Model-agnostic meta-learners for estimating heterogeneous treatment effects over time

Model-agnostic Meta-learners for Estimating Heterogeneous Treatment Effects Over Time

The paper by Dennis Frauen, Konstantin Hess, and Stefan Feuerriegel addresses the challenge of estimating heterogeneous treatment effects (HTEs) over time from observational data. This task is particularly relevant in fields like personalized medicine, where treatment decisions must be adapted over multiple time periods based on patient responses recorded in electronic health records. The authors propose model-agnostic meta-learners to estimate HTEs, a relatively unexplored approach in this context, which stands in contrast to the traditionally employed model-based learners.

Key Contributions

1. Introduction of Meta-learners: The authors propose several meta-learners based on different adjustment strategies, including history adjustment, regression adjustment (G-computation), propensity adjustment, and a novel doubly robust adjustment. These learners are designed to be model-agnostic, meaning they can be used with any machine learning model, such as transformers, to estimate HTEs over time.
2. Theoretical Analysis: A comprehensive theoretical analysis is provided, characterizing the conditions under which specific learners are preferable. This includes the derivation of asymptotic bounds on the point-wise risk and the establishment of properties such as Neyman-orthogonality and double robustness for the proposed learners.
3. Numerical Experiments: The theoretical insights are confirmed through extensive numerical experiments using both synthetic and semi-synthetic data. These experiments demonstrate that the proposed meta-learners perform as predicted by the theoretical analysis.
4. Novel Adjustment Mechanisms: The paper introduces an inverse-variance weighted doubly robust learner (IVW-DR-learner) to address the instability issues in the doubly robust learner caused by small propensity scores in the time-varying setting. The derived weights stabilize the DR-loss and enhance its performance in low-overlap scenarios.

Detailed Overview

The problem setting involves covariates, treatments, and outcomes observed over multiple time periods. The authors utilize potential outcomes framework to define the causal estimands and impose standard assumptions such as consistency, overlap, and sequential ignorability to ensure identifiability. They emphasize the challenges unique to the time-varying setting, such as runtime confounding and the need for tailored adjustment mechanisms.

Several meta-learners are proposed:

• PI-HA-learner: Utilizes history adjustment, is straightforward but biased due to runtime confounding.
• PI-RA-learner: Implements regression adjustment, provides unbiased estimates but may suffer from high estimation variance.
• RA-learner: A two-stage learner using regression adjustment, designed to directly estimate CATE, potentially reducing the variance.
• IPW-learner: Leverages propensity adjustment, appropriate under conditions of well-estimated propensity scores.
• DR-learner: Employs doubly robust adjustment, combining propensity and regression adjustments for potentially superior convergence rates and robustness to misspecification.
• IVW-DR-learner: An enhancement of the DR-learner with inverse-variance weighting to stabilize the learner in scenarios with low overlap.

Theoretical Implications

The theoretical analysis reveals that the PI-HA-learner is biased due to its simplistic adjustment mechanism, especially when runtime confounding is present. In contrast, the PI-RA- and RA-learners, as well as the IPW- and DR-learners, are unbiased under correct modeling assumptions. The DR-learner's doubly robust nature makes it particularly appealing as it leverages information from both response surfaces and propensity scores.

Practical Implications and Future Work

Practically, these model-agnostic learners can be instantiated with advanced machine learning models like transformers, making them highly versatile and adaptable to various data-generating processes. The numerical experiments validate the theoretical results, showing that the proposed meta-learners improve estimation accuracy in multiple scenarios.

Future developments could explore continuous time models to further extend the applicability of these meta-learners, given that current methods are tailored for discrete time periods. Additionally, optimizing the transformer-based architectures for specific causal inference tasks could yield further performance improvements.

Conclusion

This paper enriches the causal inference literature by introducing model-agnostic meta-learners for the time-varying setting, backed by robust theoretical guarantees and validated through rigorous experimentation. These contributions hold promise for advancing personalized treatment decisions in fields like medicine, where the accurate estimation of HTEs is crucial.