A new method for dealing with collider bias in the PWP model for recurrent events in randomized controlled trials

Evaluating recurrent events within a time-to-event analysis framework effectively utilizes all relevant information to address the clinical question of interest fully and has certain advantages in randomized controlled trials (RCTs). However, the Prentice, Williams, and Peterson (PWP) model disrupts the randomness of the risk set for subsequent recurrent events other than the first and consequently introduces bias in estimating effects. This study aimed to propose a weighted PWP model, evaluate its statistical performance, and assess the potential consequences of using common practices when each recurrence has different baseline hazard functions.

We proposed adjusting the estimate of treatment effect through a weighting strategy that constructed a virtual population balanced between groups in each risk set. A simulation study was carried out. The characteristic of the simulation data was the baseline hazard changed with the number of events. The proposed weighted PWP model was compared with current methods, including Cox for time-to-first-event, Poisson, negative binomial (NB), Andersen-Gill (AG), Lin-Wei-Yang-Ying (LWYY), and PWP models. Model performance was evaluated by bias, type I error rates, and statistical power. All models were applied to a real case from a randomization trial of Chemoprophylaxis treatment for Recurrent Stage I Bladder Tumors.

The results showed that the proposed weighted PWP model performed best with the lowest bias and highest statistical power. However, other models, including the Cox for time-to-first-event, Poisson, NB, AG, LWYY, and PWP models, all showed different degrees of bias and inflated type I error rates or low statistical power in the case of the baseline hazard changed with the number of events. Covariate adjustment via outcome regression can lead to inflated type I error rates. When the number of recurrent events was restricted, all weighting strategies yielded stable and nearly consistent results.

Recurrent event data should be analyzed with caution. The proposed methods may be generalized to model recurrent events. Our findings serve as an important clarification of how to deal with collider bias in the PWP model in RCTs.