Linkage analysis of complex human traits using identity by descent data

We present a unified likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from small pedigrees. We consider the likelihood of (IBD) data conditional on phenotypes (discrete or continuous), and propose testing the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction &thetas; between the two loci. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows various pedigree types from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. The linkage score statistic is derived under general genetic models, which may include multiple genes and make no population genetic assumptions such as random mating or Hardy-Weinberg equilibrium. The score statistic readily extends to accommodate incomplete (IBD) data at the test locus using a hidden Markov model. For a given pedigree type, the form of the linkage score statistic is determined by the second largest eigenvalue and corresponding eigenvectors of the transition matrix T(&thetas;) between (IBD) configurations. In particular, if the second largest eigenvalue has multiplicity one, the score statistic is independent of the genetic model for the trait. Properties of the eigenvalues of T(&thetas;) are derived by relating its infinitesimal generator to the adjacency matrix of a quotient graph. In this thesis, we derive linkage score statistics for sibships of any size and for arbitrary relative pairs. For sibships with only affected individuals, the linkage score test is based on the widely used non-parametric statistic S_pairs, regardless of the genetic model for the trait. Simulation studies indicate that for sib-pairs, the linkage score test for quantitative traits generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes. In addition to its known optimality properties, the robustness properties of the linkage score test make it particularly promising for the linkage analysis of complex human traits using IBD data from small pedigrees.