A simulation study on matched case-control designs in the perspective of causal diagrams

Abstract

Background: In observational studies, matched case-control designs are routinely conducted to improve study precision. How to select covariates for match or adjustment, however, is still a great challenge for estimating causal effect between the exposure E and outcome D. Methods: From the perspective of causal diagrams, 9 scenarios of causal relationships among exposure (E), outcome (D) and their related covariates (C) were investigated. Further various simulation strategies were performed to explore whether match or adjustment should be adopted. The "do calculus" and "back-door criterion" were used to calculate the true causal effect (β) of E on D on the log-odds ratio scale. 1:1 matching method was used to create matched case-control data, and the conditional or unconditional logistic regression was utilized to get the estimators (β\overset{\frown }{\beta } $$) of causal effect. The bias (β β $$ \overset{\frown }{\beta}\hbox{-} \beta $$) and standard error (S E βSE\left(\overset{\frown }{\beta}\right) $$) were used to evaluate their performances. Results: When C is exactly a confounder for E and D, matching on it did not illustrate distinct improvement in the precision; the benefit of match was to greatly reduce the bias for β though failed to completely remove the bias; further adjustment for C in matched case-control designs is still essential. When C is associated with E or D, but not a confounder, including an independent cause of D, a cause of E but has no direct causal effect on D, a collider of E and D, an effect of exposure E, a mediator of causal path from E to D, arbitrary match or adjustment of this kind of plausible confounders C will create unexpected bias. When C is not a confounder but an effect of D, match or adjustment is unnecessary. Specifically, when C is an instrumental variable, match or adjustment could not reduce the bias due to existence of unobserved confounders U. Conclusions: Arbitrary match or adjustment of the plausible confounder C is very dangerous before figuring out the possible causal relationships among E, D and their related covariates.