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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 γ ) for quantitative and qualitative traits based on unrelated females. However, there is no method available for estimating γ based on general pedigrees. Therefore, in this paper, we propose a Bayesian method to obtain the point estimate and the credible interval of γ 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 γ . 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 γ . Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use. [ABSTRACT FROM AUTHOR]

Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases, and currently several methods have been proposed to estimate the degree of the XCI-S (denoted as γ) for a single locus. However, no method has been available to estimate γ for genes. Therefore, in this paper, we first propose the point estimate and the penalized point estimate of γ for genes, and then derive its confidence intervals based on the Fieller's and penalized Fieller's methods, respectively. Further, we consider the constraint condition of γ ∈ [ 0 ,   2 ] and propose the Bayesian methods to obtain the point estimates and the credible intervals of γ , where a truncated normal prior and a uniform prior are respectively used (denoted as GBN and GBU). The simulation results show that the Bayesian methods can avoid the extreme point estimates (0 or 2), the empty sets, the noninformative intervals ( [ 0 ,   2 ] ) and the discontinuous intervals to occur. GBN performs best in both the point estimation and the interval estimation. Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use. In summary, in practical applications, we recommend using GBN to estimate γ of genes. [ABSTRACT FROM AUTHOR]