Fig. 4.

Empirical type 1 error rates of the single-variant tests at significance level of 0.01, according to the number $\widetilde{MAC}$ of observations with genotype dosage G > 0 in the 1862 individuals with complete information on AGE and SEX. For the count-specific assessment, the results were pooled for the variants with the same $\widetilde{MAC}$ value, and the proportions of the p values <0.01 were then computed. Tests are the standard likelihood ratio test (LRT), penalized likelihood ratio test (PLRT), standard score test (Score) and small-sample-adjusted score tests (Score-Var-Adj and Score-Var-Kurt-Adj), which are indicated by yellow squares, black circles, red point-down triangles, purple diamonds, and green point-up triangles, respectively. The vertical line segments indicate ±2 simulation error bars, which were calculated based on the total number of the polymorphic variants in each $\widetilde{MAC}$ -specific group. For example, for the variants with $\widetilde{MAC}$ = 1, the error bars were obtained based on 200 × 44 = 8800 simulated data sets