Abstract
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.
Highlights
The X chromosome is unique in that males have only one, maternally-derived copy, while females are diploid
We present a new method, the sex-stratified X chromosome likelihood ratio test (SSX-LRT), which prevents that bias by allowing distinct mating type parameters for male vs. female affected offspring
NON-CENTRALITY PARAMETERS Under a null scenario, with an admixed population, where the relative risks are 1, the non-centrality parameter (NCP) calculated for parent-informed X chromosome likelihood ratio test” (PIX-LRT) and SSXLRT (Equations 4 and 7) and XTDT are all zero, which ensures
Summary
The X chromosome is unique in that males have only one, maternally-derived copy, while females are diploid. For complete data, closed-form maximum likelihood estimates of the relative risk and a likelihood ratio test statistic could be obtained from this method ignoring the genotype of the affected offspring and instead using only parents (see Supplement S.3). For CL/P, we compared our top five SNPs using PIX-LRT with the EM to the top five identified in Patel et al (2013) For these SNPs, we apply SSX-LRT and the parent-only analysis (Equation 5) to complete triads stratifying on sex of the affected offspring to better understand similarities and differences between our two results. SSX-LRT and the parent-only analysis are independent when complete triads are used, which enables estimates of relative risks to be compared in terms of agreement for parental vs offspring-based findings, and affected-boy families vs affected-girl families. H0: no disease-locus effect in male or female, H0m: no effect in males and test done in boy-affected families, H0f : no effect in females and test done in girl-affected families
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