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A measure of association is said to be collapsible over a set of baselinecovariates if the marginal value of the measure of association is equal to aweighted average of the stratum-specific measures of association. In thispaper, we consider two subtly different definitions of collapsibility, and showthat by considering causal measures of effect based on counterfactual variablesit is possible to separate out the component of non-collapsibility which is dueto the mathematical properties of the effect measure. We provide weights suchthat the causal risk difference and the causal risk ratio are collapsible overarbitrary baseline covariates, and demonstrate that such general weights do notexist for the odds ratio.

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