Because the average treatment effect (ATE) measures the change in social welfare, even if positive, there is a risk of negative effect on, say, some 10% of the population. Assessing such risk is difficult, however, because any one individual treatment effect (ITE) is never observed, so the 10% worst-affected cannot be identified, whereas distributional treatment effects only compare the first deciles within each treatment group, which does not correspond to any 10% subpopulation. In this paper, we consider how to nonetheless assess this important risk measure, formalized as the conditional value at risk (CVaR) of the ITE distribution. We leverage the availability of pretreatment covariates and characterize the tightest possible upper and lower bounds on ITE-CVaR given by the covariate-conditional average treatment effect (CATE) function. We then proceed to study how to estimate these bounds efficiently from data and construct confidence intervals. This is challenging even in randomized experiments as it requires understanding the distribution of the unknown CATE function, which can be very complex if we use rich covariates to best control for heterogeneity. We develop a debiasing method that overcomes this and prove it enjoys favorable statistical properties even when CATE and other nuisances are estimated by black box machine learning or even inconsistently. Studying a hypothetical change to French job search counseling services, our bounds and inference demonstrate a small social benefit entails a negative impact on a substantial subpopulation. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the Division of Information and Intelligent Systems [Grant 1939704]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4819 .
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Robust and Agnostic Learning of Conditional Distributional Treatment Effects
The conditional average treatment effect (CATE) is the best measure of individual causal effects given baseline covariates. However, the CATE only captures the (conditional) average, and can overlook risks and tail events, which are important to treatment choice. In aggregate analyses, this is usually addressed by measuring the distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a class of problems that includes conditional quantile treatment effects, conditional super-quantile treatment effects, and conditional treatment effects on coherent risk measures given by f-divergences. Our method is based on constructing a special pseudo-outcome and regressing it on covariates using any regression learner. Our method is model-agnostic in that it can provide the best projection of CDTE onto the regression model class. Our method is robust in that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the behavior of our proposal in simulations, as well as in a case study of 401(k) eligibility effects on wealth.
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- Award ID(s):
- 1846210
- NSF-PAR ID:
- 10406744
- Date Published:
- Journal Name:
- Proceedings of the 26th International Conference on Artificial Intelligence and Statistics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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There is growing interest in estimating and analyzing heterogeneous treatment effects in experimental and observational studies. We describe a number of metaalgorithms that can take advantage of any supervised learning or regression method in machine learning and statistics to estimate the conditional average treatment effect (CATE) function. Metaalgorithms build on base algorithms—such as random forests (RFs), Bayesian additive regression trees (BARTs), or neural networks—to estimate the CATE, a function that the base algorithms are not designed to estimate directly. We introduce a metaalgorithm, the X-learner, that is provably efficient when the number of units in one treatment group is much larger than in the other and can exploit structural properties of the CATE function. For example, if the CATE function is linear and the response functions in treatment and control are Lipschitz-continuous, the X-learner can still achieve the parametric rate under regularity conditions. We then introduce versions of the X-learner that use RF and BART as base learners. In extensive simulation studies, the X-learner performs favorably, although none of the metalearners is uniformly the best. In two persuasion field experiments from political science, we demonstrate how our X-learner can be used to target treatment regimes and to shed light on underlying mechanisms. A software package is provided that implements our methods.
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When analyzing bivariate outcome data, it is often of scientific interest to measure and estimate the association between the bivariate outcomes. In the presence of influential covariates for one or both of the outcomes, conditional association measures can quantify the strength of association without the disturbance of the marginal covariate effects, to provide cleaner and less‐confounded insights into the bivariate association. In this work, we propose estimation and inferential procedures for assessing the conditional Kendall's tau coefficient given the covariates, by adopting the quantile regression and quantile copula framework to handle marginal covariate effects. The proposed method can flexibly accommodate right censoring and be readily applied to bivariate survival data. It also facilitates an estimator of the conditional concordance measure, namely, a conditional
index, where the unconditional index is commonly used to assess the predictive capacity for survival outcomes. The proposed method is flexible and robust and can be easily implemented using standard software. The method performed satisfactorily in extensive simulation studies with and without censoring. Application of our methods to two real‐life data examples demonstrates their desirable practical utility. -
We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, i.e., when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator takes the form of a weighted kernel estimator with weights that vary adversarially. We prove that our estimator is sharp in that it converges exactly to the tightest bounds possible on CATE when there may be unobserved confounders. Further, we study personalized decision rules derived from our estimator and prove that they achieve optimal minimax regret asymptotically. We assess our approach in a simulation study as well as demonstrate its application in the case of hormone replacement therapy by comparing conclusions from a real observational study and clinical trial.more » « less
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Abstract Cluster-randomized experiments are widely used due to their logistical convenience and policy relevance. To analyse them properly, we must address the fact that the treatment is assigned at the cluster level instead of the individual level. Standard analytic strategies are regressions based on individual data, cluster averages and cluster totals, which differ when the cluster sizes vary. These methods are often motivated by models with strong and unverifiable assumptions, and the choice among them can be subjective. Without any outcome modelling assumption, we evaluate these regression estimators and the associated robust standard errors from the design-based perspective where only the treatment assignment itself is random and controlled by the experimenter. We demonstrate that regression based on cluster averages targets a weighted average treatment effect, regression based on individual data is suboptimal in terms of efficiency and regression based on cluster totals is consistent and more efficient with a large number of clusters. We highlight the critical role of covariates in improving estimation efficiency and illustrate the efficiency gain via both simulation studies and data analysis. The asymptotic analysis also reveals the efficiency-robustness trade-off by comparing the properties of various estimators using data at different levels with and without covariate adjustment. Moreover, we show that the robust standard errors are convenient approximations to the true asymptotic standard errors under the design-based perspective. Our theory holds even when the outcome models are misspecified, so it is model-assisted rather than model-based. We also extend the theory to a wider class of weighted average treatment effects.
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Accepted Manuscript1.0
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