Statistical inference for data‐adaptive doubly robust estimators with survival outcomes

Abstract Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

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Doubly robust nonparametric inference on the average treatment effect

Biometrika ◽

10.1093/biomet/asx053 ◽

2017 ◽

Vol 104 (4) ◽

pp. 863-880 ◽

Cited By ~ 22

Author(s):

D Benkeser ◽

M Carone ◽

M J Van Der Laan ◽

P B Gilbert

Keyword(s):

Treatment Effect ◽

Theoretical Study ◽

Average Treatment Effect ◽

Robust Inference ◽

Nuisance Parameters ◽

Robust Estimators ◽

Average Treatment ◽

Adaptive Estimators ◽

Data Adaptive ◽

Doubly Robust

Summary Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

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314Data-adaptive methods for high-dimensional mediation analysis: Application to a randomised trial of tuberculosis vaccination

International Journal of Epidemiology ◽

10.1093/ije/dyab168.456 ◽

2021 ◽

Vol 50 (Supplement_1) ◽

Author(s):

Margarita Moreno-Betancur ◽

Nicole L Messina ◽

Kaya Gardiner ◽

Nigel Curtis ◽

Stijn Vansteelandt

Keyword(s):

Machine Learning ◽

Statistical Inference ◽

Mediation Analysis ◽

Learning Algorithms ◽

Adaptive Methods ◽

Machine Learning Algorithms ◽

High Dimensional ◽

Data Adaptive ◽

Randomised Controlled ◽

Doubly Robust

Abstract Focus of Presentation Statistical methods for causal mediation analysis are useful for understanding the pathways by which a certain treatment or exposure impacts health outcomes. Existing methods necessitate modelling of the distribution of the mediators, which quickly becomes infeasible when mediators are high-dimensional (e.g., biomarkers). We propose novel data-adaptive methods for estimating the indirect effect of a randomised treatment that acts via a pathway represented by a high-dimensional set of measurements. This work was motivated by the Melbourne Infant Study: BCG for Allergy and Infection Reduction (MIS BAIR), a randomised controlled trial investigating the effect of neonatal tuberculosis vaccination on clinical allergy and infection outcomes, and its mechanisms of action. Findings The proposed methods are doubly robust, which allows us to achieve (uniformly) valid statistical inference, even when machine learning algorithms are used for the two required models. We illustrate these in the context of the MIS BAIR study, investigating the mediating role of immune pathways represented by a high-dimensional vector of cytokine responses under various stimulants. We confirm adequate performance of the proposed methods in an extensive simulation study. Conclusions/Implications The proposed methods provide a feasible and flexible analytic strategy for examining high-dimensional mediators in randomised controlled trials. Key messages Data-adaptive methods for mediation analysis are desirable in the context of high-dimensional mediators, such as biomarkers. We propose novel doubly robust methods, which enable valid statistical inference when using machine learning algorithms for estimation.

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Causal inference for recurrent event data using pseudo-observations

Biostatistics ◽

10.1093/biostatistics/kxaa020 ◽

2020 ◽

Author(s):

Chien-Lin Su ◽

Robert W Platt ◽

Jean-François Plante

Keyword(s):

Goodness Of Fit ◽

Variance Estimation ◽

Recurrent Event ◽

Event Data ◽

Robust Estimators ◽

Recurrent Event Data ◽

Finite Sample ◽

Data Set ◽

Asymptotically Normal ◽

Doubly Robust

Summary Recurrent event data are commonly encountered in observational studies where each subject may experience a particular event repeatedly over time. In this article, we aim to compare cumulative rate functions (CRFs) of two groups when treatment assignment may depend on the unbalanced distribution of confounders. Several estimators based on pseudo-observations are proposed to adjust for the confounding effects, namely inverse probability of treatment weighting estimator, regression model-based estimators, and doubly robust estimators. The proposed marginal regression estimator and doubly robust estimators based on pseudo-observations are shown to be consistent and asymptotically normal. A bootstrap approach is proposed for the variance estimation of the proposed estimators. Model diagnostic plots of residuals are presented to assess the goodness-of-fit for the proposed regression models. A family of adjusted two-sample pseudo-score tests is proposed to compare two CRFs. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a hospital readmission data set.

