Augmented Inverse Probability Weighting and the Double Robustness Property

This article discusses the augmented inverse propensity weighted (AIPW) estimator as an estimator for average treatment effects. The AIPW combines both the properties of the regression-based estimator and the inverse probability weighted (IPW) estimator and is therefore a “doubly robust” method in that it requires only either the propensity or outcome model to be correctly specified but not both. Even though this estimator has been known for years, it is rarely used in practice. After explaining the estimator and proving the double robustness property, I conduct a simulation study to compare the AIPW efficiency with IPW and regression under different scenarios of misspecification. In 2 real-world examples, I provide a step-by-step guide on implementing the AIPW estimator in practice. I show that it is an easily usable method that extends the IPW to reduce variability and improve estimation accuracy. [Box: see text]

Double/Debiased Machine Learning for Logistic Partially Linear Model

We propose double/debiased machine learning approaches to infer parametric component of a logistic partially linear model. Our framework is based on a Neyman orthogonal score equation consisting two nuisance models for nonparametric component of the logistic model and conditional mean of the exposure with among the control group. To estimate the nuisance models, we separately consider the use of high dimensional (HD) sparse regression and (nonparametric) machine learning (ML) methods. In the HD case, we derive certain moment equations to calibrate the first order bias of the nuisance models, which preserves model double robustness property. In the ML case, we handle the non-linearity of the logit link through a novel and easy-to-implement “full model refitting” procedure. We evaluate our methods through simulation and apply them in assessing the effect of the emergency contraceptive (EC) pill on early gestation and new births based on a 2008 policy reform in Chile.

A Falsifiability Characterization of Double Robustness Through Logical Operators

We address the characterization of problems in which a consistent estimator exists in a union of two models, also termed as a doubly robust estimator. Such estimators are important in missing information, including causal inference problems. Existing characterizations, based on the semiparametric theory of projections, have seen sufficient progress, but can still leave one’s understanding less than satisfied as to when and especially why such estimation works. We explore here a different, explanatory characterization – an exegesis based on logical operators. We show that double robustness exists if and only if we can produce consistent estimators for each contributing model based on an “AND” estimator, i. e., an estimator whose consistency generally needs both models to be correct. We show how this characterization explains double robustness through falsifiability.

Model validation and selection for personalized medicine using dynamic-weighted ordinary least squares

Model assessment is a standard component of statistical analysis, but it has received relatively little attention within the dynamic treatment regime literature. In this paper, we focus on the dynamic-weighted ordinary least squares approach to optimal dynamic treatment regime estimation, introducing how its double-robustness property may be leveraged for model assessment, and how quasilikelihood may be used for model selection. These ideas are demonstrated through simulation studies, as well as through application to data from the sequenced treatment alternatives to relieve depression study.

A GENERAL DOUBLE ROBUSTNESS RESULT FOR ESTIMATING AVERAGE TREATMENT EFFECTS

In this paper we study doubly robust estimators of various average and quantile treatment effects under unconfoundedness; we also consider an application to a setting with an instrumental variable. We unify and extend much of the recent literature by providing a very general identification result which covers binary and multi-valued treatments; unnormalized and normalized weighting; and both inverse-probability weighted (IPW) and doubly robust estimators. We also allow for subpopulation-specific average treatment effects where subpopulations can be based on covariate values in an arbitrary way. Similar to Wooldridge (2007), we then discuss estimation of the conditional mean using quasi-log likelihoods (QLL) from the linear exponential family.