Ra. Betensky et D. Rabinowitz, Simple approximations for the maximal transmission/disequilibrium test with a multi-allelic marker, ANN HUM GEN, 64, 2000, pp. 567-574
Spielman et al. (1993) popularized the transmission/disequilibrium test (TD
T) to test for linkage between disease and marker loci that show a populati
on association. Several authors have proposed extensions to the TDT for mul
ti-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) p
roposed using the maximum of the Isi-allelic TDT statistics computed for ea
ch allele versus all others combined. The maximal TDT statistic, however. n
o longer follows a chi-square distribution. Here, a refinement to Bonferron
i's correction for multiple testing provided by Worsley (1982) based on max
imal spanning trees is applied to calculate accurate upper bounds for the t
ype I error and p-values for the maximal TDT. In addition, an accurate lowe
r Bonferroni bound, is applied to calculate power. This approach does not r
equire any simulation-based analysis and is less conservative than the stan
dard Bonferroni correction. The bounds are given for both the exact probabi
lity calculations and for those based on the normal approximation. The resu
lts are assessed through simulations.