Because the traditional TDT is a simple representation of the χ 2 statistics, it requires single counts of the transmitted/non-transmitted alleles from the heterozygous parents to the affected offspring. Thus the inferred dosage probabilities cannot be processed through this setup. In this study, we generalize the original TDT by taking all possible allele transmissions in a pedigree into account. Table 2 shows the dosage probabilities of three alternative genotypes (1/1, 1/2 and 2/2) in a trio (named a trio-dosage set in this work) from the inferred results. Table 3 lists all 11 TDT-informative allele transmissions in a trio where at least one of the parents is heterozygous. The values of bi and ci used in the χ 2 calculation of the TDT in each trio i are calculated by summing up the probabilities across all these 11 types of transmissions. Let t denote the probability that allele 1 is transmitted by a heterozygote parent of an affected child. We can then write the dosage probabilities of a child in terms of the dosage probabilities of its parents and t as follows:(3) (4) (5)
