Recursive partitioning for heterogeneous causal effects
Susan Athey,Guido W. Imbens +1 more
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This paper provides a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects, and proposes an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation.Abstract:
In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without “sparsity” assumptions. We propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7–22%.read more
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Abstract: Precision medicine seeks to identify the optimal treatment for each individual based on his or her unique features. This invariably involves some form of estimation of causal effects for different patient subgroups to determine the treatment that leads to superior outcomes. Implementing methods to estimate causal effects in modern large and rich data sources such as electronic medical records (EMR), however, still faces challenges as information on patients is imperfectly captured in the observed data. In this work, we propose approaches to address some of the primary issues encountered in estimating causal effects in these pragmatic settings. In Chapter 1, we consider estimating average treatment effects (ATE) in observational data where the number of covariates is not small relative to the sample size. We develop a double-index propensity score (DiPS) obtained by smoothing treatment over linear predictors for the covariates from initial working parametric propensity score (PS) and outcome models fit with regularization. We show that an inverse probability weighting (IPW) estimator based on DiPS maintains the doubly-robustness and local semiparametric efficiency properties of the usual doubly-robust estimator and achieves further gains in robustness and efficiency under model misspecification. Simulations demonstrate the benefit of the approach in finite samples, and the method is illustrated by applications estimating the effects of statins on colorectal cancer risk and smoking on C-reactive protein. In Chapter 2, we extend the work from Chapter 1 to allow for incorporation of a large set of unlabeled data. This arises in EMR data when chart review is performed to ascertain gold-standard outcomes in case outcomes of interest are not directly observed. We frame the problem in a semi-supervised learning setting, where a small set of observations
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