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