Spielman et al. (1993) popularized the transmission/disequilibrium test (TDT) to test for linkage
between disease and marker loci that show a population association. Several authors have proposed
extensions to the TDT for multi-allelic markers. Many of these approaches exhibit a ‘swamping’ effect
in which a marker with a strong effect is not detected by a global test that includes many markers
with no effect. To avoid this effect, Schaid (1996) proposed using the maximum of the bi-allelic TDT
statistics computed for each allele versus all others combined. The maximal TDT statistic, however,
no longer follows a chi-square distribution. Here, a refinement to Bonferroni's correction for multiple
testing provided by Worsley (1982) based on maximal spanning trees is applied to calculate accurate
upper bounds for the type I error and p-values for the maximal TDT. In addition, an accurate lower
Bonferroni bound is applied to calculate power. This approach does not require any simulation-based
analysis and is less conservative than the standard Bonferroni correction. The bounds are given for
both the exact probability calculations and for those based on the normal approximation. The results
are assessed through simulations.