Calculating Exact P-Values from the McNamara Transmission/Disequilibrium Test Statistic

The transmission/disequilibrium test (TDT) is a popular method for analyzing genetic data in studies of complex disease. It is often assumed that the P-values for the test are wellcalculated using the asymptotic, chi-squared distribution. However, that is not always an accurate assumption. A formula is derived for the exact P-value of the TDT McNamara statistic and we show that the asymptotic P-values for the McNemar statistic can often depart considerably from the exact P-values, even when sample sizes are relatively large. Notably, the asymptotic P-values can be either too large or too small, leading to either false positive or false negative results. Since the exact P-value for this statistic is simple to calculate, it will be preferable to do so. We also anticipate that our derivation may find utility in other applications of the McNemar statistic where the underlying variables are binomially-distributed.