Journal
STATISTICAL METHODS IN MEDICAL RESEARCH
Volume 28, Issue 7, Pages 2049-2068Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/0962280217743777
Keywords
Asymptotic bias; causal inference; doubly robust; efficiency; estimating function; inverse probability weighting; measurement error; misclassification
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada
- Canadian Institutes of Health Research (CIHR) Drug Safety and Effectiveness Network
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Inverse probability weighting estimation has been popularly used to consistently estimate the average treatment effect. Its validity, however, is challenged by the presence of error-prone variables. In this paper, we explore the inverse probability weighting estimation with mismeasured outcome variables. We study the impact of measurement error for both continuous and discrete outcome variables and reveal interesting consequences of the naive analysis which ignores measurement error. When a continuous outcome variable is mismeasured under an additive measurement error model, the naive analysis may still yield a consistent estimator; when the outcome is binary, we derive the asymptotic bias in a closed-form. Furthermore, we develop consistent estimation procedures for practical scenarios where either validation data or replicates are available. With validation data, we propose an efficient method for estimation of average treatment effect; the efficiency gain is substantial relative to usual methods of using validation data. To provide protection against model misspecification, we further propose a doubly robust estimator which is consistent even when either the treatment model or the outcome model is misspecified. Simulation studies are reported to assess the performance of the proposed methods. An application to a smoking cessation dataset is presented.
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