Instrumental Variable Methods for Continuous Outcomes That Accommodate Nonignorable Missing Baseline Values

Instrumental variable (IV) methods provide unbiased treatment effect estimation in the presence of unmeasured confounders under certain assumptions. To provide valid estimates of treatment effect, treatment effect confounders that are associated with the IV (IV-confounders) must be included in the analysis, and not including observations with missing values may lead to bias. Missing covariate data are particularly problematic when the probability that a value is missing is related to the value itself, which is known as nonignorable missingness. In such cases, imputation-based methods are biased. Using health-care provider preference as an IV method, we propose a 2-step procedure with which to estimate a valid treatment effect in the presence of baseline variables with nonignorable missing values. First, the provider preference IV value is estimated by performing a complete-case analysis using a random-effects model that includes IV-confounders. Second, the treatment effect is estimated using a 2-stage least squares IV approach that excludes IV-confounders with missing values. Simulation results are presented, and the method is applied to an analysis comparing the effects of sulfonylureas versus metformin on body mass index, where the variables baseline body mass index and glycosylated hemoglobin have missing values. Our result supports the association of sulfonylureas with weight gain.