Learning about the X from our parents.

The X chromosome is generally understudied in association studies, in part because the analyst has had limited methodological options. For nuclear-family-based association studies, most current methods extend the transmission disequilibrium test (TDT) to the X chromosome. We present a new method to study association in case-parent triads: the parent-informed likelihood ratio test for the X chromosome (PIX-LRT). Our method enables estimation of relative risks and takes advantage of parental genotype information and the sex of the affected offspring to increase statistical power to detect an effect. Under a parental exchangeability assumption for the X, if case-parent triads are complete, the parents of affected offspring provide an independent replication sample for estimates based on transmission distortion to their affected offspring. For each offspring sex we combine the parent-level and the offspring-level information to form a likelihood ratio test statistic; we then combine the two to form a combined test statistic. Our method can estimate relative risks under different modes of inheritance or a more general co-dominant model. In triads with missing parental genotypes, the method accounts for missingness with the Expectation-Maximization algorithm. We calculate non-centrality parameters to assess the power gain and robustness of our method compared to alternative methods. We apply PIX-LRT to publically available data from an international consortium of genotyped families affected by the birth defect oral cleft and find a strong, internally-replicated signal for a SNP marker related to cleft lip with or without cleft palate.