Effect of allelic heterogeneity on the power of the transmission disequilibrium test

Due in part to an influential paper by Risch and Merikangas [(1996) Science 273:1516-1517], which suggested that disequilibrium tests would have greater power to detect genes of small effect than would linkage tests, interest in the use of the Transmission Disequilibrium Test (TDT) as an analysis tool for genomewide studies is steadily growing. However, the paper by Risch and Merikangas made several simplifying assumptions. One such assumption was that the underlying gene showed allelic homogeneity, and another was that the allele being measured was the actual susceptibility allele. Here we investigate the effect of allelic heterogeneity on the power of the TDT using multiplicative, additive, dominant, and recessive modes of inheritances in the context of a genomewide study. We further distinguish two cases: first, that the marker alleles are the actual susceptibility alleles, and second, that alleles are measured at a marker linked to the disease gene with zero recombination. We consider two family structures, either a single affected offspring (SAO) and two parents, or an affected sib-pair (ASP) and two parents. We find that, as expected, the power of the TDT declines as the number of susceptibility alleles at the locus being tested increases and the effect on power can be substantial. When a linked marker is measured rather than a susceptibility allele itself, sample sizes reach unattainable levels when as few as two susceptibility alleles are present. Across all the models we consider, the required number of families for a TDT with ASP sampling varies from 19 to over a million families. Thus, the TDT may not be an optimal test in the context of genomic screens under more biologically realistic assumptions.