The corrected χ2 test using kinship coefficients reduced the false positive rate substantially. The Q – Q plots of p-values of the four association tests for 50 and 400 markers are shown in Figure 3. Results for 100 and 200 multiallelic markers were consistent with these (not shown). Since genotypes of all markers were simulated under the null hypothesis of no association, p-values are expected to be uniformly distributed. Figure 3A suggests a high false positive rate when the classical χ2 test was used. Panels B, C and D of Figure 3 demonstrate that the corrected χ2 test reduces the false positive rate, producing a distribution of p-values that is close to uniform. Since the entire genealogy was known, ϕped was close to ϕact and the p-values were uniformly distributed (Figure 3D). The ϕpost had the same results as the pedigree-based results (not shown). When ϕest was used, the Q – Q plots of p-values were slightly different from the uniform distribution (Figure 3C). Overestimated kinship coefficients for UN pairs, especially when one individual is from the case group and the other is from the control group, may lead to slightly inflated false positive rates.
