Multiple linear regression is commonly used to test for association between genetic variants and continuous traits and estimate genetic effect sizes. Confounding variables are controlled for by including them as additional covariates. An alternative technique that is increasingly used is to regress out covariates from the raw trait and then perform regression analysis with only the genetic variants included as predictors. In the case of single‐variant analysis, this adjusted trait regression (ATR) technique is known to be less powerful than the traditional technique when the genetic variant is correlated with the covariates We extend previous results for single‐variant tests by deriving exact relationships between the single‐variant score, Wald, likelihood‐ratio, and F test statistics and their ATR analogs. We also derive the asymptotic power of ATR analogs of the multiple‐variant score and burden tests. We show that the maximum power loss of the ATR analog of the multiple‐variant score test is completely characterized by the canonical correlations between the set of genetic variants and the set of covariates. Further, we show that for both single‐ and multiple‐variant tests, the power loss for ATR analogs increases with increasing stringency of Type 1 error control () and increasing correlation (or canonical correlations) between the genetic variant (or multiple variants) and covariates. We recommend using ATR only when maximum canonical correlation between variants and covariates is low, as is typically true.

中文翻译：

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由于测试协变量调整性状和遗传变异之间的关联而导致的功率损失。

多元线性回归通常用于测试遗传变异和连续性状之间的关联并估计遗传效应大小。通过将它们作为附加协变量包含来控制混杂变量。一种越来越多使用的替代技术是从原始特征中回归协变量，然后仅将遗传变异作为预测变量进行回归分析。在单变体分析的情况下，当遗传变体与协变量相关时，已知这种调整性状回归 (ATR) 技术不如传统技术强大。单变量得分、Wald、似然比和F测试统计数据及其 ATR 类似物。我们还推导出了多变量评分和负担测试的 ATR 类似物的渐近能力。我们表明，多变体评分测试的 ATR 类似物的最大功率损失完全由遗传变体集和协变量集之间的典型相关性表征。此外，我们表明，两个单和多变体测试，ATR的功率损耗类似物以增加的严格类型1的差错控制（增加）和增加基因变体（或多个变体）之间的相关性（或典型相关）和协变量。我们建议仅在变体和协变量之间的最大规范相关性较低时才使用 ATR，这通常是正确的。