| First, I discussed the false positives that arise because of cryptic relatedness and population substructure and my aims to extend and evaluate the Hardy-Weinberg disequilibrium (HWD) methods for finding a disease-susceptibility locus, allowing for an inbreeding coefficient (F) in a similar way that Devlin and Roeder (1999) allowed for inbreeding in a case-control study. Then I compared the HWD measure, the common direct measure of linkage disequilibrium and Armitage's trend test, both without population substructure (F = 0) and with population substructure (F ≠ 0), for a single marker. The HWD test statistic has a small rate of false positives caused by the effect of the population stratification. In addition, the rate of power loss for the HWD test is much less than that for the genomic control (GC) test after each test statistic is adjusted by the estimate of its λ, which measures the amount of variance inflation caused by the inbreeding coefficient (F). However, in the multiplicative model, the HWD test has no power and high Type I error. Second, I presented a new method for fine-mapping using a case control design. The new method, termed “the weighted average” (WA), was developed by averaging Armitage's trend test statistic and the difference between the HWD test statistic for N cases and N controls. Thus, one of the main features of the weighted average method is to reinforce the weaknesses, and to maintain the strong points, of both Armitage's trend test and the HWD test. From the simulation, the weighted average test statistic has better power than either Armitage's trend test or the HWD test (N cases only) in the recessive and additive model. In the multiplicative model, the WA test has 30%∼45% power in the peak area. |
