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 great er power to detect genes of small effect than would Linkage tests, interest in the use of the Transmission Disequilibrium Test (TDT) as an analysis to ol for genomewide studies is steadily growing. However, the paper by Risch and Merikangas made several simplifying assumptions. One such assumption wa s that the underlying gene showed allelic homogeneity, and another was that the allele being measured was the actual susceptibility allele. Here we in vestigate 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 zer o recombination. We consider two family structures, either a single affecte d offspring (SAO) and two parents, or an affected sib-pair (ASP) and two pa rents. We find that, as expected, the power of the TDT declines as the numb er of susceptibility alleles at the locus being tested increases and the ef fect on power can be substantial. When a linked marker is measured rather t han a susceptibility allele itself, sample sizes reach unattainable levels when as few as two susceptibility alleles are present. Across all the model s 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 opti mal test in the context of genomic screens under more biologically realisti c assumptions. Genet. Epidemiol. 18:143-156, 2000. (C) 2000 Wiley-Liss, Inc .