Empirical Type I Error Rate, Power, Sensitivity, and Specificity of the Proposed Test. We displayed the type I error rate and power for the proposed test at the nominal significance level of 5% as a function of CRR. The estimation was performed at the nominal significance level of α = 0.05 over 1000 independent simulation datasets of 1000 cases and 1000 controls. (a) Solid black and red lines denote the standard and joint power, respectively, at CRR = 2.0, 3.0, 4.0, or 5.0. The standard power at CRR = 1.0 represents the type I error rate. The dashed blue line indicates the nominal significance level of 0.05. (b) Solid black and red lines show sensitivity and specificity at each CRR, respectively.