Efficient Methods for Genotype-Specific Distributions with Unobserved Genotypes.

描述(由申请人提供)：这项建议开发了一系列新的半参数有效的遗传数据方法，在这些方法中，受试者的基因类型没有被观察到，因此表型数据来自于基因特定亚群的混合。一个例子是在一项亲属队列研究中收集的数据，其中科学兴趣是估计一种特征或时间的分布函数，以患有害突变携带者的疾病(外显函数)。在一项亲属队列研究中，可能富含突变携带者的指标受试者(先证者)被抽样并进行基因分型。收集先证者亲属的病史，但亲属没有基因分型，因此可能不知道他们是否携带突变。然而，人们可以使用先证者的基因型和孟德尔定律来计算每个亲属成为突变携带者的概率。另一个例子是数量性状的区间定位(QTL)。在这样的研究中，没有观察到QTL的基因型，因此性状分布采取QTL-基因型特定分布的混合形式。根据标记的基因类型和标记与QTL之间的重组比例来计算该QTL具有特定基因类型的概率。人们感兴趣的是估计QTL特定基因型的分布。这些例子的一个共同特征是，科学兴趣在于推断特定于基因型的亚群，但尚不清楚每个观察结果属于哪个亚群。每个观察值在任何子总体中的概率是不同的，并且可以估计。在不对这些特定的基因型分布进行预先指定的、容易出错的参数假设的情况下，文献中唯一可用的统计方法是两个截然不同的非参数最大似然估计(NPMLE1、NPMLE2)。然而，我们将证明NPMLE1是不有效的，并且NPMLE2是不一致的。因此，迫切需要为这类数据开发有效和高效的统计工具。我们使用现代半参数理论来进行形式化的半参数分析，其中我们定义了丰富的估计类。我们证明了任何基于最小二乘的估计量都是这个估计类的一个成员。我们构造了这个族中的一个最优成员，它可以获得最小的估计方差，从而达到半参数效率界。对于删失结果，我们给出了完全未删失数据的影响函数的半参数有效估计。我们提出了一种逆概率加权估计器，并增加了增广项以获得最优的效率。我们还构造了一个易于实现且不需要额外的模型假设的补偿估计器。此外，我们还提出了处理其他观察到的协变量的方法，如性别和家庭成员之间的附加残差相关性。我们还开发了一系列关于两个分布在单个或多个时间点同时相等的检验，以及两个分布在所有时间点都相等的总体检验。我们将应用开发的方法来分析一个关于帕金森氏病的亲属队列研究，一个关于亨廷顿病的大型家庭研究和两个QTL研究。

DESCRIPTION (provided by applicant): This proposal develops a series of new semiparametric efficient methods for genetic data where subjects' genotypes are not observed therefore phenotype data arise from a mixture of genotype-specific subpopulations. One example is data collected in a kin-cohort study, where the scientific interest is in estimating the distribution function of a trait or time to developing a disease for deleterious mutation carriers (penetrance function). In a kin- cohort study, index subjects (probands) possibly enriched with mutation carriers are sampled and genotyped. Disease history in relatives of the probands is collected, but the relatives are not genotyped therefore it may be unknown whether they carry a mutation. However, one can calculate the probability of each relative being a mutation carrier using the proband's genotype and Mendelian laws. Another example is interval mapping of quantitative traits (QTL). In such studies, genotype at a QTL is unobserved therefore the trait distribution takes the form of a mixture of QTL-genotype specific distributions. The probability of the QTL having a specific geno- type is computed based on marker genotypes and recombination fractions between the marker and the QTL. Interest is on estimating the QTL genotype-specific distributions. A common feature of these examples is that the scientific interest is in inference of genotype-specific subpopulations but it is unknown which subpopulation each observation belongs to. The probability of each observation being in any subpopulation varies and can be estimated. Without making a prespecified, error prone parametric assumption on these genotype-specific distributions, the only available statistical methods in the literature are two distinct nonparametric maximum like- lihood estimators (NPMLE1, NPMLE2). However, we will show that NPMLE1 is not efficient, and NPMLE2 is not consistent. There is therefore great need to develop valid and efficient statistical tools for such data. We use modern semiparametric theory to carry out a formal semiparametric analysis where we define a rich class of estimators. We show that any least squares based estimator is a member of this estimation class. We construct an optimal member of this family which obtains the minimum estimation variance hence reaches the semipara- metric efficiency bound. For censored outcomes, we propose a semiparametric efficient estimator given an influence function of the complete uncensored data. We propose an inverse probability weighting estimator, and add an augmentation term to obtain optimal efficiency. We also construct an imputation estimator which is easy to implement and does not require additional model assumption for the imputation step. Furthermore we propose methods to handle other observed covariates such as gender and additional residual correlation among family members. We also develop a series of tests for equality of two distributions at single or multi- ple time points simultaneously and an overall test of two distributions being equal at all time points. We will apply apply developed methods to analyze a kin-cohort study on Parkinson's disease, a large family study on Huntington's disease and two QTL studies.