X Chromosomal Genetic Association Tests For Quantitative Traits Incorporating X Chromosome Inactivation

Background:Genome-wide association study has found many genetic loci which are associated with complex traits in human.However,most of these tests have been developed for autosomes and only a few have been proposed for identifying X-chromosomal loci.Further,the existing methods have some limitations.For example,only a few methods incorporate the information on X chromosome inactivation into analysis.Some methods are only applicable to the quantitative traits which follow normal distributions,but not suitable for skewed distributions.In addition,these methods were originally developed for single loci,and there has been no method proposed for multiple loci on X chromosome at present.Therefore,it is particularly important to further propose association tests for single and multiple loci on X chromosome that can effectively combine different inactivation patterns.Objective:(1)For quantitative traits,we propose three association tests for single loci on X chromosome which incorporate different X chromosome inactivation patterns.Two of them are only applicable to the quantitative traits which follow normal distributions,and the other one is valid whether the trait value follows a normal distribution or not.(2)For quantitative traits,we propose an association test for multiple loci on X chromosome,which can incorporate different X chromosome inactivation patterns.Methods:(1)When the quantitative trait value under study follows a normal distribution,we respectively use the Fisher's method and the weighted method to combine the test statistics for females and males,which are respectively denoted by Q-Xcat and Q-Zmax.When the quantitative trait value does not follow a normal distribution,the test statistic is constructed based on the ranks of the quantitative trait values under different inactivation patterns,which is denoted by Q-XRank.Computer simulations are used to compare the type ? error rates and powers of the three proposed single locus tests with the existing three methods.(2)We construct a semiparametric model under heteroscedasticity for genetic loci and quantitative trait values.By establishing a relationship with a linear mixed model,we construct the score test statistics under different XCI patterns.Then,we use the Cauchy method to combine the P values of these test statistics and obtain the final test statistic(WS-X).We compare the type ? error rates and powers of the proposed multiple locus association test and the existing SKAT method by using computer simulation technology.Results:(1)When the quantitative trait value follows a normal distribution,all the.single locus methods control the type ? error rates well,while when the trait value follows a skew distribution(e.g.,lognormal distribution),only Q-XRank controls the type ? error rates well.In addition,compared with the existing methods,the proposed three methods have higher powers.(2)Both the proposed multiple locus method and the existing SKAT method can control the type ? error rates well when the variances of trait values for females and males are equal.Otherwise,only the proposed method can still maintain the type ? error rates close to the nominal level,while the type ? error rates of the SKAT method may be inflated.In addition,the WS-X method has higher powers in most cases.Conclusion:(1)We proposed three robust and efficient X-chromosomal single locus association tests when the quantitative trait value follows or does not follow normal distributions.Thus,our proposed method is worth recommending in practice.(2)We propose a multiple locus association test for X chromosome,which can effectively combine different XCI patterns.Taken together,the proposed method has better performance and can be further used in practice.