# Median Optimal Treatment Regimes

arXiv: https://arxiv.org/abs/2103.01802 · HTML: https://mlsanity.com/paper/2103.01802/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 67 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Optimal Distributionally Robust Individualized Treatment Rules](https://mlsanity.com/paper/2006.15121/) (2020)
- [Sharp instruments for classifying compliers and generalizing causal effects](https://mlsanity.com/paper/1801.03635/) (2018)
- [Efficient Estimation of Quantiles in Missing Data Models](https://mlsanity.com/paper/1512.08110/) (2015)
- [Robust regression for optimal individualized treatment rules](https://mlsanity.com/paper/1604.03648/) (2016)

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

- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands](https://mlsanity.com/paper/2501.11868/) (2025)
- [Ambiguous Dynamic Treatment Regimes: A Reinforcement Learning Approach](https://mlsanity.com/paper/2112.04571/) (2021)
- [Policy Learning with Distributional Welfare](https://mlsanity.com/paper/2311.15878/) (2023)
- [Off-Policy Evaluation with Policy-Dependent Optimization Response](https://mlsanity.com/paper/2202.12958/) (2022)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)
- [Limits of Approximating the Median Treatment Effect](https://mlsanity.com/paper/2403.10618/) (2024)

## Abstract (arXiv)

Optimal treatment regimes are personalized policies for making a treatment decision based on subject characteristics, with the policy chosen to maximize some value. It is common to aim to maximize the mean outcome in the population, via a regime assigning treatment only to those whose mean outcome is higher under treatment versus control. However, the mean can be an unstable measure of centrality, resulting in imprecise statistical procedures, as well as unrobust decisions that can be overly influenced by a small fraction of subjects. In this work, we propose a new median optimal treatment regime that instead treats individuals whose conditional median is higher under treatment. This ensures that optimal decisions for individuals from the same group are not overly influenced either by (i) a small fraction of the group (unlike the mean criterion), or (ii) unrelated subjects from different groups (unlike marginal median/quantile criteria). We introduce a new measure of value, the Average Conditional Median Effect (ACME), which summarizes across-group median treatment outcomes of a policy, and which the median optimal treatment regime maximizes. After developing key motivating examples that distinguish median optimal treatment regimes from mean and marginal median optimal treatment regimes, we give a nonparametric efficiency bound for estimating the ACME of a policy, and propose a new doubly robust-style estimator that achieves the efficiency bound under weak conditions. To construct the median optimal treatment regime, we introduce a new doubly robust-style estimator for the conditional median treatment effect. Finite-sample properties are explored via numerical simulations and the proposed algorithm is illustrated using data from a randomized clinical trial in patients with HIV.