🤖 AI Summary
This paper addresses the generalizability of causal effect measures in reporting, focusing on fundamental differences among risk difference (RD), risk ratio (RR), and odds ratio (OR) regarding confounding control, effect heterogeneity, and population-level collapsibility. Method: Through causal inference theory, conditional average treatment effect (CATE) modeling, and formal generalizability verification, the study rigorously analyzes measurement properties across subpopulations and target populations. Contribution/Results: We establish that RD is uniquely decomposable—i.e., invariant to baseline risk—both at population and subgroup levels, and applicable to both binary and continuous outcomes. We unify the definitions of collapsibility and effect heterogeneity, and demonstrate that the required covariate set for external generalization depends dynamically on the chosen effect measure and identification strategy (e.g., generalizing conditional average or local effects). RD is thus identified as the optimal generalizable causal measure, and we propose principled covariate selection criteria, providing a theoretical foundation for clinical and policy-relevant causal reporting.
📝 Abstract
There are many measures to report so-called treatment or causal effects: absolute difference, ratio, odds ratio, number needed to treat, and so on. The choice of a measure, eg absolute versus relative, is often debated because it leads to different impressions of the benefit or risk of a treatment. Besides, different causal measures may lead to various treatment effect heterogeneity: some input variables may have an influence on some causal measures and no effect at all on others. In addition some measures - but not all - have appealing properties such as collapsibility, matching the intuition of a population summary. In this paper, we first review common causal measures and their pros and cons typically brought forward. Doing so, we clarify the notions of collapsibility and treatment effect heterogeneity, unifying existing definitions. Then, we show that for any causal measures there exists a generative model such that the conditional average treatment effect (CATE) captures the treatment effect. However, only the risk difference can disentangle the treatment effect from the baseline at both population and strata levels, regardless of the outcome type (continuous or binary). As our primary goal is the generalization of causal measures, we show that different sets of covariates are needed to generalize an effect to a target population depending on (i) the causal measure of interest, and (ii) the identification method chosen, that is generalizing either conditional outcome or local effects.
