# Non-parametric efficient estimation of marginal structural models with multi-valued time-varying treatments

arXiv: https://arxiv.org/abs/2409.18782 · HTML: https://mlsanity.com/paper/2409.18782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 72 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 15 of 15)

- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
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- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference](https://mlsanity.com/paper/1908.11523/) (2019)
- [Non-parametric causal effects based on longitudinal modified treatment policies](https://mlsanity.com/paper/2006.01366/) (2020)
- [Sequential Double Robustness in Right-Censored Longitudinal Models](https://mlsanity.com/paper/1705.02459/) (2017)
- [Assumption-lean inference for generalised linear model parameters](https://mlsanity.com/paper/2006.08402/) (2020)
- [Fast convergence rates for dose-response estimation](https://mlsanity.com/paper/2207.11825/) (2022)
- [On the multiply robust estimation of the mean of the g-functional](https://mlsanity.com/paper/1705.08582/) (2017)
- [A nonparametric projection-based estimator for the probability of causation, with application to water sanitation in Kenya](https://mlsanity.com/paper/1810.00767/) (2018)
- [Doubly Robust Inference for Targeted Minimum Loss Based Estimation in Randomized Trials with Missing Outcome Data](https://mlsanity.com/paper/1704.01538/) (2017)
- [Evaluating the Impact of State-Level Public Masking Mandates on New COVID-19 Cases and Deaths in the United States: A Demonstration of the Causal Roadmap](https://mlsanity.com/paper/2110.06115/) (2021)
- [Causal isotonic regression](https://mlsanity.com/paper/1810.03269/) (2018)
- [Causal survival analysis under competing risks using longitudinal modified treatment policies](https://mlsanity.com/paper/2202.03513/) (2022)

## Abstract (arXiv)

Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with multi-valued and time-varying treatments. In this paper, we use machine learning together with recent developments in semiparametric efficiency theory for longitudinal studies to propose such an estimator. The proposed estimator is based on a study of the non-parametric identifying functional, including first order von-Mises expansions as well as the efficient influence function and the efficiency bound. We show conditions under which the proposed estimator is efficient, asymptotically normal, and sequentially doubly robust in the sense that it is consistent if, for each time point, either the outcome or the treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on a COVID-19 dataset studying the impact of mobility on the cumulative number of observed cases.