Abstract:
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The effect of treatment on the treated is a common parameter of interest in causal inference. Traditional approaches break down when some confounders are subject to missingness or measurement error. For completely missing confounders, external data, with more detailed confounding information, is often incorporated into the main study data to help mitigate bias. It is common to control for the measured confounding by using propensity scores. Some existing methods consider the propensity score to be mismeasured and proceed by adapting classical measurement error techniques. However, these new methods require strong assumptions about the missingness mechanism and measurement error model. We develop a novel approach which entails constructing a modified propensity score which depends only on fully observed covariates and the counterfactual outcome when unexposed and which, by virtue of being observed for all individuals in the sample, is likely to yield more efficient estimates than standard inverse probability weighting. The approach is universal in the sense that it applies virtually to any scale one routinely evaluates the effect of treatment on the treated.
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