Inference with imputed conditional means

In this article we present analytic techniques for inference from a dataset in which missing values have been replaced by predictive means derived fro m an imputation model. The derivations are based on asymptotic expansions o f point estimators and their associated variance estimators, and the result ing formulas can be thought of as first-order approximations to standard mu ltiple-imputation procedures with an infinite number of imputations for the missing values. Our method, where applicable. may require substantially le ss computational effort than creating and managing a multiply imputed datab ase; moreover, the resulting inferences can be more precise than those deri ved from multiple imputation, because they do not rely on simulation. Our t echniques use components of the standard complete-data analysis, along with two summary measures from the fitted imputation model. If the imputation a nd analysis phases are carried out by the same person or organization, then the method provides a quick assessment of the variability due to missing d ata. If a data producer is supplying the imputed data set to outside analys ts, then the necessary summary measures could be supplied to the analysts, enabling them to apply the method themselves. We emphasize situations with lid samples, univariate missing data, and complete-data point estimators th at are smooth functions uf means, but also discuss extensions to more compl icated situations. We illustrate properties of our methods in several examp les, including an application to a large dataset on fatal accidents maintai ned by the National Highway Traffic Safety Administration.