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Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross-fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our method can be used to optimize either binary treatments or infinitesimal nudges to continuous treatments, and can leverage observational data where causal effects are identified using a variety of strategies, including selection on observables and instrumental variables. Given a doubly robust estimator of the causal effect of assigning everyone to treatment, we develop an algorithm for choosing whom to treat, and establish strong guarantees for the asymptotic utilitarian regret of the resulting policy.

We consider integrating a non-probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly robust estimator of the finite population mean and re-estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first-step selection error and renders the doubly robust estimator root n consistent if either the sampling probability or the outcome model is correctly specified.

We consider methods for causal inference in randomized trials nested within cohorts of trial-eligible individuals, including those who are not randomized. We show how baseline covariate data from the entire cohort, and treatment and outcome data only from randomized individuals, can be used to identify potential (counterfactual) outcome means and average treatment effects in the target population of all eligible individuals. We review identifiability conditions, propose estimators, and assess the estimators' finite-sample performance in simulation studies. As an illustration, we apply the estimators in a trial nested within a cohort of trial-eligible individuals to compare coronary artery bypass grafting surgery plus medical therapy vs. medical therapy alone for chronic coronary artery disease.

Standard methods for inference about direct and indirect effects require stringent no-unmeasured-confounding assumptions which often fail to hold in practice, particularly in observational studies. The goal of the paper is to introduce a new form of indirect effect, the population intervention indirect effect, that can be non-parametrically identified in the presence of an unmeasured common cause of exposure and outcome. This new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value. The population intervention indirect effect is in fact the indirect component of the population intervention effect, introduced by Hubbard and Van der Laan. Interestingly, our identification criterion generalizes Judea Pearl’s front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable. For inference, we develop both parametric and semiparametric methods, including a novel doubly robust semiparametric locally efficient estimator, that perform very well in simulation studies. Finally, the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in Tanzania.

Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root- n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance. It moreover improves the stability of the weights in those doubly robust estimators which invoke inverse probability weighting. Simulation studies confirm the desirable finite-sample performance of the proposed estimators. Supplementary materials for this article are available online.

Precision medicine is a framework that adapts treatment strategies to a patient’s individual characteristics and provides helpful clinical decision support. Existing research has been extended to various situations but high-dimensional data have not yet been fully incorporated into the paradigm. We propose a new precision medicine approach called deep doubly robust outcome weighted learning (DDROWL) that can handle big and complex data. This is a machine learning tool that directly estimates the optimal decision rule and achieves the best of three worlds: deep learning, double robustness, and residual weighted learning. Two architectures have been implemented in the proposed method, a fully-connected feedforward neural network and the Deep Kernel Learning model, a Gaussian process with deep learning-filtered inputs. We compare and discuss the performance and limitation of different methods through a range of simulations. Using longitudinal and brain imaging data from patients with Alzheimer’s disease, we demonstrate the application of the proposed method in real-world clinical practice. With the implementation of deep learning, the proposed method can expand the influence of precision medicine to high-dimensional abundant data with greater flexibility and computational power.

A dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient's history. Q-and A-learning are two main approaches for estimating the optimal regime, i.e., that yielding the most beneficial outcome in the patient population, using data from a clinical trial or observational study. Q-learning requires postulated regression models for the outcome, while A-learning involves models for that part of the outcome regression representing treatment contrasts and for treatment assignment. We propose an alternative to Q-and A-learning that maximizes a doubly robust augmented inverse probability weighted estimator for population mean outcome over a restricted class of regimes. Simulations demonstrate the method's performance and robustness to model misspecification, which is a key concern.

This commentary deals with issues related to the article by Chen, Zeng, and Kosorok. We present several potential modifications of the outcome weighted learning approach. Those modifications are based on truncated l 2 loss. One advantage of l 2 loss is that it is differentiable everywhere, which makes it more stable and computationally more tractable.

When generalizing inferences from a randomized trial to a target population, two classes of estimators are used: g-formula estimators that depend on modeling the conditional outcome mean among trial participants and inverse probability (IP) weighting estimators that depend onmodeling the probability of participation in the trial. In this article, we take a closer look at the relation between these two classes of estimators. We propose IP weighting estimators that combine models for the probability of trial participation and the probability of treatment among trial participants. We show that, when all models are estimated using nonparametric frequency methods, these estimators are finite-sample equivalent to the g-formula estimator. We argue for the use of augmented IP weighting (doubly robust) generalizability estimators when nonparametric estimation is infeasible due to the curse of dimensionality, and examine the finite-sample behavior of different estimators using parametric models in a simulation study.