Testing similarity of competing risks models by comparing transition probabilities

TL;DR

This paper introduces a statistical framework for testing the similarity of competing risks models based on transition probabilities, with applications in clinical data analysis.

Contribution

It develops a novel bootstrap test for comparing transition probability matrices in multistate processes, improving power over existing methods.

Findings

The method reliably controls type I error in simulations.

It achieves higher statistical power than existing approaches.

Applied to prostate cancer data, it identifies thresholds of similarity in patient readmission dynamics.

Abstract

Assessing whether two patient populations exhibit comparable event dynamics is essential for evaluating treatment equivalence, pooling data across cohorts, or comparing clinical pathways across hospitals or strategies. We introduce a statistical framework for formally testing the similarity of competing risks models based on transition probabilities, which represent the cumulative risk of each event over time. Our method defines a maximum-type distance between the transition probability matrices of two multistate processes and employs a novel constrained parametric bootstrap test to evaluate similarity under both administrative and random right censoring. We theoretically establish the asymptotic validity and consistency of the bootstrap test. Through extensive simulation studies, we show that our method reliably controls the type I error and achieves higher statistical power than existing intensity-based approaches. Applying the framework to routine clinical data of prostate cancer patients treated with radical prostatectomy, we identify the smallest similarity threshold at which patients with and without prior in-house fusion biopsy exhibit comparable readmission dynamics. The proposed method provides a robust and interpretable tool for quantifying similarity in event history models.