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. Author manuscript; available in PMC: 2021 Dec 8.
Published in final edited form as: J R Stat Soc Ser C Appl Stat. 2021 Sep 12;70(5):1391–1412. doi: 10.1111/rssc.12518

Table 1.

Simulation results for fixed effects under n = 100, p = 200 and n = 1000, p = 2000, p11 is the number of truly active mediators. TPR: true positive rate at false discovery rate (FDR) = 0.10. MSEnon-null: mean squared error for the indirect contributions of truly active mediators. MSEnull: mean squared error for the indirect contributions of truly inactive mediators. The results are based on 200 replicates for each setting, and the standard errors are shown within parentheses. For PTG, we include the pre-defined thresholds (λ0, λ1, λ2) under each setting. Bolded TPRs indicate the top two performers.

n = 100, p = 200, p11 = 10, fixed effects (I)
Method AUC TPR MSE non-null MSEnull × 10−4
PTG (0.15,0.4,0.4) 0.99(0.001) 0.52(0.026) 0.043 0.395
GMM 0.98(0.001) 0.44(0.022) 0.047 1.409
BAMA 0.97(0.002) 0.38(0.021) 0.063 2.471
Bi-BLasso 0.90(0.005) 0.27(0.015) 0.092 21.879
PathLasso 0.81(0.004) 0.35(0.019) 0.045 1.418
Bi-Lasso 0.80(0.008) 0.36(0.018) 0.043 0.661
HIMA 0.61(0.005) 0.23(0.010) 0.056 2.895
Univariate 0.80(0.007) 0.25(0.014) 0.060 49.764
n = 100, p = 200, p11 = 10, fixed effects (II)
Method AUC TPR MSE non-null MSEnull × 10−4
PTG (0.15,0.4,0.4) 0.96(0.003) 0.35(0.016) 0.073 0.309
GMM 0.96(0.003) 0.37(0.017) 0.062 0.940
BAMA 0.95(0.003) 0.31(0.015) 0.075 2.389
Bi-BLasso 0.90(0.005) 0.25(0.013) 0.044 11.040
PathLasso 0.70(0.009) 0.28(0.015) 0.092 0.576
Bi-Lasso 0.72(0.006) 0.29(0.013) 0.079 0.422
HIMA 0.60(0.005) 0.21(0.010) 0.083 1.923
Univariate 0.82(0.007) 0.23(0.013) 0.081 26.540
n = 1000, p = 2000, p11 = 100, fixed effects (I)
Method AUC TPR MSE non-null MSEnull × 10−4
PTG (0.15,0.4,0.4) 0.98(0.001) 0.64(0.008) 0.028 0.070
GMM 0.99(0.001) 0.61(0.009) 0.023 0.134
BAMA 0.98(0.001) 0.54(0.007) 0.040 0.150
Bi-BLasso 0.90(0.002) 0.23(0.004) 0.063 5.711
PathLasso 0.70(0.002) 0.20(0.005) 0.057 3.982
Bi-Lasso 0.72(0.001) 0.23(0.003) 0.051 0.293
HIMA 0.54(0.001) 0.15(0.003) 0.077 1.780
Univariate 0.89(0.002) 0.10(0.005) 0.092 225.056
n = 1000, p = 2000, p11 = 100, fixed effects (II)
Method AUC TPR MSE non-null MSEnull × 10−6
PTG (0.15,0.4,0.4) 0.96(0.002) 0.40(0.008) 0.008 0.164
GMM 0.97(0.001) 0.48(0.006) 0.003 3.437
BAMA 0.95(0.001) 0.35(0.005) 0.005 7.485
Bi-BLasso 0.85(0.001) 0.18(0.004) 0.011 184.761
PathLasso 0.67(0.002) 0.19(0.003) 0.017 19.540
Bi-Lasso 0.70(0.001) 0.23(0.005) 0.007 5.059
HIMA 0.56(0.002) 0.08(0.003) 0.013 25.432
Univariate 0.85(0.001) 0.12(0.003) 0.075 208.660