Inverse probability weighted estimates are widely used in applications where data are missing due to nonresponse or censoring and in the estimation of causal effects from observational studies. The current estimators rely on ignorability assumptions for response indicators or treatment assignment, and outcomes, conditional on observed covariates which are assumed to be measured without error. However, measurement error is common in variables collected for many applications. For example, in studies of educational interventions, student achievement as measured by standardized tests is almost always used as the key covariate for removing hidden biases but standardized test scores often have substantial measurement errors for many students. The authors provide several expressions for a weighting function that can yield a consistent estimator for population means using incomplete data and covariates measured with error.
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