A statistically valid alternative to the TDT

To present an alternative linkage test to the transmission/disequilibrium test (TDT) which is conservative under the null hypothesis and generally more powerful under alternatives.

The exact distribution of the TDT is examined under both the null hypothesis and relevant alternatives. The TDT is rewritten in an alternate form based on the contributions from each of the three relevant parental mating types. This makes it possible to show that a particular term in the estimate is an exact tie and thus to rewrite the estimate without this term and to replace the multinomial 'variance estimate' of Spielman et al. [Am J Hum Genet 1993;52:506-516] by the binomial variance.

The resulting test is shown to be a stratified McNemar test (SMN). The significance level attained by the SMN is shown to be conservative when compared to the asymptotic chi(2) distribution, while the TDT often exceeds the nominal level alpha. Under alternatives, the proposed test is shown to be typically more powerful than the TDT.

The properties of the TDT as a statistical test have never been fully investigated. The proposed test replaces the heuristically motivated TDT by a formally derived test, which is also computationally simple.