GWAS：表型的标准化（the normalization of phenotype）

GWAS表型的标准化方法一般有Quantile normalization、Inverse rank normalization、Z-score normalization等。

各自区别如下：

一、Quantile normalization

该方法将每个样本中表型值进行排序，然后将其规范化到一个标准分布，通常是正态分布。规范化是通过将每个样本的分布等同于目标分布来完成的，使得同样比例的样本落在目标分布的每个值下方、上方或相等。这种方法确保了所有样本中表型的分布是一致的。
优点：可以消除由于偏斜导致的数据极端值和异常值的影响，而且对小批量数据的处理效果比较好。

使用该方法进行表型标准化的文章有：

1. Genome-wide association studies of brain imaging phenotypes in UK Biobank[J]. Nature, 2018, 562(7726): 210-216.

To ameliorate this, we quantile-normalized each of the image-derived phenotypes (IDPs) before association testing. This transformation also helped to avoid undue influence of outlier values.
https://www.nature.com/articles/s41586-018-0571-7

2. A multiple-phenotype imputation method for genetic studies[J]. Nature genetics, 2016, 48(4): 466-472.

Traits were mean and variance standardized and quantile normalized before analysis.
https://www.nature.com/articles/ng.3513

3. Components of genetic associations across 2,138 phenotypes in the UK Biobank highlight adipocyte biology[J]. Nature communications, 2019, 10(1): 4064.

We applied quantile normalization for phenotype (--pheno-quantile-normalize option), where we fit a linear model with covariates and transform the phenotypes to normal distribution N(0,1).
https://www.nature.com/articles/s41467-019-11953-9

二、Inverse rank normalization

一种将数据转换为正态分布的方法。该方法按照数据的大小对其进行排序，并将它们转换为百分位（即在所有数据中占据的位置百分比），并使用累积分布函数将这些百分位值转换为标准正态分布中的z分数。因此，排名越靠前的数据将被映射到较大的正态分布的值，排名越靠后的数据将被映射到较小的正态分布的值。这种方法适用于数据集中有许多离群值或非正态分布时，它可以将数据的分布形态转化为近似正态分布，方便后续的统计分析。

使用该方法进行表型标准化的文章有：

Association analyses of 249,796 individuals reveal 18 new loci associated with body mass index[J]. Nature genetics, 2010, 42(11): 937-948.

BMI was adjusted for age, age2 and other appropriate covariates (for example, principal components) and inverse normally transformed to a mean of 0 and a standard deviation of 1.
https://www.nature.com/articles/ng.686

三、Z-score normalization

该方法是通过计算每个样本的Z-score来标准化所有样本中观察到的表型值。Z-score 测量了一个特定样本的表型与所有样本的均值表型值相差多少个标准差。这种方法允许比较不同单位或量表的表型。

使用该方法进行表型标准化的文章有：

A genome-wide association study in 19 633 Japanese subjects identified LHX3-QSOX2 and IGF1 as adult height loci[J]. Human molecular genetics, 2010, 19(11): 2303-2312.

The scores were then normalized as Z scores. The effects of the Z scores on height were evaluated using the multivariate linear regression model incorporating height as a dependent variable and the Z scores, gender and age as the independent variables, using R statistical software. Differences in height between the subjects with low Z scores (less than or equal to −2) and high Z scores (≥2) were obtained by comparing the means of the non-adjusted height between subject groups.
https://academic.oup.com/hmg/article-abstract/19/11/2303/579594

总结

Quantile normalization 适用于偏态分布或异常值较多的情况， Inverse rank normalization 在样本量较小时具有更高的准确性，Z-score 适用于具有不同单位或量表的表型，允许比较不同单位或量表的表型。
从我查阅的文献来看，在GWAS中，使用Quantile normalization进行连续型表型标准化的比较多。

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