Statistical Methods For Measuring The Degree Of The Skewness Of X Chromosome Inactivation Based On General Pedigree Data

Background:In females,there are twice as many copies of genes on X chromosome as in males.To compensate for the imbalance of this kind between two sexes,one of the two alleles on X chromosome in females may be inactivated in the early stages of embryonic development.This mechanism is called dosage compensation.X chromosome inactivation(XCI)is an epigenetic phenomenon of dosage compensation of X chromosomal genes between males and females.It is generally believed that the probability of the inactivation of the paternal X chromosome is equal to that of the maternal one,otherwise,it is called skewed XCI.Existing studies claimed that females with diseases are more prone to having skewed XCI than normal females.So,the biological process of the skewed XCI should be considered when conducting the genetic association between the X chromosomal alleles and diseases.As such,the statistical methods for measuring the skewness of X chromosome inactivation is also particularly important.Although there have been several methods for measuring the degree of the XCI skewing from the perspective of population genetics,these statistical methods cannot handle general pedigree data.Objectives:(1)According to the generalized linear mixed model,the statistical index to measure the degree of the skewness of the XCI using general pedigree data is proposed,including the point estimates and the confidence intervals(CIs)of the statistical index,and the model is applicable to both quantitative and qualitative traits;(2)We further propose the methods which can tackle the situations with some individuals’ genotypes missing in some pedigrees;(3)Finally,we apply the proposed methods to the data from the Minnesota Center for Twin and Family Research for the practical use of these proposed methods and explore if the loci associated with behavioral disinhibition undergo the skewed XCI.Methods:The expression of the statistical index for measuring the degree of the XCI skewing is obtained by a simple reparameterization.The index is the ratio of two regression coefficients of the generalized linear mixed models.Then,the corresponding point estimates and CIs are constructed based on the Fieller’s method and the penalized Fieller’s method,respectively.We conduct extensive simulation studies under various simulation settings and compare two proposed methods based on various evaluation indicators of the point estimation and the interval estimation.When the genotypes of some members in some pedigrees are missing,we impute the missing genotypes multiple times based on the Monte Carlo resampling method,and then the best imputation sample is selected.This thesis proposes 12 selection methods,which correspond to 12 imputation modes.Results:(1)For complete pedigrees and quantitative traits,our study found that when the degree of the XCI skewing is 0 or 0.5,the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths for the penalized Fieller’ s method perform better than those for the Fieller’s method;when the degree of the XCI skewing is 1 or 1.5,there is no significant difference between these two methods in the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths;when the degree of the XCI skewing is 2,the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths for the penalized Fieller’s method have worse performance than those for the Fieller’s method.The CIs of the Fieller’s method can be well controlled around 95%,and the CIs of the penalized Fieller’s method can also be basically controlled.The proportion of the noninformative intervals(i.e.,the probability that the CI is[0,2]),the proportion of the empty sets(i.e.,the probability that the CI is an empty set),the proportion of the discontinuous intervals,the standard deviation(SD)and the interquartile range of the interval lengths for the penalized Fieller’s method are all better than those for the Fieller’s method.(2)The results for complete pedigrees and qualitative traits are similar to the results for complete pedigrees and quantitative traits,but their statistical performances are reduced.When the number of the families is 3 00,or when the number of the families is 900 and the degree of the XCI skewing is 0,0.5 or 1,the point estimation and the interval estimation of the Fieller’s method is not so good and the proportion of the noninformative intervals exceeds 50%;when the number of the families is 300 and the degree of the XCI skewing is 0,0.5,1 or 1.5,the point estimation and the interval estimation of the penalized Fieller’s method is not so good.Our study found that when the degree of the XCI skewing is 0,the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths for the penalized Fieller’s method perform better than those for the Fieller’s method;when the degree of the XCI skewing is 0.5,1 or 1.5,there is no significant difference between these two methods in the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths;when the degree of the XCI skewing is 2,the median and the mean squared error of the point estimates,and the mean and the median of the interval lengths for the penalized Fieller’s method have worse performance than those for the Fieller’s method.The CIs of the Fieller’s method can be well controlled around 95%,and the CIs of the penalized Fieller’s method can also be basically controlled in most cases.The proportion of the noninformative intervals,the proportion of the empty sets,the proportion of the discontinuous intervals,the SD and the interquartile range of the interval lengths for the penalized Fieller’s method are all better than those for the Fieller’s method.(3)Imputation methods can improve the statistical performance of the point estimation and the interval estimation for incomplete pedigree data.For quantitative traits,according to the evaluation indicator of the mean squared error of the point estimates,we recommend using the imputation mode of Fmedop or Fmedtp for the Fieller’s method(i.e.,the two imputation modes obtained from the median of the point estimates based on the Fieller’s method and truncated or not truncated within the interval[0,2]),and using the imputation mode of PFmedop or PFmedtp for the penalized Fieller’s method(i.e.,the two imputation modes obtained from the median of the point estimates based on the penalized Fieller’s method and truncated or not truncated within the interval[0,2]).For the qualitative traits,according to the two evaluation indicators of the mean squared error of the point estimates and the median of the interval lengths,it is recommended to use the imputation mode of Fmedtp(i.e.,the imputation mode obtained from the median of the point estimates based on the Fieller’s method and truncated within the interval[0,2]).(4)In the real data analysis,the penalized Fieller’s method identifies one locus(i.e.,rs12014119)which undergoes the skewed XCI and is skewed to the minor allele A,with the point estimate being 0 and the CI being[0,0.4225,while the Fieller’s method does not provide information about XCI at this locus,with the point estimate being 0 and the CI being the noninformative[0,2].This result validates the relevant conclusions in the simulation study.Conclusions:We proposed a statistical measure(y)of the skewness of the XCI based on general pedigree data and derived the corresponding point estimates and CIs,which are applicable to both quantitative and qualitative traits.The proposed methods can deal with the pedigree data with missing genotypes.When the degree of the XCI skewing is 0,the penalized Fieller’s method is recommended.And when the degree of the XCI skewing is 2,the Fieller’s method is recommended.