Expectation maximization algorithm based haplotype relative risk (EM-HRR): test of linkage disequilibrium using incomplete case-parents trios.

The Haplotype Relative Risk (HRR) was first proposed [Falk et al., Ann Hum Genet 1987] to test for Linkage Disequilibrium (LD) between a marker and a putative disease locus using case-parent trios. Spurious association does not appear in such family-based studies under population admixture. In this paper, we extend the HRR to accommodate incomplete trios via the Expectation-Maximization (EM) algorithm [Dempster et al., J R Stat Soc Ser B, 1977]. In addition to triads and dyads (parent-offspring pair), the EM-HRR easily incorporates individuals with no parental genotype information available, which is excluded from the one parent Transmission/Disequilibrium Test (1-TDT) [Sun et al., Am J Epidemiol 1999]. Due to the data structure of EM-HRR, transmitted alleles are always available regardless of the number of missing parental genotypes. As a result of having a larger sample size, computer simulations reveal that the EM-HRR is more powerful in detecting LD than the 1-TDT in a population under Hardy-Weinberg Equilibirum (HWE). If admixture is not extreme, the EM-HRR remains more powerful. When a large degree of admixture exists, the EM-HRR performs better the 1-TDT when the association is strong, though not as well when the association is weak. We illustrate the proposed method with an application to the Framingham Heart Study. Copyright (c) 2005 S. Karger AG, Basel.