Sequential Treatment Effect Estimation with Unmeasured Confounders

TL;DR

The paper tackles estimating cumulative effects of sequential treatments in the presence of unmeasured confounders in time-series data. It introduces DSIV-CFR, a framework that combines transformer-based learning for instrument-like latent representations and a generalized method of moments (GMM) counterfactual regression, guided by negative-control assumptions where an instrumental variable acts as a negative control exposure and the prior outcome serves as a negative control outcome. The method uses mutual-information and adversarial losses to decompose latent confounding from observed covariates and solves a generalized moment condition to recover causal effects, enabling robust estimation of future outcomes $\boldsymbol{Y}_t(\boldsymbol{a}_t)$. Experiments on synthetic and real-world datasets, including tumor growth, cryptocurrency, and MIMIC-III, show that DSIV-CFR outperforms baselines in one-step and extends effectively to multi-step sequential decision making, highlighting its potential for real-world dynamic systems where unmeasured confounding is prevalent.

Abstract

This paper studies the cumulative causal effects of sequential treatments in the presence of unmeasured confounders. It is a critical issue in sequential decision-making scenarios where treatment decisions and outcomes dynamically evolve over time. Advanced causal methods apply transformer as a backbone to model such time sequences, which shows superiority in capturing long time dependence and periodic patterns via attention mechanism. However, even they control the observed confounding, these estimators still suffer from unmeasured confounders, which influence both treatment assignments and outcomes. How to adjust the latent confounding bias in sequential treatment effect estimation remains an open challenge. Therefore, we propose a novel Decomposing Sequential Instrumental Variable framework for CounterFactual Regression (DSIV-CFR), relying on a common negative control assumption. Specifically, an instrumental variable (IV) is a special negative control exposure, while the previous outcome serves as a negative control outcome. This allows us to recover the IVs latent in observation variables and estimate sequential treatment effects via a generalized moment condition. We conducted experiments on 4 datasets and achieved significant performance in one- and multi-step prediction, supported by which we can identify optimal treatments for dynamic systems.

Figures (6)

• Figure 1: A case of counterfactual prediction and decision making on the time series data in a medical setting.
• Figure 2: Casual graphs for illustrating the relationships between different variables from time series data. On the left, we describe the causalities in details, where the subscript associated with $t$ in each variable reflects the time dependence. Unobserved variables are marked in shadow. In this paper, we focus on the cumulative effect of treatment $(\boldsymbol{A}_1,\dots,\boldsymbol{A}_t)$ on outcome $\boldsymbol{Y}_t$. For simplicity, we give its summary graph on the right, where the historical information of all treatments and confounders are denoted as $\bar{\boldsymbol{A}}_{t-1}$ and $\bar{\boldsymbol{C}}_{t-1}$.
• Figure 3: Overview of our model DSIV-CFR. Some explanations have been displayed in the right panel. Historical observations $\bar{\boldsymbol{H}}$ are input into the first transformer $\psi(\cdot)$ to learn the representation of IVs $\phi_Z$ and confounders $\phi_C$, which is optimized by the mutual information (MI) loss. The second transformer $h(\cdot)$ is trained as a backbone with the objective of accurately predicting future potential outcomes $\boldsymbol{Y}$, measured by the MSE loss. In addition, an adversarial loss derived from IVs and confounders is considered to build up a GMM framework, requiring another bridge function $f(\cdot)$ to learn a weight $\boldsymbol{M}$ so as to train against $h(\cdot)$.
• Figure 4: Results of hyper-parameter analysis on the Cryptocurrency dataset. Setting the $\alpha$ to $0$ is equivalent to removing $\mathcal{L}_{MI}$, and $\beta=0$ means $\mathcal{L}_{adv}$ is deleted. The heatmap on the right represents the changes in performance. If a cell's color is closer to a warm color (orange), it means that the model trained with the corresponding $\{\alpha,\beta\}$ combination has better performance. Conversely, if the cell's color is closer to a cool color (green), it indicates poorer performance.
• Figure 5: Results of decision making $5$ steps ahead. Values on the vertical axis represent the differences between oracle and the corresponding results of predicted optimal treatments (lower=better).

Theorems & Definitions (3)

• Proposition 3.6: IV Decomposition
• Theorem 3.8: IV Identification
• proof