Misspecified Mixed Model Analysis: Theory and Application

该项目是统计学家和统计遗传学家之间的合作，重点是发展统计理论和方法，用于分析全基因组关联研究（GWAS）的数据。 在过去的十年中，虽然GWAS在检测影响复杂人类特征/疾病的遗传变异方面非常成功，但这些发现只占遗传因素的一小部分。 近年来，基于一类称为混合效应模型的统计模型的统计分析取得了重大进展。 然而，在理解为什么该方法有效方面存在差距，因为在某种程度上，分析中使用的统计模型是错误的。 该项目旨在通过开发新的理论和方法来填补差距，并通过应用于真实的数据来评估这些方法。 该项目将促进教学、培训和学习，扩大代表性不足群体的学生的参与，并在各机构之间建立研究网络。 这项研究将对许多其他科学领域产生极大的兴趣，其结果将在主题领域期刊上广泛传播。在过去的十年中，超过24，000个单核苷酸多态性（SNP）已被报道与全基因组显著性水平上的至少一种性状/疾病相关。 然而，这些显著相关的SNP仅占复杂人类性状/疾病的遗传因素的一小部分，在遗传学界被称为“缺失遗传力”。 近年来，基于线性混合模型（LMM）的约束最大似然（REML）方法取得了重大进展。 虽然REML方法似乎为许多实际问题提供了正确的答案，但研究人员一直困惑于这样一个事实，即导出REML估计量的LMM是错误的。 在最近发表的一篇文章中，研究人员证明了一些重要的遗传量的REML估计，如遗传力和环境误差的方差，尽管模型错误指定，但仍然是一致的。 虽然这项开创性的工作导致了一个新的领域，称为误指定混合模型分析（MMMA），许多理论和实践的挑战仍然没有解决。 本项目旨在解决以下问题：（1）MMMA扩展到相关SNP，（2）在错误指定的LMM下REML估计量的渐近分布的发展，（3）MMMA的恢复方法，（4）估计非零随机效应的数量，（5）扩展到多个随机效应因子和离散性状。 该研究还将包括软件开发，以实现这些方法。

This project, a collaboration between statisticians and a statistical geneticist, focuses on the development of statistical theory and methods for the analysis of data from genome-wide association studies (GWAS). Over the past decade, while GWAS have been very successful in detecting genetic variants that affect complex human traits/diseases, these discoveries have only accounted for a small portion of the genetic factors. Recently, significant progress has been made using statistical analysis based on a class of statistical models called mixed effects models. However, there is a gap in understanding why the method works, because, in a way, the statistical model used in the analysis is misspecified. This project aims to fill the gap by developing new theory and methods, and evaluating the methods through applications to real data. The project will promote teaching, training and learning, broaden the participation of students from under-represented groups, and build research networks between institutions. The research will be of great interest to many other areas of science, and the results will be widely disseminated in subject matter domain journals. In the past decade, more than 24,000 single-nucleotide polymorphisms (SNPs) have been reported to be associated with at least one trait/disease at the genome-wide significance level. However, these significantly associated SNPs only account for a small portion of the genetic factors underlying complex human traits/diseases, referred to as "missing heritability" in the genetics community. Recently, significant progress has been made in using the restricted maximum likelihood (REML) approach based on linear mixed models (LMM). While the REML approach appears to provide the right answer to many problems of practical interest, researchers have been puzzled by the fact that the LMM, under which the REML estimators are derived, is misspecified. In a recently published article, the investigators proved that the REML estimators of some important genetic quantities, such as heritability and the variance of the environmental error, are consistent despite the model misspecification. While this pioneering work led to a new field called misspecified mixed model analysis (MMMA), many theoretical and practical challenges remain unsolved. This project seeks to address the following problems: (1) extension of MMMA to correlated SNPs, (2) development of the asymptotic distribution of the REML estimator under misspecified LMM, (3) resampling methods for MMMA, (4) estimation of the number of nonzero random effects, and (5) extensions to multiple random effect factors and discrete traits. The research will also include software development to implement the methods.