Testing similarity of competing risks models by comparing transition probabilities

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.