n R
Without Heterogeneity (α=0.05)
Without Heterogeneity (α=0.01)
β M N β M N
10 5 38.77 (1.07) 42.65 (0.95) 50.32 (0.69) 63.77 (2.04) 69.02 (1.77) 80.26 (1.02)
10 55.44 (0.92) 59.42 (0.81) 66.97 (0.63) 77.55 (1.37) 81.39 (1.13) 89.11 (0.61)
15 67.13 (0.76) 70.58 (0.67) 76.96 (0.52) 84.94 (0.97) 87.71 (0.81) 93.04 (0.41)
20 73.40 (0.70) 76.60 (0.59) 82.07 (0.42) 88.27 (0.80) 90.57 (0.63) 94.74 (0.33)
20 5 48.81 (0.82) 50.71 (0.71) 52.43 (0.69) 79.26 (1.23) 81.52 (1.02) 84.56 (0.78)
10 65.37 (0.71) 67.09 (0.65) 68.72 (0.58) 88.22 (0.72) 89.68 (0.60) 91.57 (0.46)
15 75.67 (0.56) 77.10 (0.51) 78.43 (0.47) 92.47 (0.47) 93.44 (0.39) 94.72 (0.32)
20 80.89 (0.47) 82.23 (0.44) 83.43 (0.40) 94.26 (0.40) 95.11 (0.32) 96.14 (0.25)
n R With Heterogeneity (α=0.05) With Heterogeneity (α=0.01)
β M N β M N
10 5 40.51 (1.21) 32.88 (1.27) 46.41 (0.83) 65.63 (2.38) 62.37 (2.99) 73.59 (1.40)
10 57.64 (1.09) 49.11 (1.26) 63.18 (0.71) 79.35 (1.59) 76.47 (2.12) 84.57 (0.87)
15 68.59 (0.91) 61.25 (1.09) 74.11 (0.59) 86.00 (1.11) 83.98 (1.59) 90.26 (0.57)
20 74.89 (0.76) 67.72 (0.98) 79.42 (0.49) 89.14 (0.90) 87.22 (1.27) 92.43 (0.48)
20 5 51.73 (0.90) 48.49 (1.05) 52.31 (0.68) 81.26 (1.34) 80.26 (1.52) 84.23 (0.80)
10 68.04 (0.74) 65.23 (0.86) 68.59 (0.59) 89.59 (0.78) 88.94 (0.85) 91.38 (0.48)
15 77.50 (0.61) 75.41 (0.65) 78.33 (0.48) 93.25 (0.50) 92.89 (0.56) 94.61 (0.33)
20 82.55 (0.49) 80.54 (0.58) 83.36 (0.41) 94.92 (0.40) 94.52 (0.47) 96.03 (0.26)
The average (standard deviation) of the true positive percent in 1,000 simulations is shown. The significance level (Type I error) of the test is α, the per group sample size is n, and the percent CpG sites that are differentially methylated is denoted by R. Results shown are for the scenario in which the case standard deviation was shifted by 1
Table 2: True positive rates for all CpG sites in simulation study without and with sample heterogeneity.