Validity evaluation of indirect adjustment method for multiple unmeasured confounders: A simulation and empirical study

An indirect adjustment method was developed to control for unmeasured confounders in a large administrative cohort study. A previous study that proposed the indirect adjustment method assessed the validity of the method by simulations but did not consider the direction of bias and scenarios with multiple missing confounders. In this study, we evaluated the direction and the magnitude of bias of the indirect adjustment method with multiple correlated unmeasured confounders using simulation and empirical datasets.

A simulation study was conducted to compare the bias of the indirect adjustment by varying the number of confounders, magnitude of correlation between confounders, and the number of adjustment variables. An empirical study was conducted by applying the indirect adjustment method to the association between PM₁₀ and mortality using the Korea National Health and Nutrition Examination Survey linked Cause of Death data for 2007-2016.

The simulations of the present study demonstrated that 1) when a confounder is positively associated with both exposure and outcome, indirect adjustment might bias the effect size downward; 2) the magnitude of bias might depend on the correlation between unmeasured confounders; and 3) indirect adjustment for multiple missing confounders at once could result in a higher bias than that for some of the missing confounders. Empirical analyses also showed consistent results, but the bias of indirectly adjusted effect estimates was sometimes larger than that of unadjusted effect estimates.

The indirect adjustment method is a promising technique to reduce the bias from unmeasured confounding; however, it should be implemented carefully, particularly when there are multiple correlated unmeasured confounders of the same direction.