Many genetic studies that aim to identify genetic variants associated with complex phenotypes are subject to unobserved confounding factors arising from environmental heterogeneity. This poses a challenge to detecting associations of interest and is known to induce spurious associations when left unaccounted for. Penalized linear mixed models (LMMs) are an attractive method to correct for unobserved confounding. These methods correct for varying levels of relatedness and population structure by modeling it as a random effect with a covariance structure estimated from observed genetic data. Despite an extensive literature on penalized regression and LMMs separately, the two are rarely discussed together. The aim of this review is to do so while examining the statistical properties of penalized LMMs in the genetic association setting. Specifically, the ability of penalized LMMs to accurately estimate genetic effects in the presence of environmental confounding has not been well studied. To clarify the important yet subtle distinction between population structure and environmental heterogeneity, we present a detailed review of relevant concepts and methods. In addition, we evaluate the performance of penalized LMMs and competing methods in terms of estimation and selection accuracy in the presence of a number of confounding structures.

中文翻译：

---

结构化遗传数据的惩罚线性混合模型

许多旨在鉴定与复杂表型相关的遗传变异的遗传研究都受到环境异质性引起的未观察到的混杂因素的影响。这对检测感兴趣的关联构成了挑战，并且已知会在不去考虑的情况下诱发虚假关联。惩罚线性混合模型 (LMM) 是一种用于纠正未观察到的混淆的有吸引力的方法。这些方法通过将其建模为具有从观察到的遗传数据估计的协方差结构的随机效应来校正不同水平的相关性和种群结构。尽管有大量关于惩罚回归和 LMM 的文献，但很少一起讨论这两者。本次审查的目的是在检查遗传关联设置中受惩罚的 LMM 的统计特性时这样做。具体来说，在存在环境混杂的情况下，受惩罚的 LMM 准确估计遗传效应的能力尚未得到充分研究。为了阐明种群结构和环境异质性之间重要而微妙的区别，我们详细回顾了相关概念和方法。此外，在存在许多混杂结构的情况下，我们在估计和选择准确性方面评估了受惩罚的 LMM 和竞争方法的性能。