Multiple Imputation Inference with Integer-Valued Point Estimates

We consider settings where an analyst of multiply imputed data desires an integer-valued point estimate and an associated interval estimate, for example, a count of the number of individuals with certain characteristics in a population. Even when the point estimate in each completed dataset is an integer, the multiple imputation point estimator, that is, the average of these completed-data estimators, is not guaranteed to be an integer. One natural approach is to round the standard multiple imputation point estimator to an integer. Another seemingly natural approach is to use the median of the completed-data point estimates (when they are integers). However, these two approaches have not been compared; indeed, methods for obtaining multiple imputation inferences associated with the median of the completed-data point estimates do not even exist. In this article, we evaluate and compare these two approaches. In doing so, we derive an estimator of the variance of the median-based multiple imputation point estimator, as well as a method for obtaining associated multiple imputation confidence intervals. Using simulation studies, we show that both methods can offer well-calibrated coverage rates and have similar repeated sampling properties, and hence are both useful for this analysis task.