics: area under the receiver-operating characteristic curve (AUC), Brier score, and expected predictive cross-entropy (EPCE). The evaluation is conducted over a medically relevant time interval of interest, $[t, \Delta t)$. The model-based approach includes all subjects in the risk set, using their predicted risks to contribute to the accuracy metrics. In contrast, the IPCW approach only considers the subset of subjects who are known to be event-free or experience the event within the interval of interest. we performed a simulation study to compare the performance of the two approaches with regard to the three metrics.