Genetic analysis of complex diseases

The probability that a heterozygous Bb subject carries A in coupling when B is alpha sub(1) = p + delta /m, and the probability that the same subject carries A in coupling with b is alpha sub(2) = p - delta (1 - m). In a sample of single affected individuals for a Bb parent to transmit B to his affected child is P(tr - B) = [1 + ( gamma - 1) alpha sub(1)]/[2 + ( gamma - 1)( alpha sub(1) + alpha sub(2))]. The situation described by Risch and Merikangas corresponds to complete linkage disequilibrium, that is, delta = delta sub(max) with m = p, with P(tr - B) reducing to gamma /(1 + gamma ). In other cases, the number of necessary families increases dramatically as p differs from m even when delta = delta sub(max), and also as delta decreases. Thus, the power of association studies such as the TDT can be quite strong when there is a high probability that the allele studied is the causal allele as shown by Risch and Merikangas. In other cases, researchers should be aware that the power of such association studies can be greatly diminished as soon as the ratio m/p departs from unity and the linkage disequilibrium becomes weaker.