As shown in Figure 2, the QTLD test enjoys an advantage in power relative to the QTDT that increases as a function of the marker-specific heritability. Similarly, the classical measured genotype test uses even more of the relative association information and exhibits the most power. Although this would seem to suggest that the measured genotype would be the optimal test to use in the absence of population stratification it can be shown that for rare alleles, linkage alone can influence the measured genotype test (i.e., linkage can inflate the type I error rate for the test of linkage disequilibrium). In contrast, both the QTDT and the QTLD test are specific indicators of linkage disequilibrium between the marker and any causal variants. These results were obtained for a simulated minor allele frequency of 0.25. Simulations with an allele frequency of 0.1 yielded similar results (not shown), indicating that the difference in power is not primarily a function of the marker allele frequencies. Note that the marker-specific heritability is proportional to the QTL effect size, where the constant of proportionality is equal
