Model Misspecification When Excluding Instrumental Variables From PS Models in Settings Where Instruments Modify the Effects of Covariates on Treatment.

Theory and simulations show that variables affecting the outcome only through exposure, known as instrumental variables (IVs), should be excluded from propensity score (PS) models. In pharmacoepidemiologic studies based on automated healthcare databases, researchers will sometimes use a single PS model to control for confounding when evaluating the effect of a treatment on multiple outcomes. Because these "full" models are not constructed with a specific outcome in mind, they will usually contain a large number of IVs for any individual study or outcome. If researchers subsequently decide to evaluate a subset of the outcomes in more detail, they can construct reduced "outcome-specific" models that exclude IVs for the particular study. Accurate estimates of PSs that do not condition on IVs, however, can be compromised when simply excluding instruments from the full PS model. This misspecification may have a negligible impact on effect estimates in many settings, but is likely to be more pronounced for situations where instruments modify the effects of covariates on treatment (instrument-confounder interactions). In studies evaluating drugs during early dissemination, the effects of covariates on treatment are likely modified over calendar time and IV-confounder interaction effects on treatment are likely to exist. In these settings, refitting more flexible PS models after excluding IVs and IV-confounder interactions can work well. The authors propose an alternative method based on the concept of marginalization that can be used to remove the negative effects of controlling for IVs and IV-confounder interactions without having to refit the full PS model. This method fits the full PS model, including IVs and IV-confounder interactions, but marginalizes over values of the instruments. Fitting more flexible PS models after excluding IVs or using the full model to marginalize over IVs can prevent model misspecification along with the negative effects of balancing instruments in certain settings.