A Bayesian Framework for Causal Analysis of Recurrent Events in Presence of Immortal Risk

Observational studies of recurrent event rates are common in biomedical statistics. Broadly, the goal is to estimate differences in event rates under two treatments within a defined target population over a specified followup window. Estimation with observational claims data is challenging because while membership in the target population is defined in terms of eligibility criteria, treatment is rarely assigned exactly at the time of eligibility. Ad-hoc solutions to this timing misalignment, such as assigning treatment at eligibility based on subsequent assignment, incorrectly attribute prior event rates to treatment - resulting in immortal risk bias. Even if eligibility and treatment are aligned, a terminal event process (e.g. death) often stops the recurrent event process of interest. Both processes are also censored so that events are not observed over the entire followup window. Our approach addresses misalignment by casting it as a treatment switching problem: some patients are on treatment at eligibility while others are off treatment but may switch to treatment at a specified time - if they survive long enough. We define and identify an average causal effect of switching under specified causal assumptions. Estimation is done using a g-computation framework with a joint semiparametric Bayesian model for the death and recurrent event processes. Computing the estimand for various switching times allows us to assess the impact of treatment timing. We apply the method to contrast hospitalization rates under different opioid treatment strategies among patients with chronic back pain using Medicare claims data.