Causal Inference with Recurrent Data via Propensity Score Methods

Abstract

Propensity score methods are increasingly being used to reduce estimation bias of treatment effects for observational studies. Previous research has shown that propensity score methods consistently estimate the marginal hazard ratio for time to event data. However, recurrent data frequently arise in the biomedical literature and there is a paucity of research into the use of propensity score methods when data are recurrent in nature. The objective of my thesis is to extend the existing propensity score methods to recurrent data setting. We review current propensity score methods for estimating treatment effects when the outcome is a single time to event. Then we propose a new class of inverse probability treatment weighting (IPTW) estimators to estimate treatment effects for recurrent data. We illustrate our methods through both estimating equation theory and a series of Monte Carlo simulations. The simulation results indicate that when there is no censoring, the newly proposed IPTW estimators allow us to consistently estimate the marginal hazard ratio for each event. Under administrative censoring regime, the stabilized IPTW estimator consistently estimates the marginal hazard ratio while the conventional IPTW estimator yields significant bias, especially when the proportion of subjects being censored is high. For variance estimation, we incorporate the robust variance estimator and the bootstrap variance estimator to deal with the within-subject correlation induced by weighting. In addition, we apply our methods to a real life example. We note that although the Cox proportional hazards model we used for estimating the marginal hazard ratio may be subject to misspecification, the estimate still converges and has meaningful interpretations.