# Risk ratio, odds ratio, risk difference... Which causal measure is easier to generalize?

arXiv: https://arxiv.org/abs/2303.16008 · HTML: https://mlsanity.com/paper/2303.16008/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2023.

## Built on by (most cited first, 8 of 8)

- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Variable importance for causal forests: breaking down the heterogeneity of treatment effects](https://mlsanity.com/paper/2308.03369/) (2023)
- [Reflections from Research Roundtables at the Conference on Health, Inference, and Learning (CHIL) 2025](https://mlsanity.com/paper/2510.15217/) (2025)
- [Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap](https://mlsanity.com/paper/2604.00811/) (2026)
- [Targeting relative risk heterogeneity with causal forests](https://mlsanity.com/paper/2309.15793/) (2023)
- [Preference-based Conditional Treatment Effects and Policy Learning](https://mlsanity.com/paper/2602.03823/) (2026)
- [Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption](https://mlsanity.com/paper/2309.16409/) (2023)
- [Prognostic Covariate Adjustment for Logistic Regression in Randomized Controlled Trials](https://mlsanity.com/paper/2402.18900/) (2024)

## Abstract (arXiv)

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, e.g. 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 discriminative model such that the conditional average treatment effect (CATE) captures the treatment effect. However, only the risk difference has its CATE and ATE (average treatment effect) disentangled from the baseline, 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.