# Non-parametric causal effects based on longitudinal modified treatment policies

arXiv: https://arxiv.org/abs/2006.01366 · HTML: https://mlsanity.com/paper/2006.01366/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 14 of 14)

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- [Efficient Evaluation of Natural Stochastic Policies in Offline Reinforcement Learning](https://mlsanity.com/paper/2006.03886/) (2020)
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- [Causal inference through multi-stage learning and doubly robust deep neural networks](https://mlsanity.com/paper/2407.08560/) (2024)
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- [Causal Estimation of Exposure Shifts with Neural Networks](https://mlsanity.com/paper/2302.02560/) (2023)
- [Non-parametric efficient estimation of marginal structural models with multi-valued time-varying treatments](https://mlsanity.com/paper/2409.18782/) (2024)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Deep Doubly Debiased Longitudinal Effect Estimation with ICE G-Computation](https://mlsanity.com/paper/2602.12379/) (2026)
- [Data Attribution in Adaptive Learning](https://mlsanity.com/paper/2604.04892/) (2026)
- [Smooth Multi-Policy Causal Effect Estimation in Longitudinal Settings](https://mlsanity.com/paper/2605.14284/) (2026)
- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)

## Abstract (arXiv)

Most causal inference methods consider counterfactual variables under interventions that set the treatment deterministically. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Furthermore, violations to the positivity assumption, necessary for identification, are exacerbated with continuous and multi-valued treatments and deterministic interventions. In this paper we propose longitudinal modified treatment policies (LMTPs) as a non-parametric alternative. LMTPs can be designed to guarantee positivity, and yield effects of immediate practical relevance with an interpretation that is familiar to regular users of linear regression adjustment. We study the identification of the LMTP parameter, study properties of the statistical estimand such as the efficient influence function, and propose four different estimators. Two of our estimators are efficient, and one is sequentially doubly robust in the sense that it is consistent if, for each time point, either an outcome regression or a 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 hypoxemia and mortality in Intensive Care Unit (ICU) patients. Software implementing our methods is provided in the form of the open source textttR package textttlmtp freely available on GitHub (urlhttps://github.com/nt-williams/lmtp).