On the collapsibility of measures of effect in the counterfactual causal framework

A measure of association is said to be collapsible over a set of baseline covariates if the marginal value of the measure of association is equal to a weighted average of the stratum-specific measures of association. In this paper, we consider two subtly different definitions of collapsibility, and show that by considering causal measures of effect based on counterfactual variables it is possible to separate out the component of non-collapsibility which is due to the mathematical properties of the effect measure. We provide weights such that the causal risk difference and the causal risk ratio are collapsible over arbitrary baseline covariates, and demonstrate that such general weights do not exist for the odds ratio.