Definition and identification of causal ratio effects

In generalized linear models, the effect of a treatment or intervention is often expressed as a ratio (e.g., risk ratio and odds ratio). There is discussion about when ratio effect measures can be interpreted in a causal way. For example, ratio effect measures suffer from noncollapsibility, that is, even in randomized experiments, the average over individual ratio effects is not identical to the (unconditional) ratio effect based on group means. Even more, different ratio effect measures (e.g., simple ratio and odds ratio) can point into different directions regarding the effectiveness of the treatment making it difficult to decide which one is the causal effect of interest. While causality theories do in principle allow for ratio effects, the literature lacks a comprehensive derivation and definition of ratio effect measures and their possible identification from a causal perspective (including, but not restricted to randomized experiments). In this article, we show how both simple ratios and odds ratios can be defined based on the stochastic theory of causal effects. Then, we examine if and how expectations of these effect measures can be identified under four causality conditions. Finally, we discuss an alternative computation of ratio effects as ratios of causally unbiased expectations instead of expectations of individual ratios, which is identifiable under all causality conditions and consistent with difference effects. (PsycInfo Database Record (c) 2025 APA, all rights reserved).