# Optimal Balancing of Time-Dependent Confounders for Marginal Structural Models

arXiv: https://arxiv.org/abs/1806.01083 · HTML: https://mlsanity.com/paper/1806.01083/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2018.

## Built on by (most cited first, 3 of 3)

- [Dynamic covariate balancing: estimating treatment effects over time with potential local projections](https://mlsanity.com/paper/2103.01280/) (2021)
- [A Stable and Efficient Covariate-Balancing Estimator for Causal Survival Effects](https://mlsanity.com/paper/2310.02278/) (2023)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)

## Abstract (arXiv)

Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel Optimal Weighting (KOW), a convex-optimization-based approach that finds weights for fitting the MSM that optimally balance time-dependent confounders while simultaneously controlling for precision, directly addressing the above limitations. KOW directly minimizes the error in estimation due to time-dependent confounding via a new decomposition as a functional. We further extend KOW to control for informative censoring. We evaluate the performance of KOW in a simulation study, comparing it with IPTW, stabilized-IPTW, and CBPS. We demonstrate the use of KOW in studying the effect of treatment initiation on time-to-death among people living with HIV and the effect of negative advertising on elections in the United States.