General targeted machine learning for modern causal mediation analysis (2408.14620v2)

Abstract: Causal mediation analyses investigate the mechanisms through which causes exert their effects, and are therefore central to scientific progress. The literature on the non-parametric definition and identification of mediational effects in rigourous causal models has grown significantly in recent years, and there has been important progress to address challenges in the interpretation and identification of such effects. Despite great progress in the causal inference front, statistical methodology for non-parametric estimation has lagged behind, with few or no methods available for tackling non-parametric estimation in the presence of multiple, continuous, or high-dimensional mediators. In this paper we show that the identification formulas for six popular non-parametric approaches to mediation analysis proposed in recent years can be recovered from just two statistical estimands. We leverage this finding to propose an all-purpose one-step estimation algorithm that can be coupled with machine learning in any mediation study that uses any of these six definitions of mediation. The estimators have desirable properties, such as $\sqrt{n}$-convergence and asymptotic normality. Estimating the first-order correction for the one-step estimator requires estimation of complex density ratios on the potentially high-dimensional mediators, a challenge that is solved using recent advancements in so-called Riesz learning. We illustrate the properties of our methods in a simulation study and illustrate its use on real data to estimate the extent to which pain management practices mediate the total effect of having a chronic pain disorder on opioid use disorder.

• The paper introduces a unified framework that derives identification formulas for multiple causal mediation effects from two fundamental statistical functionals.
• The authors propose a one-step machine learning algorithm using cross-fitting and Riesz learning to achieve consistent, efficient estimators in high-dimensional settings.
• Simulation studies and real-data applications validate the approach, showing reduced MSE and revealing significant mediation of pain management in opioid risk.

Essay: General Targeted Machine Learning for Modern Causal Mediation Analysis

The paper presented by Richard Liu, Nicholas T. Williams, Kara E. Rudolph, and Iván Díaz introduces a novel methodology for conducting non-parametric causal mediation analysis in complex settings. Causal mediation analysis is crucial for understanding the mechanisms through which an exposure affects an outcome, which in turn informs effective intervention strategies. Traditional methods for causal mediation often make restrictive assumptions that can lead to biased estimates or may not be applicable in high-dimensional settings with multiple mediators. This paper addresses these limitations by proposing general, machine learning-based estimators for six popular causal mediation parameters, underpinned by robust theoretical guarantees and adaptable to high-dimensional data.

Key Contributions

This paper makes several pivotal contributions to the field of causal mediation analysis:

1. Unified Framework: It demonstrates that the identification formulas for six well-known non-parametric mediation approaches—natural direct and indirect effects (NDE/NIE), randomized interventional direct and indirect effects (RIDE/RIIE), separable effects (SE), organic direct and indirect effects (ODE/OIE), recanting twin effects (RT), and decision-theoretic effects (DTDE/DTIE)—can be derived from just two fundamental statistical functionals, $\psi^N$ and $\psi^R$. This unification simplifies the estimation process and broadens the applicability of mediation analysis.
2. One-Step Machine Learning Algorithm: Leveraging the unified identification formulas, the authors propose an all-purpose, one-step estimation algorithm that integrates machine learning for flexible model fitting. The estimators are designed to handle high-dimensional mediators and confounders while retaining desirable statistical properties, such as $\sqrt{n}$-consistency and asymptotic normality.
3. Riesz Learning: To address estimation challenges involving complex density ratios, the paper employs an innovative approach known as Riesz learning. This method sidesteps the need for direct density estimation by utilizing the Riesz representation theorem, thus facilitating the application of modern machine learning techniques.
4. Cross-Fitting for Bias Reduction: The paper employs cross-fitting to mitigate the potential biases introduced by flexible machine learning models, thereby improving the robustness and accuracy of the resulting estimators.
5. Theoretical Guarantees: The authors provide rigorous semi-parametric efficiency theory for the proposed estimators, including first-order von Mises expansions and efficiency bounds. This theoretical foundation ensures that the estimators achieve minimum variance among all unbiased estimators in the non-parametric model.

Numerical Simulations and Practical Implications

The paper includes comprehensive simulation studies to validate the performance of the proposed estimators. Key metrics such as bias, mean squared error (MSE), and coverage probability demonstrate that the estimators exhibit robust performance across varying sample sizes. The consistency in reducing MSE with increasing sample size illustrates the practical utility of the estimators.

Real-World Application

The authors apply their methodology to a real-world dataset to investigate the mediation effects of pain management practices on the risk of opioid use disorder (OUD) among Medicaid beneficiaries. The analysis reveals that approximately 80% of the total effect of having a chronic pain condition on the risk of OUD is mediated through the pathway involving pain management practices ($A \rightarrow M \rightarrow Y$). This empirical finding highlights the potential of the proposed methodological framework to uncover nuanced mediation mechanisms in complex, high-dimensional settings.

Future Research Directions

The methodologies and findings in this paper open several avenues for future research:

1. Extension to Longitudinal Data: While the current framework focuses on cross-sectional data, extending these methods to longitudinal settings would be valuable for understanding dynamic mediation mechanisms over time.
2. Application to Various Scientific Fields: The adaptability of the proposed methods to high-dimensional data makes them suitable for applications in genomics, neuroscience, and other fields where complex mediating mechanisms are prevalent.
3. Integration with Causal Discovery: Combining these mediation analysis techniques with causal discovery algorithms could further enhance the understanding of causal structures in observational data.

Conclusion

This paper makes significant strides in the field of causal mediation analysis by providing a unified, flexible, and theoretically sound framework for non-parametric estimation. The use of machine learning, particularly in the context of high-dimensional mediators and confounders, addresses key limitations of existing methods and paves the way for more accurate and interpretable causal mediation analyses in diverse scientific applications. The practical implications and robust performance of the proposed estimators underscore their potential to advance both theoretical and applied research in causal inference.