McCaffrey Daniel F, Lockwood J R, Setodji Claude M
RAND Corporation, 4570 Fifth Avenue, Suite 600, Pittsburgh, Pennsylvania, U.S.A.
Biometrika. 2013;100(3):671-680. doi: 10.1093/biomet/ast022.
Inverse probability-weighted estimators are widely used in applications where data are missing due to nonresponse or censoring and in the estimation of causal effects from observational studies. Current estimators rely on ignorability assumptions for response indicators or treatment assignment and outcomes being conditional on observed covariates which are assumed to be measured without error. However, measurement error is common for the variables collected in 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 may have substantial measurement errors. We provide several expressions for a weighting function that can yield a consistent estimator for population means using incomplete data and covariates measured with error. We propose a method to estimate the weighting function from data. The results of a simulation study show that the estimator is consistent and has no bias and small variance.
逆概率加权估计器在因无应答或删失导致数据缺失的应用中以及在观测研究的因果效应估计中被广泛使用。当前的估计器依赖于响应指标或处理分配的可忽略性假设，以及结果以观测协变量为条件，而这些协变量被假定为无误差测量。然而，测量误差在许多应用中收集的变量中很常见。例如，在教育干预研究中，几乎总是使用标准化测试衡量的学生成绩作为消除隐藏偏差的关键协变量，但标准化测试分数可能存在大量测量误差。我们给出了一个加权函数的几种表达式，该函数可以使用不完整数据和有测量误差的协变量得出总体均值的一致估计器。我们提出了一种从数据中估计加权函数的方法。模拟研究结果表明，该估计器是一致的，无偏差且方差较小。
