Transmission/disequilibrium tests for quantitative traits

Spielman et al. [1993] proposed a transmission-disequilibrium test (TDT), based on marker data collected on affected offspring and their parents, to test for linkage between a genetic marker and a binary trait provided there is allelic association. It has been shown that this TDT is powerful and is not affected by allelic association due to population stratification in the absence of linkage. For quantitative traits, George and Elston [1987] proposed a likelihood method to detect the effect of a candidate gene in pedigree data when familial correlations are present. This test will detect allelic association but will do so in the absence of linkage. In this paper, we investigate two new likelihood-ratio test statistics for multi-generational quantitative traits to test either for linkage in the presence of allelic association or for allelic association in the presence of linkage, such as may be due to linkage disequilibrium. We compare these two tests analytically and by simulation with respect to 1) the sample size required for the asymptotic null distributions to be valid and 2) their power to detect association in those cases in which they are not sensitive to population stratification unless linkage is present. In general, 80 nuclear families with two children each and at least one heterozygous parent, or the equivalent number of children in large pedigrees, are enough for the asymptotic null distribution of the proposed conditional and TDT methods to be valid. The theoretical power is close to the simulated power except for the case of a recessive allele with low frequency. A sampling strategy is proposed that dramatically improves power.