TABLE 1
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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

MethodAUCTPRMSEnon-nullMSEnull×10−4
n = 100, p = 200, p11 = 10, fixed effects (I)
PTG (0.15,0.4,0.4)0.99 (0.001)0.52 (0.026)0.0430.395
GMM0.98 (0.001)0.44 (0.022)0.0471.409
BAMA0.97 (0.002)0.38 (0.021)0.0632.471
Bi-BLasso0.90 (0.005)0.27 (0.015)0.09221.879
PathLasso0.81 (0.004)0.35 (0.019)0.0451.418
Bi-Lasso0.80 (0.008)0.36 (0.018)0.0430.661
HIMA0.61 (0.005)0.23 (0.010)0.0562.895
Univariate0.80 (0.007)0.25 (0.014)0.06049.764
n = 100, p = .200, p11 = 10, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.003)0.35 (0.016)0.0730.309
GMM0.96 (0.003)0.37 (0.017)0.0620.940
BAMA0.95 (0.003)0.31 (0.015)0.0752.389
Bi-BLasso0.90 (0.005)0.25 (0.013)0.04411.040
PathLasso0.70 (0.009)0.28 (0.015)0.0920.576
Bi-Lasso0.72 (0.006)0.29 (0.013)0.0790.422
HIMA0.60 (0.005)0.21 (0.010)0.0831.923
Univariate0.82 (0.007)0.23 (0.013)0.08126.540
n = 1000, p = 2000, p11 = 100, fixed effects (I)
PTG (0.15,0.4,0.4)0.98 (0.001)0.64 (0.008)0.0280.070
GMM0.99 (0.001)0.61 (0.009)0.0230.134
BAMA0.98 (0.001)0.54 (0.007)0.0400.150
Bi-BLasso0.90 (0.002)0.23 (0.004)0.0635.711
PathLasso0.70 (0.002)0.20 (0.005)0.0573.982
Bi-Lasso0.72 (0.001)0.23 (0.003)0.0510.293
HIMA0.54 (0.001)0.15 (0.003)0.0771.780
Univariate0.89 (0.002)0.10 (0.005)0.092225.056
MethodAUCTPRMSEnon-nullMSEnull×10−6
n = 1000, p =2000, p11 = 100, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.002)0.40 (0.008)0.0080.164
GMM0.97 (0.001)0.48 (0.006)0.0033.437
BAMA0.95 (0.001)0.35 (0.005)0.0057.485
Bi-BLasso0.85 (0.001)0.18 (0.004)0.011184.761
PathLasso0.67 (0.002)0.19 (0.003)0.01719.540
Bi-Lasso0.70 (0.001)0.23 (0.005)0.0075.059
HIMA0.56 (0.002)0.08 (0.003)0.01325.432
Univariate0.85 (0.001)0.12 (0.003)0.075208.660
MethodAUCTPRMSEnon-nullMSEnull×10−4
n = 100, p = 200, p11 = 10, fixed effects (I)
PTG (0.15,0.4,0.4)0.99 (0.001)0.52 (0.026)0.0430.395
GMM0.98 (0.001)0.44 (0.022)0.0471.409
BAMA0.97 (0.002)0.38 (0.021)0.0632.471
Bi-BLasso0.90 (0.005)0.27 (0.015)0.09221.879
PathLasso0.81 (0.004)0.35 (0.019)0.0451.418
Bi-Lasso0.80 (0.008)0.36 (0.018)0.0430.661
HIMA0.61 (0.005)0.23 (0.010)0.0562.895
Univariate0.80 (0.007)0.25 (0.014)0.06049.764
n = 100, p = .200, p11 = 10, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.003)0.35 (0.016)0.0730.309
GMM0.96 (0.003)0.37 (0.017)0.0620.940
BAMA0.95 (0.003)0.31 (0.015)0.0752.389
Bi-BLasso0.90 (0.005)0.25 (0.013)0.04411.040
PathLasso0.70 (0.009)0.28 (0.015)0.0920.576
Bi-Lasso0.72 (0.006)0.29 (0.013)0.0790.422
HIMA0.60 (0.005)0.21 (0.010)0.0831.923
Univariate0.82 (0.007)0.23 (0.013)0.08126.540
n = 1000, p = 2000, p11 = 100, fixed effects (I)
PTG (0.15,0.4,0.4)0.98 (0.001)0.64 (0.008)0.0280.070
GMM0.99 (0.001)0.61 (0.009)0.0230.134
BAMA0.98 (0.001)0.54 (0.007)0.0400.150
Bi-BLasso0.90 (0.002)0.23 (0.004)0.0635.711
PathLasso0.70 (0.002)0.20 (0.005)0.0573.982
Bi-Lasso0.72 (0.001)0.23 (0.003)0.0510.293
HIMA0.54 (0.001)0.15 (0.003)0.0771.780
Univariate0.89 (0.002)0.10 (0.005)0.092225.056
MethodAUCTPRMSEnon-nullMSEnull×10−6
n = 1000, p =2000, p11 = 100, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.002)0.40 (0.008)0.0080.164
GMM0.97 (0.001)0.48 (0.006)0.0033.437
BAMA0.95 (0.001)0.35 (0.005)0.0057.485
Bi-BLasso0.85 (0.001)0.18 (0.004)0.011184.761
PathLasso0.67 (0.002)0.19 (0.003)0.01719.540
Bi-Lasso0.70 (0.001)0.23 (0.005)0.0075.059
HIMA0.56 (0.002)0.08 (0.003)0.01325.432
Univariate0.85 (0.001)0.12 (0.003)0.075208.660
TABLE 1
