Optimal Balancing of Time-Dependent Confounders for Marginal Structural Models

TL;DR

This paper introduces Kernel Optimal Weighting (KOW), a convex-optimization method that improves causal inference in marginal structural models by balancing confounders and controlling variance, addressing limitations of existing weighting techniques.

Contribution

The paper proposes KOW, a novel convex-optimization approach that directly balances time-dependent confounders and controls for variance, enhancing causal effect estimation in MSMs.

Findings

KOW outperforms IPTW, stabilized-IPTW, and CBPS in simulations.

KOW effectively balances confounders and reduces variance.

Application to HIV treatment and US elections demonstrates practical utility.

Abstract

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.