Bayesian analysis of longitudinal studies with treatment by indication

In a medical setting, observational studies commonly involve patients who initiate a particular treatment (e.g., medication therapy) and others who do not, and the goal is to draw causal inferences about the effect of treatment on a time-to-event outcome. A difficulty with such studies is that the notion of a treatment initiation time is not well-defined for the control group. In this paper, we propose a Bayesian approach to estimate treatment effects in longitudinal observational studies where treatment is given by indication and thereby the exact timing of treatment is only observed for treated units. We present a framework for conceptualizing an underlying randomized experiment in this setting based on separating the time of indication for treatment, which we model using a latent state-space process, from the mechanism that determines assignment to treatment versus control. Next, we develop a two-step inferential approach that uses Markov Chain Monte Carlo (MCMC) posterior sampling to (1) infer the unobserved indication times for units in the control group, and (2) estimate treatment effects based on inferential conclusions from Step 1. This approach allows us to incorporate uncertainty about the unobserved indication times which induces uncertainty in both the selection of the control group and the measurement of time-to-event outcomes for these controls. We demonstrate our approach to study the effects on mortality of inappropriately prescribing phosphodiesterase type 5 inhibitors (PDE5Is), a medication contraindicated for certain types of pulmonary hypertension, using data from the Veterans Affairs (VA) health care system.