Supplementary materials: Comparing the performance of two-stage residual inclusion methods when using physician’s prescribing preference as an instrumental variable: unmeasured confounding and noncollapsibility

These are peer-reviewed supplementary materials for the article 'Supplementary materials: Comparing the performance of two-stage residual inclusion methods when using physician’s prescribing preference as an instrumental variable: unmeasured confounding and noncollapsibility' published in the Journal of Comparative Effectiveness Research.Figure S1. Results from prior 1 prescription as IVFigure S2. Results from prior 2 prescriptions as IVFigure S3. Results from prior 3 prescriptions as IVFigure S4. Results from prior 4 prescriptions as IVR CodeAim: The first objective is to compare the performance of two-stage residual inclusion (2SRI), two-stage least square (2SLS) with the multivariable generalized linear model (GLM) in terms of the reducing unmeasured confounding bias. The second objective is to demonstrate the ability of 2SRI and 2SPS in alleviating unmeasured confounding when noncollapsibility exists. Materials & methods: This study comprises a simulation study and an empirical example from a real-world UK population health dataset (Clinical Practice Research Datalink). The instrumental variable (IV) used is based on physicians’ prescribing preferences (defined by prescribing history). Results: The percent bias of 2SRI in terms of treatment effect estimates to be lower than GLM and 2SPS and was less than 15% in most scenarios. Further, 2SRI was found to be robust to mild noncollapsibility with the percent bias less than 50%. As the level of unmeasured confounding increased, the ability to alleviate the noncollapsibility decreased. Strong IVs tended to be more robust to noncollapsibility than weak IVs. Conclusion: 2SRI tends to be less biased than GLM and 2SPS in terms of estimating treatment effect. It can be robust to noncollapsibility in the case of the mild unmeasured confounding effect.