Marginal and Conditional Confounding Using Logits

This article presents two ways of quantifying confounding using logistic response models for binary outcomes. Drawing on the distinction between marginal and conditional odds ratios in statistics, we define two corresponding measures of confounding (marginal and conditional) that can be recovered from a simple standardization approach. We investigate when marginal and conditional confounding may differ, outline why the method by Karlson, Holm, and Breen recovers conditional confounding under a "no interaction"-assumption, and suggest that researchers may measure marginal confounding by using inverse probability weighting. We provide two empirical examples that illustrate our standardization approach.