Nonparametric and semiparametric models for missing covariates in parametric regression
Nonparametric and semiparametric models for missing covariates in parametric regression
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DOI：
10.1198/016214504000001727
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发表时间：
2004-12-01
影响因子：
3.7
通讯作者：
Chen, HY
中科院分区：
文献类型：
--
作者：
Chen, HY
在随机缺失假设下，研究了参数回归中缺失协变量问题的协变量建模的鲁棒性。对于一个简单的缺少协变量模式，提出了非参数协变量模型，并证明了该模型对回归参数的估计是一致的和半参数有效的，在这种情况下实现了全鲁棒性。对于更普遍的协变量缺失模式，提出了一种新的协变量半参数建模方法。在这种方法中，协变量分布首先根据总体缺失数据模式分解为一系列条件分布的乘积，然后条件分布以一般的优势比形式表示。一般优势比采用参数化建模，协变量分布的其他组成部分采用非参数化建模。使用最大半参数似然来求参数估计。当比值比建模正确时，所提出的方法对回归参数产生一致的估计。总的来说，与Lipsitz和Ibrahim提出的参数化建模策略相比，半参数协变量建模策略增强了对协变量、模型错配的鲁棒性。新的协变量建模方法也可以合并到Robins等人的双鲁棒过程中，以增加对丢失数据机制的错误说明的保护。此外，所提出的建模策略避免了通常难以处理的与参数协变量模型的不完整数据似然最大化的集成。该方法可应用于多种不完全协变量的回归模型。
Robustness of covariate modeling for the missing-covariate problem in parametric regression is studied under the missing-at-random assumption. For a simple missing-covariate pattern, nonparametric covariate model is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter, Total robustness is achieved in this situation. For more general missing-covariate patterns, a novel semiparametric modeling approach is proposed for the covariates. In this approach, the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing-data patterns, and the conditional distributions are then represented in the general odds ratio form. The general odds ratios are modeled parametrically, and the other components of the covariate distribution are modeled nonparametrically. Maximum semiparametric likelihood is used to find the parameter estimates. The proposed method yields a consistent estimator for the regression parameter when the odds ratios are modeled correctly. In general, the semiparametric covariate modeling strategy increases the robustness against covariate, model misspecification when compared with the parametric modeling strategy proposed by Lipsitz and Ibrahim. The new covariate modeling approach can also be incorporated into the doubly robust procedure of Robins et al. to increase protection against misspecification of the missing-data mechanism. In addition, the proposed modeling strategy avoids the usually intractable integrations involved in the maximization of the incomplete-data likelihood with parametric covariate models. The proposed method can be applied to many regression models to handle incomplete covariates.