skip to main content


Title: Quasi-oracle estimation of heterogeneous treatment effects
Summary Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical applications, such as personalized medicine and optimal resource allocation. In this article we develop a general class of two-step algorithms for heterogeneous treatment effect estimation in observational studies. First, we estimate marginal effects and treatment propensities to form an objective function that isolates the causal component of the signal. Then, we optimize this data-adaptive objective function. The proposed approach has several advantages over existing methods. From a practical perspective, our method is flexible and easy to use: in both steps, any loss-minimization method can be employed, such as penalized regression, deep neural networks, or boosting; moreover, these methods can be fine-tuned by cross-validation. Meanwhile, in the case of penalized kernel regression, we show that our method has a quasi-oracle property. Even when the pilot estimates for marginal effects and treatment propensities are not particularly accurate, we achieve the same error bounds as an oracle with prior knowledge of these two nuisance components. We implement variants of our approach based on penalized regression, kernel ridge regression, and boosting in a variety of simulation set-ups, and observe promising performance relative to existing baselines.  more » « less
Award ID(s):
1916163
NSF-PAR ID:
10311702
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Biometrika
Volume:
108
Issue:
2
ISSN:
0006-3444
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. Root-n consistent and asymptotically normal estimation of the object of interest requires debiasing to reduce the effects of regularization and/or model selection on the object of interest. Debiasing is typically achieved by adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality. We implement an automatic debiasing procedure based on automatically learning the Riesz representation of the linear functional using Neural Nets and Random Forests. Our method only relies on black-box evaluation oracle access to the linear functional and does not require knowledge of its analytic form. We propose a multitasking Neural Net debiasing method with stochastic gradient descent minimization of a combined Riesz representer and regression loss, while sharing representation layers for the two functions. We also propose a Random Forest method which learns a locally linear representation of the Riesz function. Even though our method applies to arbitrary functionals, we experimentally find that it performs well compared to the state of art neural net based algorithm of Shi et al. (2019) for the case of the average treatment effect functional. We also evaluate our method on the problem of estimating average marginal effects with continuous treatments, using semi-synthetic data of gasoline price changes on gasoline demand. Code available at github.com/victor5as/RieszLearning. 
    more » « less
  2. Generalized linear mixed models are commonly used to describe relationships between correlated responses and covariates in medical research. In this paper, we propose a simple and easily implementable regularized estimation approach to select both fixed and random effects in generalized linear mixed model. Specifically, we propose to construct and optimize the objective functions using the confidence distributions of model parameters, as opposed to using the observed data likelihood functions, to perform effect selections. Two estimation methods are developed. The first one is to use the joint confidence distribution of model parameters to perform simultaneous fixed and random effect selections. The second method is to use the marginal confidence distributions of model parameters to perform the selections of fixed and random effects separately. With a proper choice of regularization parameters in the adaptive LASSO framework, we show the consistency and oracle properties of the proposed regularized estimators. Simulation studies have been conducted to assess the performance of the proposed estimators and demonstrate computational efficiency. Our method has also been applied to two longitudinal cancer studies to identify demographic and clinical factors associated with patient health outcomes after cancer therapies.

     
    more » « less
  3. Multi‐view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi‐view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced‐rank regression (iRRR), where each view has its own low‐rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non‐Gaussian and incomplete data are discussed. Theoretically, we derive non‐asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso, and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group‐sparse and low‐rank methods and can achieve substantially faster convergence rate under realistic settings of multi‐view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods. 
    more » « less
  4. Abstract

    Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced-rank regression (iRRR), where each view has its own low-rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non-Gaussian and incomplete data are discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso, and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group-sparse and low-rank methods and can achieve substantially faster convergence rate under realistic settings of multi-view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods.

     
    more » « less
  5. We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Most existing methods for differential graph estimation are based on a lasso penalized loss function. In this paper, we analyze a log-sum penalized D-trace loss function approach for differential graph learning. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in estimation in high-dimensional settings is provided. We illustrate our approach using a numerical example where log-sum penalized D-trace loss significantly outperforms lasso-penalized D-trace loss as well as smoothly clipped absolute deviation (SCAD) penalized D-trace loss. 
    more » « less