Exchangeability of Measures of Association Before and After Exposure Status Is Flipped: Its Relationship With Confounding in the Counterfactual Model

Abstract

Background: The counterfactual definition of confounding is often explained in the context of exchangeability between the exposed and unexposed groups. One recent approach is to examine whether the measures of association (eg, associational risk difference) are exchangeable when exposure status is flipped in the population of interest. We discuss the meaning and utility of this approach, showing their relationships with the concept of confounding in the counterfactual framework. Methods: Three hypothetical cohort studies are used, in which the target population is the total population. After providing an overview of the notions of confounding in distribution and in measure, we discuss the approach from the perspective of exchangeability of measures of association (eg, factual associational risk difference vs counterfactual associational risk difference). Results: In general, if the measures of association are non-exchangeable when exposure status is flipped, confounding in distribution is always present, although confounding in measure may or may not be present. Even if the measures of association are exchangeable when exposure status is flipped, there could be confounding both in distribution and in measure. When we use risk difference or risk ratio as a measure of interest and the exposure prevalence in the population is 0.5, testing the exchangeability of measures of association is equivalent to testing the absence of confounding in the corresponding measures. Conclusion: The approach based on exchangeability of measures of association essentially does not provide a definition of confounding in the counterfactual framework. Subtly differing notions of confounding should be distinguished carefully.

Keywords

• causality
• causal inference
• confounding
• counterfactual
• exchangeability
• target population