Performance of a propensity score adjustment in longitudinal studies with covariate-dependent representation

Longitudinal observational studies provide rich opportunities to examine treatment effectiveness during the course of a chronic illness. However, there are threats to the validity of observational inferences. For instance, clinician judgment and self-selection play key roles in treatment assignment. To account for this, an adjustment such as the propensity score can be used if certain assumptions are fulfilled. Here, we consider a problem that could surface in a longitudinal observational study and has been largely overlooked. It can occur when subjects have a varying number of distinct periods of therapeutic intervention. We evaluate the implications of baseline variables in the propensity model being associated with the number of post baseline observations per subject and refer to it as 'covariate-dependent representation'. An observational study of antidepressant treatment effectiveness serves as a motivating example. The analyses examine the first 20 years of follow-up data from the National Institute of Mental Health Collaborative Depression Study, a longitudinal, observational study. A simulation study evaluates the consequences of covariate-dependent representation in longitudinal observational studies of treatment effectiveness under a range of data specifications.The simulations found that estimates were adversely affected by underrepresentation when there was lower ICC among repeated doses and among repeated outcomes.