# Estimating scaled treatment effects with multiple outcomes

arXiv: https://arxiv.org/abs/1608.02273 · HTML: https://mlsanity.com/paper/1608.02273/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2016.

## Built on by (most cited first, 7 of 7)

- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [Comparing Targeting Strategies for Maximizing Social Welfare with Limited Resources](https://mlsanity.com/paper/2411.07414/) (2024)
- [A Diffusion-Based Method for Learning the Multi-Outcome Distribution of Medical Treatments](https://mlsanity.com/paper/2506.01533/) (2025)
- [The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation](https://mlsanity.com/paper/2309.17283/) (2023)
- [Continuous Treatment Effects with Surrogate Outcomes](https://mlsanity.com/paper/2402.00168/) (2024)
- [Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes](https://mlsanity.com/paper/2404.09119/) (2024)
- [Reduced-Rank Multi-objective Policy Learning and Optimization](https://mlsanity.com/paper/2404.18490/) (2024)

## Abstract (arXiv)

In classical study designs, the aim is often to learn about the effects of a treatment or intervention on a single outcome; in many modern studies, however, data on multiple outcomes are collected and it is of interest to explore effects on multiple outcomes simultaneously. Such designs can be particularly useful in patient-centered research, where different outcomes might be more or less important to different patients. In this paper we propose scaled effect measures (via potential outcome notation) that translate effects on multiple outcomes to a common scale, using mean-variance and median-interquartile-range -based standardizations. We present efficient, nonparametric, doubly robust methods for estimating these scaled effects (and weighted average summary measures), and for testing the null hypothesis that treatment affects all outcomes equally. We also discuss methods for exploring how treatment effects depend on covariates (i.e., effect modification). In addition to describing efficiency theory for our estimands and the asymptotic behavior of our estimators, we illustrate the methods in a simulation study and a data analysis. Importantly, and in contrast to much of the literature concerning effects on multiple outcomes, our methods are nonparametric and can be used not only in randomized trials to yield increased efficiency, but also in observational studies with high-dimensional covariates to reduce confounding bias.