An Efficient Bayesian Method for Estimating the Degree of the Skewness of X Chromosome Inactivation Based on the Mixture of General Pedigrees and Unrelated Females

Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases. Several methods have been proposed to estimate the degree of XCI-S (denoted as [Formula: see text]) for quantitative and qualitative traits based on unrelated females. However, there is no method available for estimating [Formula: see text] based on general pedigrees. Therefore, in this paper, we propose a Bayesian method to obtain the point estimate and the credible interval of [Formula: see text] based on the mixture of general pedigrees and unrelated females (called mixed data for brevity), which is also suitable for only general pedigrees. We consider the truncated normal prior and the uniform prior for [Formula: see text]. Further, we apply the eigenvalue decomposition and Cholesky decomposition to our proposed methods to accelerate the computation speed. We conduct extensive simulation studies to compare the performances of our proposed methods and two existing Bayesian methods which are only applicable to unrelated females. The simulation results show that the incorporation of general pedigrees can improve the efficiency of the point estimation and the precision and the accuracy of the interval estimation of [Formula: see text]. Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use.