Statistical Methods For X Chromosome Inactivation And Disease Gene Mapping At X Chromosomal Quantitative Trait Loci

Background:X chromosome plays an important role in gene mapping.Many researches have found that some diseases and traits are associated with genes on X chromosome.There are generally two mechanisms to occur on X chromosome:X chromosome inactivation(XCI)and genomic imprinting.Females have two copies of X chromosome while males have only one X chromosome.X chromosome inactivation is a process that happens in female mammals to equalize the X chromosomal effects between males(XY)and females(XX).It has been found that the skewness of XCI is associated with many severe disorders.Numerous studies have attempted to incorporate the XCI into the genetic association tests on X chromosome.However,there is no statistical method in the literature to evaluate the skewness of XCI in population genetics.XCI is the mechanism where gene dosage compensation between two sexes is achieved.It happens during early embryonic development,by which one of the two copies of X chromosome is inactivated,leading to females being mosaics for each cell with paternal or maternal X chromosome active.XCI occurs generally at random in females carrying an average inactivation ratio of 50:50 distributed normally.However,skewed or nonrandom XCI is biological plausibility.The skewed XCI is defined that 75%or above of cells in females keep one X chromosome inactive,and the remaining 25%of the cells keep another X chromosome inactive.Another special feature on X chromosome is the escape from XCI where both X chromosomes are active.About three quarters of genes are silenced on one of the female X chromosomes,while the remaining one quarter of genes may escape from XCI in some females.Thus,it is necessary to propose a measure for the skewness of XCI.Up to now,no statistical method is available to measure the degree of the X chromosome inactivation.On the other hand,genomic imprinting is a mechanism which is also related to many diseases and traits.Genomic imprinting controls the expression of the allele based on its parental origin.A lot of statistical methods have been proposed to test for association between genes and traits.However,some do consider neither XCI or genetic imprinting,and others only incorporate XCI while ignoring imprinting effect,which may reduce the test power.Methods:(1)In this thesis,we propose a novel measure to estimate the degree of XCI skewing for quantitative traits,which is obtained from a series of mathematical calculations of coefficients in a linear regression model.Then,we get its point estimate,and its confidence interval which is based on the likelihood ratio test statistic.Extensive simulation studies have been conducted to investigate the type I error rate,the power and the coverage rates of our proposed tests.(2)We put forward a method for testing association,which could incorporate the XCI and imprinting effects simultaneously.We also conduct simulation studies to assess the type I error rate and the power of our proposed tests under various simulation settings.Results:(1)The simulation study is conducted under various simulation settings,including two sample sizes,two groups of allele frequencies,two different values of inbreeding coefficient,five different values of the parameter for XCI skewing and two different values of the variance of the quantitative trait under study.The simulation results show that our proposed method provides the correct coverage rates under three different values of significant levels.The areas of the tails are fluctuated around 0.5.This indicates the symmetry of the confidence interval.Besides,the type I error rates of the proposed tests are controlled well.Generally,with the distance of the value of skewness between the null hypothesis and the alternative hypothesis increases,the test powers increase simultaneously.(2)The simulation study is conducted under various types of imprinting effects and XCI,with three groups of allele frequencies,three sample sizes of males and females.The simulation results show our proposed method could control the size well.Our proposed method has high test powers.Conclusions:(1)Our proposed method is powerful and suitable for measuring the skewness of XCI.The simulation shows that our proposed approach is robust and effective in the measure of the skewness of XCI for quantitative traits.(2)The proposed method we put forward simultaneously considers the information on the XCI and genomic imprinting effects in association study.As such,the proposed method has the high test powers,thus is recommended in practice.