Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments

Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments

The paper "Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments" by Jonas Schweisthal, Dennis Frauen, Mihaela van der Schaar, and Stefan Feuerriegel addresses the challenge of estimating the conditional average treatment effect (CATE) from observational data collected across multiple environments. This paper is particularly relevant for scenarios such as personalized medicine, where the observational data might be sourced from different hospitals, countries, or healthcare practitioners.

Problem Setting and Contributions

The authors recognize that real-world data often violate key causal inference assumptions: overlap (each individual has a positive probability of receiving any treatment) and unconfoundedness (all confounders are observed). These violations render traditional CATE estimators potentially biased. To tackle this issue, the authors propose moving away from point identification towards partial identification and introduce new model-agnostic meta-learners to estimate bounds on the CATE, leveraging differences in treatment assignment mechanisms across environments.

Key Contributions

1. Interpretation of Multiple Environments as IVs: The paper shows that the environment can be interpreted as an instrumental variable (IV) allowing researchers to adapt bounds from the IV literature for CATE.
2. Flexible Meta-Learners: The authors propose various model-agnostic meta-learners (namely WB-learner and CB-learners) to estimate the bounds for the CATE, which can be combined with arbitrary machine learning models.
3. Theoretical Guarantees: The paper provides theoretical results showing the consistency and double robustness properties of the proposed meta-learners.
4. Empirical Validation: The effectiveness of these meta-learners is demonstrated through experiments using both simulated and real-world data, showcasing their ability to yield reliable bounds even under violations of standard causal assumptions.

Methodological Innovations

The meta-learners introduced are divided into two main categories:

1. WB-learner: Targets within-environment bounds using a simple pseudo-outcome based on a single environment.
2. CB-learners: Focuses on cross-environment bounds, leveraging the variation across environments to tighten the bounds on the CATE.
   • CB-PI: Plugin learner.
   • CB-RA: Regression adjustment learner.
   • CB-IPW: Inverse propensity weighted learner.
   • CB-DR: Doubly robust learner.

The pseudo-outcomes of these learners facilitate a two-stage estimation process. The first stage estimates the necessary nuisance functions while the second estimates the bounds directly using these approximations.

Numerical Results

The simulations show that the proposed meta-learners reliably learn valid bounds and that performance gains are context-dependent. Specifically:

• CB-DR-learner demonstrates superior performance when the environment probability is complex, leveraging double robustness to mitigate model misspecifications.
• The cross-environment bounds are particularly effective in tightening the estimates when treatment assignment mechanisms differ significantly across environments.

Practical Implications

The practical implications are profound, particularly in fields like personalized medicine, where treatment effects vary significantly across subgroups defined by different environments (e.g., hospitals or countries). By leveraging the heterogeneity in treatment assignments, the proposed methods yield more robust and informative bounds on the treatment effects.

Future Directions

The approach opens up multiple avenues for future research. Extensions might include meta-learners for settings with continuous instruments, leaky mediation, or sensitivity analysis. Further, refining the implementation with other machine learning models could enhance their applicability across various domains.

Conclusion

This work significantly contributes to the field of causal inference by addressing the limitations of traditional methods under the prevalent conditions of overlap and unconfoundedness violations. The proposed meta-learners for partially-identified treatment effects represent a practical tool for researchers dealing with observational data from multiple environments, enabling more robust and reliable causal inference.