  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.
