Bipolar disorder (BD) affects both sexes, but important sex differences exist with respect to its symptoms and comorbidities. For example, rapid cycling (RC) is more prevalent in females, and alcohol use disorder (AUD) is more prevalent in males. We hypothesize that X chromosome variants may be associated with sex-specific characteristics of BD. Few studies have explored the role of the X chromosome in BD, which is complicated by X chromosome inactivation (XCI). This process achieves "dosage compensation" for many X chromosome genes by silencing one of the two copies in females, and most statistical methods either ignore that XCI occurs or falsely assume that one copy is inactivated at all loci. We introduce new statistical methods that do not make these assumptions.