Should we adjust for a confounder if empirical and theoretical criteria yield contradictory results? A simulation study

Confounders can be identified by one of two main strategies: empirical or theoretical. Although confounder identification strategies that combine empirical and theoretical strategies have been proposed, the need for adjustment remains unclear if the empirical and theoretical criteria yield contradictory results due to random error. We simulated several scenarios to mimic either the presence or the absence of a confounding effect and tested the accuracy of the exposure-outcome association estimates with and without adjustment. Various criteria (significance criterion, Change-in-estimate(CIE) criterion with a 10% cutoff and with a simulated cutoff) were imposed, and a range of sample sizes were trialed. In the presence of a true confounding effect, unbiased estimates were obtained only by using the CIE criterion with a simulated cutoff. In the absence of a confounding effect, all criteria performed well regardless of adjustment. When the confounding factor was affected by both exposure and outcome, all criteria yielded accurate estimates without adjustment, but the adjusted estimates were biased. To conclude, theoretical confounders should be adjusted for regardless of the empirical evidence found. The adjustment for factors that do not have a confounding effect minimally effects. Potential confounders affected by both exposure and outcome should not be adjusted for.