Rotnitzky A, Robins J
Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA.
Stat Med. 1997;16(1-3):81-102. doi: 10.1002/(sici)1097-0258(19970115)16:1<81::aid-sim473>3.0.co;2-0.
In this article we consider the problem of making inferences about the parameter beta zero indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables (outcome or covariates) are missing for some study subjects and the probability of non-response depends upon both observed and unobserved data values, that is, non-response is non-ignorable. We propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal (CAN) for estimating beta zero when the non-response probabilities can be parametrically modelled and a CAN estimator exists. The proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration. We show that the asymptotic variance of the optimal estimator in our class attains the semi-parametric variance bound for the model. In some models, no CAN estimator of beta zero exists. We provide a general algorithm for determining when CAN estimators of beta zero exist. Our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular, asymptotically linear estimators in an arbitrary semi-parametric model with non-ignorable non-response in which the probability of observing complete data is bounded away from zero and the non-response probabilities can be parametrically modelled.
在本文中，我们考虑这样一个问题：当某些研究对象的一部分变量（结果变量或协变量）缺失，且无应答概率取决于观测到的数据值和未观测到的数据值（即无应答不可忽略）时，如何根据给定回归变量向量对结果的条件均值进行关于参数β零的推断。我们提出了一类新的删失逆概率加权估计量，当无应答概率可以进行参数建模且存在一个一致渐近正态（CAN）估计量时，这类估计量对于估计β零是一致且渐近正态的。所提出的估计量不需要完全指定似然函数，其计算也不需要数值积分。我们表明，我们这类中的最优估计量的渐近方差达到了该模型的半参数方差界。在某些模型中，不存在β零的CAN估计量。我们提供了一种通用算法来确定何时存在β零的CAN估计量。我们的结果是在将本文中描述的关于任意半参数模型中常规渐近线性估计量的有效得分和影响函数的一般表示进行特殊化之后得出的，该半参数模型具有不可忽略的无应答，其中观测到完整数据的概率有界且远离零，且无应答概率可以进行参数建模。
