The Quantile-Quantile (Q-Q) plots are used in GWAS to assess the inflation of FPRs by comparing the distribution of observed p-values against the theoretical model distribution of expected p-values [85]. In theory, without type I error arising from population stratification or other artifacts, the Q-Q plot shall align with the diagonal line. This is true if we use completely randomized data. By comparing the distortion of the Q-Q plot of the test results from this diagonal line, we can tell whether there are false positives or other errors due to genotyping or imputation. Before we draw any conclusion, we provide the Q-Q plots for results from all three Case-Control, dTDT and MH tests on the COGA data ( Figure 7 ). From the figure we can see that most of the observed p-values from Case-Control and dTDT are along the diagonal line. We do not observe significant distortion, i.e., type I error, in both tests. On the other hand, the Q-Q plot of MH test lies above the diagonal line. As stated earlier, both Case-Control and the dTDT are not
