Liang Hua, Wang Suojin, Carroll Raymond J
Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York 14642, U.S.A.
Biometrika. 2007 Mar 1;94(1):185-198. doi: 10.1093/biomet/asm010.
We consider partially linear models of the form Y = X(T)beta + nu(Z) + epsilon when the response variable Y is sometimes missing with missingness probability pi depending on (X, Z), and the covariate X is measured with error, where nu(z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest beta, as well as for the population mean E(Y). The resulting estimators are shown to be consistent and asymptotically normal under general assumptions. To construct a confidence region for beta, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. The proposed methods are applied to an AIDS clinical trial dataset. A simulation study is also reported.
当响应变量Y有时会以取决于(X, Z)的缺失概率π缺失，且协变量X存在测量误差时，我们考虑形如Y = X(T)β + ν(Z) + ε的部分线性模型，其中ν(z)是一个未指定的光滑函数。因此，缺失结构是非随机缺失，而不是通常的随机缺失。我们为感兴趣的参数β以及总体均值E(Y)提出了一类半参数估计量。在一般假设下，所得估计量被证明是一致的且渐近正态的。为了构建β的置信区域，我们还提出了一个基于经验似然的统计量，它被证明渐近地服从卡方分布。所提出的方法应用于一个艾滋病临床试验数据集。还报告了一项模拟研究。