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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

MethodAUCTPRMSEnon-nullMSEnull×10−4
n = 100, p = 200, p11 = 10, fixed effects (I)
PTG (0.15,0.4,0.4)0.99 (0.001)0.52 (0.026)0.0430.395
GMM0.98 (0.001)0.44 (0.022)0.0471.409
BAMA0.97 (0.002)0.38 (0.021)0.0632.471
Bi-BLasso0.90 (0.005)0.27 (0.015)0.09221.879
PathLasso0.81 (0.004)0.35 (0.019)0.0451.418
Bi-Lasso0.80 (0.008)0.36 (0.018)0.0430.661
HIMA0.61 (0.005)0.23 (0.010)0.0562.895
Univariate0.80 (0.007)0.25 (0.014)0.06049.764
n = 100, p = .200, p11 = 10, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.003)0.35 (0.016)0.0730.309
GMM0.96 (0.003)0.37 (0.017)0.0620.940
BAMA0.95 (0.003)0.31 (0.015)0.0752.389
Bi-BLasso0.90 (0.005)0.25 (0.013)0.04411.040
PathLasso0.70 (0.009)0.28 (0.015)0.0920.576
Bi-Lasso0.72 (0.006)0.29 (0.013)0.0790.422
HIMA0.60 (0.005)0.21 (0.010)0.0831.923
Univariate0.82 (0.007)0.23 (0.013)0.08126.540
n = 1000, p = 2000, p11 = 100, fixed effects (I)
PTG (0.15,0.4,0.4)0.98 (0.001)0.64 (0.008)0.0280.070
GMM0.99 (0.001)0.61 (0.009)0.0230.134
BAMA0.98 (0.001)0.54 (0.007)0.0400.150
Bi-BLasso0.90 (0.002)0.23 (0.004)0.0635.711
PathLasso0.70 (0.002)0.20 (0.005)0.0573.982
Bi-Lasso0.72 (0.001)0.23 (0.003)0.0510.293
HIMA0.54 (0.001)0.15 (0.003)0.0771.780
Univariate0.89 (0.002)0.10 (0.005)0.092225.056
MethodAUCTPRMSEnon-nullMSEnull×10−6
n = 1000, p =2000, p11 = 100, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.002)0.40 (0.008)0.0080.164
GMM0.97 (0.001)0.48 (0.006)0.0033.437
BAMA0.95 (0.001)0.35 (0.005)0.0057.485
Bi-BLasso0.85 (0.001)0.18 (0.004)0.011184.761
PathLasso0.67 (0.002)0.19 (0.003)0.01719.540
Bi-Lasso0.70 (0.001)0.23 (0.005)0.0075.059
HIMA0.56 (0.002)0.08 (0.003)0.01325.432
Univariate0.85 (0.001)0.12 (0.003)0.075208.660
MethodAUCTPRMSEnon-nullMSEnull×10−4
n = 100, p = 200, p11 = 10, fixed effects (I)
PTG (0.15,0.4,0.4)0.99 (0.001)0.52 (0.026)0.0430.395
GMM0.98 (0.001)0.44 (0.022)0.0471.409
BAMA0.97 (0.002)0.38 (0.021)0.0632.471
Bi-BLasso0.90 (0.005)0.27 (0.015)0.09221.879
PathLasso0.81 (0.004)0.35 (0.019)0.0451.418
Bi-Lasso0.80 (0.008)0.36 (0.018)0.0430.661
HIMA0.61 (0.005)0.23 (0.010)0.0562.895
Univariate0.80 (0.007)0.25 (0.014)0.06049.764
n = 100, p = .200, p11 = 10, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.003)0.35 (0.016)0.0730.309
GMM0.96 (0.003)0.37 (0.017)0.0620.940
BAMA0.95 (0.003)0.31 (0.015)0.0752.389
Bi-BLasso0.90 (0.005)0.25 (0.013)0.04411.040
PathLasso0.70 (0.009)0.28 (0.015)0.0920.576
Bi-Lasso0.72 (0.006)0.29 (0.013)0.0790.422
HIMA0.60 (0.005)0.21 (0.010)0.0831.923
Univariate0.82 (0.007)0.23 (0.013)0.08126.540
n = 1000, p = 2000, p11 = 100, fixed effects (I)
PTG (0.15,0.4,0.4)0.98 (0.001)0.64 (0.008)0.0280.070
GMM0.99 (0.001)0.61 (0.009)0.0230.134
BAMA0.98 (0.001)0.54 (0.007)0.0400.150
Bi-BLasso0.90 (0.002)0.23 (0.004)0.0635.711
PathLasso0.70 (0.002)0.20 (0.005)0.0573.982
Bi-Lasso0.72 (0.001)0.23 (0.003)0.0510.293
HIMA0.54 (0.001)0.15 (0.003)0.0771.780
Univariate0.89 (0.002)0.10 (0.005)0.092225.056
MethodAUCTPRMSEnon-nullMSEnull×10−6
n = 1000, p =2000, p11 = 100, fixed effects (II)
PTG (0.15,0.4,0.4)0.96 (0.002)0.40 (0.008)0.0080.164
GMM0.97 (0.001)0.48 (0.006)0.0033.437
BAMA0.95 (0.001)0.35 (0.005)0.0057.485
Bi-BLasso0.85 (0.001)0.18 (0.004)0.011184.761
PathLasso0.67 (0.002)0.19 (0.003)0.01719.540
Bi-Lasso0.70 (0.001)0.23 (0.005)0.0075.059
HIMA0.56 (0.002)0.08 (0.003)0.01325.432
Univariate0.85 (0.001)0.12 (0.003)0.075208.660
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