V. Choulakian et S. Mahdi, A new statistic for the analysis of association between trait and polymorphic marker loci, MATH BIOSCI, 164(2), 2000, pp. 139-145
Inference for detecting the existence of an association between a diallelic
marker and a trait locus is based on the chi-squared statistic with one de
gree of freedom. For polymorphic markers with m alleles (m > 2), three appr
oaches are mainly used in practice. First, one may use Pearson's chi-square
d statistic with m - 1 degrees of freedom (d.f.) but this leads to a loss i
n test power. Second, one can select an allele to be the most associated an
d then collapse the other allele categories into a single class. This reduc
es in a biased way, the locus to a diallelic system. Third, one may use the
Terwilliger [J.D. Terwilliger, Am. J, Hum. Genet. 56 (1995) 777] likelihoo
d ratio statistic which has a non-standard unknown limiting probability dis
tribution. In this paper, we propose a new statistic, L-D, based on the sec
ond testing approach. We derive the asymptotic probability distribution of
L-D in an easy way. Simulation studies show that L-D is more powerful than
Pearson's chi-squared statistic with m - 1 d.f. (C) 2000 Elsevier Science I
nc. All rights reserved.