# Propensity Score Matching and Subclassification in Observational Studies with Multi-level Treatments

arXiv: https://arxiv.org/abs/1508.06948 · HTML: https://mlsanity.com/paper/1508.06948/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2015.

## Built on by (most cited first, 6 of 6)

- [Double Machine Learning Methods for Estimating Average Treatment Effects: A Comparative Study](https://mlsanity.com/paper/2204.10969/) (2022)
- [Estimating Causal Effects of Multi-Aspect Online Reviews with Multi-Modal Proxies](https://mlsanity.com/paper/2112.10274/) (2021)
- [Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model](https://mlsanity.com/paper/2405.11377/) (2024)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)
- [Rate doubly robust estimation for weighted average treatment effects](https://mlsanity.com/paper/2509.14502/) (2025)

## Abstract (arXiv)

In this paper, we develop new methods for estimating average treatment effects in observational studies, focusing on settings with more than two treatment levels under unconfoundedness given pre-treatment variables. We emphasize subclassification and matching methods which have been found to be effective in the binary treatment literature and which are among the most popular methods in that setting. Whereas the literature has suggested that these particular propensity-based methods do not naturally extend to the multi-level treatment case, we show, using the concept of weak unconfoundedness, that adjusting for or matching on a scalar function of the pre-treatment variables removes all biases associated with observed pre-treatment variables. We apply the proposed methods to an analysis of the effect of treatments for fibromyalgia. We also carry out a simulation study to assess the finite sample performance of the methods relative to previously proposed methods.