Prior Event Rate Ratio Adjustment for Hidden Confounding in Observational Studies of Treatment Effectiveness: A Pairwise Cox Likelihood Approach

Observational studies provide a rich source of information for assessing effectiveness of treatment interventions in many situations where it is not ethical or practical to perform randomized controlled trials. However, such studies are prone to bias from hidden (unmeasured) confounding. A promising approach to identifying and reducing the impact of unmeasured confounding is Prior Event Rate Ratio (PERR) adjustment, a quasi-experimental analytic method proposed in the context of electronic medical record database studies. In this paper we present a statistical framework for using a pairwise approach to PERR adjustment that removes bias inherent in the original PERR method. A flexible pairwise Cox likelihood function is derived and used to demonstrate the consistency of the simple and convenient PERR-ALT estimator. We show how to estimate standard errors and confidence intervals for treatment effect estimates based on the observed information, and provide R code to illustrate how to implement the method. Assumptions required for the pairwise approach (as well as PERR) are clarified, and the consequences of model misspecification are explored. Our results confirm the need for researchers to consider carefully the suitability of the method in the context of each problem. Extensions of the pairwise likelihood to more complex designs involving time-varying covariates or more than two periods are considered. We illustrate the application of the method using data from a longitudinal cohort study of enzyme replacement therapy for lysosomal storage disorders.