Transmission/disequilibrium tests

Abstract

A general theory of transmission/disequilibrium test (TDT), given the information on an arbitrary number of markers on the two parents and their child, affected by the disease is developed. With k biallelic SNP markers and N=2 k types of possible haplotypes we consider a N x N table of transmission events in which N diagonal elements correspond to homozygous transmissions, not relevant to the problem of testing linkage, and N(N-1) off-diagonal elements resulting in N(N-1)/2 matched pairs of transmissions. This gives rise to N/2 chi-square tests, corresponding to different phases of the k-tuple heterozygote, each based on 1 d.f. on the null hypothesis of no linkage between the disease-susceptibility gene and all the k markers jointly. The power of the test, in terms of non-centrality parameter, has been derived algebraically for k=1 and 2 and studied numerically to show that tighter linkage results in higher power. Two pairs of markers give higher power over single marker case. The theory has been validated with the help of simulated data on 4 markers with 500 trios. Possible future investigation on TDT with two adjacent linked QTLs following risk of duplicate dominant epistasis type and involving a single marker has been indicated.