Equivalence of three score tests for association mapping of quantitative trait loci under selective genotyping

Huang and Lin ([2007] Am J Hum Genet 80:567-572) proposed a conditional-likelihood approach for mapping quantitative trait loci (QTL) under selective genotyping, and demonstrated via simulation that their model tends to be more powerful than the prospective linear regression. However, we show that the three score tests based on the conditional, prospective and retrospective likelihoods are numerically identical in testing association between a quantitative trait and a candidate locus. Two approximations are derived for calculating power and sample size for the score test. Compared to the random sampling, a single-tail selection generally reduces the power of the score test in mapping small effect QTLs. A two-tail selection generally enhances the QTL heritability; however, in small samples, the power of the test may actually decrease if the sample sizes are highly unbalanced in the upper and lower tails of the trait distribution.