A statistical measure for the skewness of X chromosome inactivation based on case-control design

Skewed X chromosome inactivation (XCI), which is a non-random process, is frequently observed in both healthy and affected females. Furthermore, skewed XCI has been reported to be related to many X-linked diseases. However, no statistical method is available in the literature to measure the degree of the skewness of XCI for case-control design. Therefore, it is necessary to develop methods for such a task.

In this article, we first proposed a statistical measure for the degree of XCI skewing by using a case-control design, which is a ratio of two logistic regression coefficients after a simple reparameterization. Based on the point estimate of the ratio, we further developed three types of confidence intervals (the likelihood ratio, Fieller's and delta methods) to evaluate its variation. Simulation results demonstrated that the likelihood ratio method and the Fieller's method have more accurate coverage probability and more balanced tail errors than the delta method. We also applied these proposed methods to analyze the Graves' disease data for their practical use and found that rs3827440 probably undergoes a skewed XCI pattern with 68.7% of cells in heterozygous females having the risk allele T active, while the other 31.3% of cells keeping the normal allele C active.

For practical application, we suggest using the Fieller's method in large samples due to the non-iterative computation procedure and using the LR method otherwise for its robustness despite its slightly heavy computational burden.