We propose a nested semiparametric model to analyze a case-control study where genuine case status is missing for some individuals. The concept of a noncase is introduced to allow for the imputation of the missing genuine cases. The odds ratio parameter of the genuine cases compared to controls is of interest. The imputation procedure predicts the probability of being a genuine case compared to a noncase semiparametrically in a dimension reduction fashion. This procedure is flexible, and vastly generalizes the existing methods. We establish the root- asymptotic normality of the odds ratio parameter estimator. Our method yields stable odds ratio parameter estimation owing to the application of an efficient semiparametric sufficient dimension reduction estimator. We conduct finite sample numerical simulations to illustrate the performance of our approach, and apply it to a dilated cardiomyopathy study.

中文翻译：

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缺失病例对照研究的嵌套半参数方法

我们提出了一个嵌套半参数模型来分析病例对照研究，其中某些个体的真实病例状态缺失。引入非案例的概念是为了对缺失的真实案例进行估算。真实病例与对照相比的优势比参数很有趣。插补过程以降维方式半参数地预测真实案例与非案例的概率。该过程非常灵活，并且极大地概括了现有方法。我们建立根-优势比参数估计量的渐近正态性。由于应用了有效的半参数充分降维估计器，我们的方法产生了稳定的优势比参数估计。我们进行有限样本数值模拟来说明我们方法的性能，并将其应用于扩张型心肌病研究。