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“Robust-Squared” Imputation Models Using Bart

Journal of Survey Statistics and Methodology ◽

10.1093/jssam/smz002 ◽

2019 ◽

Vol 7 (4) ◽

pp. 465-497

Author(s):

Yaoyuan V Tan ◽

Carol A C Flannagan ◽

Michael R Elliott

Keyword(s):

Model Misspecification ◽

Blood Alcohol Concentration ◽

Alcohol Concentration ◽

Penalized Splines ◽

Robust Estimator ◽

Robust Estimators ◽

Sampling System ◽

Additive Regression ◽

Doubly Robust ◽

Augmented Inverse Probability Weighting

Abstract Examples of “doubly robust” estimators for missing data include augmented inverse probability weighting (AIPWT) and penalized splines of propensity prediction (PSPP). Doubly robust estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, doubly robust estimators can perform poorly when modest misspecification is present in both models. Here we consider extensions of the AIPWT and PSPP that use Bayesian additive regression trees (BART) to provide highly robust propensity and mean model estimation. We term these “robust-squared” in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the doubly robust estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset and missing Blood Alcohol Concentration values from the 2015 Fatality Analysis Reporting System dataset. We found that BART, applied to PSPP and AIPWT, provides a more robust estimate compared with PSPP and AIPWT.

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A comparison of doubly robust estimators of the mean with missing data

Journal of Statistical Computation and Simulation ◽

10.1080/00949655.2014.975226 ◽

2014 ◽

Vol 85 (16) ◽

pp. 3383-3403 ◽

Cited By ~ 2

Author(s):

Ye Yang ◽

Roderick Little

Keyword(s):

Missing Data ◽

Robust Estimators ◽

The Mean ◽

Doubly Robust

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Comment: Stabilizing the Doubly-Robust Estimators of the Average Treatment Effect under Positivity Violations

Statistical Science ◽

10.1214/20-sts774 ◽

2020 ◽

Vol 35 (3) ◽

pp. 503-510

Author(s):

Fan Li

Keyword(s):

Treatment Effect ◽

Average Treatment Effect ◽

Robust Estimators ◽

Average Treatment ◽

Doubly Robust

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Handling Missing Data in Instrumental Variable Methods for Causal Inference

Annual Review of Statistics and Its Application ◽

10.1146/annurev-statistics-031017-100353 ◽

2019 ◽

Vol 6 (1) ◽

pp. 125-148

Author(s):

Edward H. Kennedy ◽

Jacqueline A. Mauro ◽

Michael J. Daniels ◽

Natalie Burns ◽

Dylan S. Small

Keyword(s):

Longitudinal Study ◽

Instrumental Variable ◽

Propensity Scores ◽

Asymptotic Properties ◽

Missing At Random ◽

Robust Estimators ◽

Genotyping Platform ◽

Wisconsin Longitudinal Study ◽

Doubly Robust ◽

Nonparametric Efficiency

In instrumental variable studies, missing instrument data are very common. For example, in the Wisconsin Longitudinal Study, one can use genotype data as a Mendelian randomization–style instrument, but this information is often missing when subjects do not contribute saliva samples or when the genotyping platform output is ambiguous. Here we review missing at random assumptions one can use to identify instrumental variable causal effects, and discuss various approaches for estimation and inference. We consider likelihood-based methods, regression and weighting estimators, and doubly robust estimators. The likelihood-based methods yield the most precise inference and are optimal under the model assumptions, while the doubly robust estimators can attain the nonparametric efficiency bound while allowing flexible nonparametric estimation of nuisance functions (e.g., instrument propensity scores). The regression and weighting estimators can sometimes be easiest to describe and implement. Our main contribution is an extensive review of this wide array of estimators under varied missing-at-random assumptions, along with discussion of asymptotic properties and inferential tools. We also implement many of the estimators in an analysis of the Wisconsin Longitudinal Study, to study effects of impaired cognitive functioning on depression.

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