A robust distribution-free test for genetic association studies of quantitative traits

A rank-based normalization method with the fully adjusted full-stage procedure in genetic association studies

In the area of genetic epidemiology, studies of the genotype-phenotype associations have made significant contributions to human complicated trait genetics. These studies depend on specialized statistical methods for uncover the association between traits and genetic variants, both common and rare variants. Often, in analyzing such studies, potentially confounding factors, such as social and environmental conditions, are required to be involved. Multiple linear regression is the most widely used type of regression analysis when the outcome of interest is quantitative traits. Many statistical tests for identifying genotype-phenotype associations using linear regression rely on the assumption that the traits (or the residuals) of the regression follow a normal distribution. In genomic research, the rank-based inverse normal transformation (INT) is one of the most popular approaches to reach normally distributed traits (or normally distributed residuals). Many researchers believe that applying the INT to the non-normality of the traits (or the non-normality of the residuals) is required for valid inference, because the phenotypic (or residual) outliers and non-normality have the significant influence on both the type I error rate control and statistical power, especially under the situation in rare-variant association testing procedures. Here we propose a test for exploring the association of the rare variant with the quantitative trait by using a fully adjusted full-stage INT. Using simulations we show that the fully adjusted full-stage INT is more appropriate than the existing INT methods, such as the fully adjusted two-stage INT and the INT-based omnibus test, in testing genotype-phenotype associations with rare variants, especially when genotypes are uncorrelated with covariates. The fully adjusted full-stage INT retains the advantages of the fully adjusted two-stage INT and ameliorates the problems of the fully adjusted two-stage INT for analysis of rare variants under non-normality of the trait. We also present theoretical results on these desirable properties. In addition, the two available methods with non-normal traits, the quantile/median regression method and the Yeo-Johnson power transformation, are also included in simulations for comparison with these desirable properties.

pKWmEB: integration of Kruskal-Wallis test with empirical Bayes under polygenic background control for multi-locus genome-wide association study

Although nonparametric methods in genome-wide association studies (GWAS) are robust in quantitative trait nucleotide (QTN) detection, the absence of polygenic background control in single-marker association in genome-wide scans results in a high false positive rate. To overcome this issue, we proposed an integrated nonparametric method for multi-locus GWAS. First, a new model transformation was used to whiten the covariance matrix of polygenic matrix K and environmental noise. Using the transferred model, Kruskal-Wallis test along with least angle regression was then used to select all the markers that were potentially associated with the trait. Finally, all the selected markers were placed into multi-locus model, these effects were estimated by empirical Bayes, and all the nonzero effects were further identified by a likelihood ratio test for true QTN detection. This method, named pKWmEB, was validated by a series of Monte Carlo simulation studies. As a result, pKWmEB effectively controlled false positive rate, although a less stringent significance criterion was adopted. More importantly, pKWmEB retained the high power of Kruskal-Wallis test, and provided QTN effect estimates. To further validate pKWmEB, we re-analyzed four flowering time related traits in Arabidopsis thaliana, and detected some previously reported genes that were not identified by the other methods.