Myers et al. Respond to "Understanding Bias Amplification"

The threat of bias amplification extends to all epidemiologic methods that rely on conditioning on covariates, so understanding its mechanisms and implications is important. We thank Dr. Pearl (1) for initially bringing the issue to our attention and for now extending the analysis of bias amplification to the case of multiple covariates (2). Here, as in our original paper (3), we attempt to clarify the implications of these results in practical settings. In particular, we focus on secondary analysis of electronically collected data sets, where there may be hundreds or thousands of measured variables available for use in adjustment. Many of these covariates may be proxies of true confounders, even if their relations with outcome and exposure are uncertain. In his commentary (2), Pearl showed that adjusting for a variable related to exposure may either increase or decrease the net confounding but will always reduce the unexplained variation in the exposure (thereby amplifying any remaining confounding bias). Thus, the potential for bias amplification compounds with each additional covariate adjustment, and large bias amplification is possible, even if each individual covariate has a relatively weak association with exposure. However, Pearl’s analysis assumes that there is an important unmeasured confounder that cannot be controlled. In that scenario, the study is flawed even without consideration of bias amplification. On the other hand, if the residual confounding can be eliminated or nearly eliminated via additional covariate adjustments, then the bias will be small regardless of the amount of independent variation in exposure.