Abstract:
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Missing data and confounding are two problems researchers face in observational studies for comparative effectiveness. Williamson et al (2012) recently proposed a unified approach to handle both issues concurrently using a multiply-robust (MR) methodology for missing confounder information. We show that while their approach is MR in theory, there are implicit assumptions regarding model congeniality that are unlikely to hold in practice, which implies their approach will in fact fail to be multiply robust under a standard parametrization. To address this, we propose an alternative transparent parametrization of the likelihood function, which makes explicit model dependencies between various nuisance functions needed to evaluate the MR efficient score. The proposed method is genuinely doubly-robust (DR) in that it is consistent and asymptotic normal if one of two sets of modeling assumptions holds, and we establish that in a sense, this is the best one can do in this framework. In addition, while MR remains theoretically possible, in practice the property will not hold exactly.
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