Abstract
BackgroundIn 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.MethodsFrom 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 ( overset{frown }{beta } ) of causal effect. The bias ( overset{frown }{beta}hbox{-} beta ) and standard error ( SEleft(overset{frown }{beta}right) ) were used to evaluate their performances.ResultsWhen 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.ConclusionsArbitrary 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.
Highlights
In observational studies, matched case-control designs are routinely conducted to improve study precision
In observational studies, confounding factors (C) that are pre-exposure variables associated with the exposure E and the outcome D will distort the estimation of the target causal effect [1,2,3,4]
Scenario 1 (C is a confounder for E and D, Fig. 1a) Theoretically, in this scenario, the confounder C is dconnected with outcome D via two natural paths: C → D and C → E → D, which contribute to the crude association between C and D
Summary
In observational studies, matched case-control designs are routinely conducted to improve study precision. The magnitude of confounding bias mainly depends on the strength of the effects from confounder C to exposure E and from confounder C to outcome D. If one of these two effects is precisely null, confounding bias does not exist at all. Various strategies could be adopted to remove confounding bias, such as Restriction, Adjustment, Stratification [6, 7], while strategy of matching on confounders C (e.g. matched case-control designs) mainly focuses on improving estimation precision of the effect of E on D, rather than removing
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