Background: X chromosome inactivation (XCI) is an important gene regulation mechanism in females to equalize\nthe expression levels of X chromosome between two sexes. Generally, one of two X chromosomes in females is\nrandomly chosen to be inactivated. Nonrandom XCI (XCI skewing) is also observed in females, which has been\nreported to play an important role in many X-linked diseases. However, there is no statistical measure available for\nthe degree of the XCI skewing based on family data in population genetics.\nResults: In this article, we propose a statistical approach to measure the degree of the XCI skewing based on family\ntrios, which is represented by a ratio of two genotypic relative risks in females. The point estimate of the ratio is\nobtained from the maximum likelihood estimates of two genotypic relative risks. When parental genotypes are\nmissing in some family trios, the expectation-conditional-maximization algorithm is adopted to obtain the corresponding\nmaximum likelihood estimates. Further, the confidence interval of the ratio is derived based on the likelihood ratio test.\nSimulation results show that the likelihood-based confidence interval has an accurate coverage probability under the\nsituations considered. Also, we apply our proposed method to the rheumatoid arthritis data from USA for its practical use,\nand find out that a locus, rs2238907, may undergo the XCI skewing against the at-risk allele. But this needs to be further\nconfirmed by molecular genetics.\nConclusions: The proposed statistical measure for the skewness of XCI is applicable to complete family trio data or family\ntrio data with some paternal genotypes missing. The likelihood-based confidence interval has an accurate coverage\nprobability under the situations considered. Therefore, our proposed statistical measure is generally recommended in\npractice for discovering the potential loci which undergo the XCI skewing.
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