Inference for competing risks based on area between curves statistics

2026-01-22

AI Summary

This study addresses the substantial loss of power experienced by existing two-sample tests for competing risks when cumulative incidence functions (CIFs) cross. To overcome this limitation, the authors propose a novel test statistic based on the integrated difference between the two CIFs and develop an asymptotically valid inference procedure using the wild bootstrap, thereby circumventing the intractable limiting distribution of the statistic. Theoretical analysis and extensive simulations demonstrate that the proposed method achieves higher statistical power and greater stability in finite samples, particularly in scenarios involving crossing CIFs. This approach offers a robust and practical solution for comparing groups in the presence of competing risks.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In competing risks models, cumulative incidence functions are commonly compared to infer differences between groups. Many existing inference methods, however, struggle when these functions cross during the time frame of interest. To address this problem, we investigate a test statistic based on the area between cumulative incidence functions. As the corresponding limiting distribution depends on quantities that are typically unknown, we propose a wild bootstrap approach to obtain a feasible and asymptotically valid two-sample test. The finite sample performance of the proposed method, in comparison with existing methods, is examined in an extensive simulation study.

Problem

• competing risks
• cumulative incidence functions
• crossing curves
• inference
• area between curves

Innovation

• competing risks
• cumulative incidence function
• area between curves
• wild bootstrap
• two-sample test