In summary, the sum of all 11 informative transmissions for bi and ci can be written as:(10) (11)where i represents the i th trio. By substituting t from equation (9) into (10) and (11) and summing up bi and ci for all trios, we can compute the χ 2 values for each SNP:(12)which follows a one degree freedom χ2 distribution under the null hypothesis of no association. We name this generalized TDT the dosage TDT (dTDT). The original TDT proposed by Spielman et al [18] can then be considered as a special case when t and the dosage probabilities in a trio-dosage set is 0 or 1.
