ABSTRACT

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.

摘要

我们考虑多重插补数据的分析师需要整数值点估计和相关区间估计的设置，例如，对人口中具有某些特征的个体数量进行计数。即使每个完整数据集中的点估计是整数，多重插补点估计，即这些完整数据估计的平均值，也不能保证是整数。一种自然的方法是将标准多重插补点估计器四舍五入为整数。另一种看似自然的方法是使用完整数据点估计的中位数（当它们是整数时）。但是，这两种方法尚未进行比较；实际上，甚至不存在用于获得与完整数据点估计的中位数相关的多重插补推论的方法。在本文中，我们评估和比较这两种方法。在此过程中，我们推导出基于中值的多重插补点估计量的方差估计量，以及获得相关多重插补置信区间的方法。通过模拟研究，我们表明这两种方法都可以提供经过良好校准的覆盖率，并且具有相似的重复采样特性，因此对于该分析任务都很有用。