Causal Inference on Sequential Treatments via Tensor Completion

TL;DR

This paper introduces a tensor completion method for causal inference on sequential treatments, leveraging low-rank structures and inverse probability weighting to improve estimation accuracy in longitudinal studies.

Contribution

It proposes a novel tensorized MSM model that captures complex potential outcomes and adjusts for confounding, with theoretical error bounds and superior empirical performance.

Findings

Outperforms existing methods in simulations

Provides theoretical error bounds for the estimator

Successfully applied to ICU ventilation data

Abstract

Marginal Structural Models (MSMs) are popular for causal inference of sequential treatments in longitudinal observational studies, which however are sensitive to model misspecification. To achieve flexible modeling, we envision the potential outcomes to form a three-dimensional tensor indexed by subject, time, and treatment regime and propose a tensorized history-restricted MSM (HRMSM). The semi-parametric tensor factor model allows us to leverage the underlying low-rank structure of the potential outcomes tensor and exploit the pre-treatment covariate information to recover the counterfactual outcomes. We incorporate the inverse probability of treatment weighting in the loss function for tensor completion to adjust for time-varying confounding. Theoretically, a non-asymptotic upper bound on the Frobenius norm error for the proposed estimator is provided. Empirically, simulation studies show that the proposed tensor completion approach outperforms the parametric HRMSM and existing matrix/tensor completion methods. Finally, we illustrate the practical utility of the proposed approach to study the effect of ventilation on organ dysfunction from the Medical Information Mart for Intensive Care database.