To demonstrate the increase in power that can be attained with the QTLD test, we conducted simulations to derive the expected χ2 test statistic for each of the association tests (measured genotype, QTDT, and QTLD) given a true allelic association between a marker and a QTL. We used SOLAR to simulate a biallelic QTL responsible for up to 5% of the phenotypic variance for a quantitative trait having a total heritability of 30%. The family structure and pattern of missing data in the COGA dataset were assumed. We also simulated a fully informative marker completely linked to the QTL, which we used to calculate the IBD allele-sharing at the QTL location. Treating the QTL genotypes as if they had been observed for a marker in complete LD with the trait locus, we then ran the QTLD procedure, with a linkage component based on the IBDs included in the model, to obtain the χ2 statistic for each of the tests. The test statistics were averaged over 100 replicates of the simulation for various values of the marker-specific heritability (i.e., the QTL effect size).
