Estimating the effect of a rare time-dependent treatment on the recurrent event rate

In many observational studies, the objective is to estimate the effect of treatment or state-change on the recurrent event rate. If treatment is assigned after the start of follow-up, traditional methods (eg, adjustment for baseline-only covariates or fully conditional adjustment for time-dependent covariates) may give biased results. We propose a two-stage modeling approach using the method of sequential stratification to accurately estimate the effect of a time-dependent treatment on the recurrent event rate. At the first stage, we estimate the pretreatment recurrent event trajectory using a proportional rates model censored at the time of treatment. Prognostic scores are estimated from the linear predictor of this model and used to match treated patients to as yet untreated controls based on prognostic score at the time of treatment for the index patient. The final model is stratified on matched sets and compares the posttreatment recurrent event rate to the recurrent event rate of the matched controls. We demonstrate through simulation that bias due to dependent censoring is negligible, provided the treatment frequency is low, and we investigate a threshold at which correction for dependent censoring is needed. The method is applied to liver transplant (LT), where we estimate the effect of development of post-LT End Stage Renal Disease (ESRD) on rate of days hospitalized.