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Instrumental variable (IV) methods are widely used to adjust for the bias in estimating treatment effects caused by unmeasured confounders in observational studies. It is common that a comparison between two treatments is focused on and that only subjects receiving one of these two treatments are considered in the analysis even though more than two treatments are available. In this paper, we provide empirical and theoretical evidence that the IV methods may result in biased treatment effects if applied on a data set in which subjects are preselected based on their received treatments. We frame this as a selection bias problem and propose a procedure that identifies the treatment effect of interest as a function of a vector of sensitivity parameters. We also list assumptions under which analyzing the preselected data does not lead to a biased treatment effect estimate. The performance of the proposed method is examined using simulation studies. We applied our method on The Health Improvement Network (THIN) database to estimate the comparative effect of metformin and sulfonylureas on weight gain among diabetic patients.

Selection Bias When Using Instrumental Variable Methods to Compare Two Treatments But More Than Two Treatments Are Available