Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts (2402.01972v1)

Abstract: We introduce efficient plug-in (EP) learning, a novel framework for the estimation of heterogeneous causal contrasts, such as the conditional average treatment effect and conditional relative risk. The EP-learning framework enjoys the same oracle-efficiency as Neyman-orthogonal learning strategies, such as DR-learning and R-learning, while addressing some of their primary drawbacks, including that (i) their practical applicability can be hindered by loss function non-convexity; and (ii) they may suffer from poor performance and instability due to inverse probability weighting and pseudo-outcomes that violate bounds. To avoid these drawbacks, EP-learner constructs an efficient plug-in estimator of the population risk function for the causal contrast, thereby inheriting the stability and robustness properties of plug-in estimation strategies like T-learning. Under reasonable conditions, EP-learners based on empirical risk minimization are oracle-efficient, exhibiting asymptotic equivalence to the minimizer of an oracle-efficient one-step debiased estimator of the population risk function. In simulation experiments, we illustrate that EP-learners of the conditional average treatment effect and conditional relative risk outperform state-of-the-art competitors, including T-learner, R-learner, and DR-learner. Open-source implementations of the proposed methods are available in our R package hte3.

• The paper introduces the Efficient Plug-In (EP) learning framework that achieves oracle-efficient estimation of heterogeneous causal effects.
• It leverages empirical risk minimization and adjusted outcome regression to overcome instability and non-convexity challenges in DR and R-learning.
• Experiments show that EP-learning outperforms state-of-the-art methods in CATE and log-CRR estimation, providing robust and stable performance.

Efficient Plug-In Learning for Estimation of Heterogeneous Causal Contrasts

The paper introduces Efficient Plug-In (EP) learning, a novel framework designed for the precise estimation of heterogeneous causal effects, focusing primarily on the conditional average treatment effect (CATE) and the conditional relative risk (CRR). This methodology addresses key limitations found in traditional orthogonal learning approaches—namely DR-learning and R-learning—that often grapple with non-convex loss functions and inconsistent inverse weighting challenges.

Overview of EP-Learning Framework

EP-learning provides a comprehensive framework that consolidates the strengths of both plug-in estimation techniques and orthogonal learning methodologies. The core thrust of EP-learning lies in constructing an efficient plug-in risk estimator for causal contrasts, facilitating stability and robustness while maintaining oracle-efficiency similar to that associated with variations of Neyman-orthogonal learning. The EP-learning strategy circumvents the non-convexity and instability issues of DR and R-learners by utilizing a stable, consistent plug-in loss function approach, coupled with innovative empirical risk minimization strategies that align with oracle-efficient one-step debiased estimators.

Steps Involved in EP-Learning

To develop a stable plug-in risk estimator, EP-learning leverages the decomposition of the population risk parameter along with its efficient influence function. EP-learning constructs a debiased estimator by employing empirical risk minimization on adjusted outcome regression estimates. This process mitigates the sensitivity and computational challenges intrinsic to traditional DR and R-learning frameworks.

Theoretical and Empirical Contributions

The primary theoretical contribution of this work is the establishment of an efficient plug-in risk estimator, specifically crafted for a broad spectrum of causal contrasts beyond CATE and CRR. This efficient estimator is both asymptotically equivalent to the oracle-efficient one-step estimator—demonstrating robustness and practical applicability—even in the presence of potential pathologies arising from misspecified nuisance functions.

From an empirical standpoint, experiments exploring CATE estimation across varying complexities of treatment overlap demonstrated that EP-learner outperformed state-of-the-art methodologies, promoting greater predictive accuracy and stability. Similarly, evaluating log-CRR estimation showcased the flexibility and applicability of EP-learning, attaining competitive mean squared error performance even in scenarios with diminished treatment overlap.

Practical Implications and Future Directions

EP-learning is poised to offer substantial contributions to medical research and policy-making where causal inference facilitates critical decision-making processes. By improving estimation stability and accuracy, EP-learning could influence how statistical models are employed to substantiate treatment efficacy across diverse population subgroups. Looking forward, expanding EP-learning algorithms to address continuous treatments and longitudinal data scenarios presents an intriguing avenue for future research, potentially broadening the scope of its applicability in complex statistical modeling spheres.

Conclusion

The advent of EP-learning marks a significant methodological advancement in the estimation of causal treatment effects, combining the tangible benefits of plug-in strategies with sophisticated empirical risk minimization tactics. As open-source implementations, such as those provided in the R package hte3, become increasingly accessible, EP-learning holds the promise of enhancing both theoretical exploration and practical application in causal inference further.