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.