Estimation of the marginal effect of antidepressants on body mass index under confounding and endogenous covariate-driven monitoring times

In studying the marginal effect of antidepressants on body mass index using electronic health records data, we face several challenges. Patients' characteristics can affect the exposure (confounding) as well as the timing of routine visits (measurement process), and those characteristics may be altered following a visit which can create dependencies between the monitoring and body mass index when viewed as a stochastic or random processes in time. This may result in a form of selection bias that distorts the estimation of the marginal effect of the antidepressant. Inverse intensity of visit weights have been proposed to adjust for these imbalances, however no approaches have addressed complex settings where the covariate and the monitoring processes affect each other in time so as to induce endogeneity, a situation likely to occur in electronic health records. We review how selection bias due to outcome-dependent follow-up times may arise and propose a new cumulated weight that models a complete monitoring path so as to address the above-mentioned challenges and produce a reliable estimate of the impact of antidepressants on body mass index. More specifically, we do so using data from the Clinical Practice Research Datalink in the United Kingdom, comparing the marginal effect of two commonly used antidepressants, citalopram and fluoxetine, on body mass index. The results are compared to those obtained with simpler methods that do not account for the extent of the dependence due to an endogenous covariate process.