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The Generalized Relative Pairs IBD Distribution: Its Use in the Detection of Linkage Open Access

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In this research we adopt the incompletely penetrant model and develop the allelic identical by descent (IBD) distributions at marker locus given dichotomous disease affectional status for siblings, uncle-nephew, grandparent-grandchild, half-sibs, and first cousin pairs. We first show that the probabilities of dichotomous disease status given trait IBD score are independent of relative relationships through Li's ITO method. We then fully derive the marker IBD distributions given dichotomous disease affectional status for various relative relationships by utilizing the relative pairs' joint probabilities of IBD scores at both trait and marker loci. We also calculated the marker IBD distributions given extreme discordant relative pairs at a quantitative trait locus (QTL) for different relative relationships. Next, we examine the power to detect the presence of a significant disease susceptibility locus through linkage analysis by perturbing the conditional marker IBD distribution. Specifically, three tests, the proportion test, the mean test and the logarithm of odds (LOD) score test, were applied to obtain the sample size required to achieve significance level p with differentpower. Simulation studies have been conducted in order to evaluate the performance of our methods. Finally, two locus models and the corresponding linkage detection strategies have been investigated for various relative relationships.

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