Statistical Measure For The Skewness Of X Chromosome Inactivation And Association Test Incorporating X Chromosome Inactivation

Background:X chromosome inactivation(XCI)is an epigenetic phenomenon in females whose one of two X chromosomes is silenced during early embryonic development to achieve dosage compensation between two sexes.Generally,XCI has been recognized as a random process.However,recent studies have revealed that skewed XCI is a biological plausibility and even a common feature in both healthy and affected females.Currently,the skewness of XCI is measured by molecular genetics,and there is no statistical method available in population genetics for such a task.Genetic association analysis tests the association between traits and genetic factors,thus is an important tool to map the disease loci.Through the genome-wide association analysis,many loci were found to be associated with the diseases under study.However,only very a few came from X chromosome.Currently,there exist some methods for marker-disease association on X chromosome.However,some of them do not incorporate the information on XCI into analysis and the others require the assumption of Hardy-Weinberg equilibrium(HWE).There is no statistical method to consider both of the two important aspects.Objective:(1)Based on case-control design,we propose a statistical measure for the skewness of XCI and further develop the corresponding point estimate as well as interval estimation.(2)Based on case-control design,we propose a robust and powerful association test for X-linked loci,which can incorporate the information on XCI into analysis and does not rely on the assumption of HWE.(3)The proposed methods are applied to the Graves' disease data for their practical use.Methods:(1)We only use the female data because XCI is unrelated to males.We assume that the mutant allele has an additive effect.After a simple reparameterization,we use a ratio of two logistic regression coefficients to measure the skewness of XCI.Based on the proposed measure,we develop a ratio estimate as well as the likelihood ratio and delta methods to construct confidence interval.Through a simulation study,we compare the statistical properties of the LR method and delta method.(2)Since the males are hemizygotes,so we construct an allele based method for marker-disease association on X chromosome.We assign different weights to femals and males according to different dosage compensation patterns and then use a weighted statistic to combine the females and males.The variance of the weighted statistic is estimated without the assumption of HWE.We adopt the maximum statistic for the situation of no dosage compensation and complete dosage compensation,then evaluate the P value by the rhombus formula and the numeric calculation.We conduct an extensive simulation study to compare the proposed method Zmax to Xcat,TA and TAD with respect to the size and test power.Results:(1)The LR method has accurate coverage probability under all the simulation settings,while the delta method either underestimates or overestimates the coverage probability.On the other hand,the tail errors of the delta method are unbalanced in all the cases.LR has unbalanced tail error when the frequency of the minor allele is 0.1,but becomes balanced when the frequency of the minor allele is increased to be 0.3.(2)Zmax can control the size well under all the situations that we consider.Xcat may have inflated size when the deviations from HWE are different between female cases and female controls.TA and TAD have incorrect size when the allele frequency varies between two sexes.The power of the Zmax method is generally larger than those of Xcat and TAD.Sometimes the power of Zmax is larger than TA,sometimes is close to TA and is smaller than TA under the other situations.Conclusion:(1)Our proposed methods can be used to screen the candidate genes when studying the skewed XCI.On the other hand,the LR method has more accurate coverage probability and more balanced tail errors than the delta method.(2)The proposed Zmax method is a robust and powerful test for marker-disease association on X chromosome by incorporating the information on XCI.It requires neither specifying the underlying genetic model nor HWE and allows for the different deviations from HWE between cases and controls.Zmax outperforms the existing methods in terms of controlling the size and the test power.(3)The statistical results from the Graves' disease data application show the reliability and effectiveness of our proposed methods.