Recursive Partitioning for Heterogeneous Causal Effects (1504.01132v3)

Abstract: In this paper we study the problems of estimating heterogeneity in causal effects in experimental or observational studies and conducting inference about the magnitude of the differences in treatment effects across subsets of the population. In applications, our method provides a data-driven approach to determine which subpopulations have large or small treatment effects and to test hypotheses about the differences in these effects. For experiments, our method allows researchers to identify heterogeneity in treatment effects that was not specified in a pre-analysis plan, without concern about invalidating inference due to multiple testing. In most of the literature on supervised machine learning (e.g. regression trees, random forests, LASSO, etc.), the goal is to build a model of the relationship between a unit's attributes and an observed outcome. A prominent role in these methods is played by cross-validation which compares predictions to actual outcomes in test samples, in order to select the level of complexity of the model that provides the best predictive power. Our method is closely related, but it differs in that it is tailored for predicting causal effects of a treatment rather than a unit's outcome. The challenge is that the "ground truth" for a causal effect is not observed for any individual unit: we observe the unit with the treatment, or without the treatment, but not both at the same time. Thus, it is not obvious how to use cross-validation to determine whether a causal effect has been accurately predicted. We propose several novel cross-validation criteria for this problem and demonstrate through simulations the conditions under which they perform better than standard methods for the problem of causal effects. We then apply the method to a large-scale field experiment re-ranking results on a search engine.

• The paper introduces an honest recursive partitioning approach to estimate heterogeneous treatment effects while ensuring unbiased inference.
• It modifies traditional regression trees by splitting the sample into distinct groups to mitigate overfitting and enhance accuracy.
• Simulation studies confirm the method yields valid confidence intervals and outperforms alternative estimators in complex scenarios.

Recursive Partitioning for Heterogeneous Causal Effects

The paper "Recursive Partitioning for Heterogeneous Causal Effects" by Susan Athey and Guido W. Imbens presents a methodology for estimating and inferring heterogeneity in causal effects within both experimental and observational studies. The proposed approach hinges on partitioning the sample space into subpopulations that exhibit different magnitudes of treatment effects. This methodology leverages a variant of regression trees, modified to focus on estimating heterogeneous treatment effects while ensuring the integrity of statistical inference.

Overview of Methods

The authors introduce an "honest" estimation approach whereby the dataset is divided into two parts: one part for constructing the partitions via recursive partitioning, and another part for estimating the treatment effects for each partition. This honest approach mitigates the bias usually introduced by adaptive methods that use the same sample for both partitioning and estimation.

Key elements of the methodology are as follows:

1. Partitioning Based on Treatment Effects: The proposed approach modifies classical regression tree algorithms to optimize for treatment effect heterogeneity rather than outcome predictivity. The model selection criteria are designed to improve the prediction of treatment effects conditional on covariates while accounting for changes in variance due to sample partitioning.
2. Honest Estimation: Treatment effects are estimated using a sample different from the one used to construct the partition. This sample-splitting strategy ensures that the parameters within each partition remain unbiased, as if the partitions were given exogenously.
3. Adjusted Splitting and Cross-Validation Criteria: The criteria for both splitting operations and cross-validation cycles are adjusted to account for honest estimation. This includes focusing the criteria on minimizing mean-squared error (MSE) of the treatment effects rather than outcomes and adapting cross-validation to accommodate the lack of "ground truth" in causal effects.

Key Contributions and Findings

Through a series of simulation studies, the authors demonstrate:

• Performance in Different Data Configurations: The honest estimation approach results in better coverage of confidence intervals for treatment effects. The method achieves nominal coverage rates even in sample sizes with numerous covariates, surpassing traditional adaptive estimations that tend to suffer from overfitting.
• Comparative Analysis: The paper compares the proposed causal tree (CT) estimator with other methods, including the Transformed Outcome Tree (TOT), Fit-based Tree (F), and Squared T-Statistic Tree (TS). While TOT methods were found to be straightforward for application, they showed inadequacies when the variance of outcomes was minimal. The Fit-based Criterion performed suboptimally due to its propensity to favor splits that improve outcome prediction over those that enhance causal inference. The squared t-statistic criterion, while effective in settings with aligned treatment and outcome covariates, failed in complex scenarios.

Implications

The methods proposed in this paper have significant theoretical and practical implications:

• Theoretical Impact: The honest estimation framework sets a robust standard for statistical methods used in heterogeneous treatment effect estimation. It challenges the conventional practice of adaptive estimation by highlighting the benefits of sample-splitting, particularly in reducing overfitting and ensuring unbiased parameter estimates.
• Practical Applications: Practitioners in fields ranging from clinical trials to economics can utilize these robust methods to uncover treatment effect heterogeneity with valid statistical inference. The ability to identify subpopulations with varying treatment responses can lead to more tailored and effective intervention strategies.

Future Directions

The following areas could benefit from further exploration:

• Model Complexity and Computational Efficiency: While sample splitting reduces estimator bias, it also decreases the effective sample size, potentially affecting the power of partitions. Developing computationally efficient algorithms that maintain the robustness of honest estimation would be beneficial.
• Extension to High-Dimensional Covariate Spaces: Adapting these methods to handle higher-dimensional covariate spaces with an even larger set of covariates relative to observations is also an area ripe for exploration.
• Applications in Dynamic Treatment Regimes: Extending this methodology to settings involving time-varying treatments or sequential decision-making frameworks can broaden its applicability.

In conclusion, Athey and Imbens provide a rigorous and principled approach to estimating heterogeneous causal effects using recursive partitioning, which stands to significantly enhance the reliability and informativeness of empirical findings in experimental and observational studies. The proposed methods balance the trade-offs between bias reduction and sample size efficiency, paving the way for more accurate and interpretable causal inferences.