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Doubly robust estimators of causal exposure effects with missing data in the outcome, exposure or a confounder

Authors

  • E.J. Williamson,

    Corresponding author
    1. Department of Epidemiology and Preventive Medicine, Monash University, Australia
    2. Centre for Molecular, Environmental, Genetic and Analytic Epidemiology, School of Population Health, University of Melbourne, Australia
    • Correspondence to: E. J. Williamson, Department of Epidemiology and Preventive Medicine, Monash University, The Alfred Centre, 99 Commercial Road, Melbourne, 3004 Victoria.

      E-mail: ewi@unimelb.edu.au

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  • A. Forbes,

    1. Department of Epidemiology and Preventive Medicine, Monash University, Australia
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  • R. Wolfe

    1. Department of Epidemiology and Preventive Medicine, Monash University, Australia
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  • Supporting information may be found in the online version of this article.

Abstract

We consider the estimation of the causal effect of a binary exposure on a continuous outcome. Confounding and missing data are both likely to occur in practice when observational data are used to estimate this causal effect. In dealing with each of these problems, model misspecification is likely to introduce bias. We present augmented inverse probability weighted (AIPW) estimators that account for both confounding and missing data, with the latter occurring in a single variable only. These estimators have an element of robustness to misspecification of the models used. Our estimators require two models to be specified to deal with confounding and two to deal with missing data. Only one of each of these models needs to be correctly specified. When either the outcome or the exposure of interest is missing, we derive explicit expressions for the AIPW estimator. When a confounder is missing, explicit derivation is complex, so we use a simple algorithm, which can be applied using standard statistical software, to obtain an approximation to the AIPW estimator. Copyright © 2012 John Wiley & Sons, Ltd.

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