Analysis of semi-parametric regression models with non-ignorable non-response
Analysis of semi-parametric regression models with non-ignorable non-response
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DOI：
10.1002/(sici)1097-0258(19970115)16:1
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发表时间：
1997-01-15
影响因子：
2
通讯作者：
Robins, J
中科院分区：
文献类型：
--
作者：
Rotnitzky, A;Robins, J
在本文中，我们考虑当某些研究对象缺少变量子集（结果或协变量）时，对给定回归向量的结果的条件平均值进行索引的参数 beta(0) 进行推断的问题，并且无响应的概率取决于观察到的和未观察到的数据值，即，无响应是不可忽略的。我们提出了一类新的审查加权估计量的逆概率，它是一致的当无响应概率可以参数化建模并且存在 CAN 估计器时，渐近正态 (CAN) 用于估计 beta(0)。所提出的估计量不需要完全指定似然性，并且它们的计算不需要数值积分。我们证明了我们类中最优估计器的渐近方差达到了模型的半参数方差界。在某些模型中，不存在 beta(0) 的 CAN 估计器。我们提供了一个通用算法来确定 beta(0) 的 CAN 估计器何时存在。我们的结果是在专门描述文章中描述的有效得分和具有不可忽略的无响应的任意半参数模型中常规渐近线性估计量的影响函数的一般表示之后得出的，其中观察完整数据的概率远离零，并且可以对无响应概率进行参数建模。
In this article we consider the problem of making inferences about the parameter beta(0) 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(0) 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(0) exists. We provide a general algorithm for determining when CAN estimators of beta(0) 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.