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. 2021 Nov 19;24(2):425–442. doi: 10.1093/biostatistics/kxab038

Table 1.

Simulation results for Scenarios 1 and 2, mean (sd) based on 100 replicates

  Subgroup Scenario 1 Scenario 2
  Proposed FMRLasso ICC BSGSS Proposed FMRLasso ICC BSGSS
Continuous E variables, a block-diagonal covariance matrix for I features
Inline graphic   2.000 (0.00)       2.000 (0.00)      
ARI   0.820 (0.05) 0.685 (0.08) 0.637 (0.17)   0.722 (0.06) 0.591 (0.08) 0.561 (0.13)  
Main I effects
TPR 1 1.000 (0.00) 0.906 (0.19) 0.524 (0.33) 0.926 (0.11) 1.000 (0.00) 0.768 (0.25) 0.422 (0.28) 0.908 (0.14)
  2 1.000 (0.00) 0.908 (0.16) 0.482 (0.33)   1.000 (0.00) 0.760 (0.23) 0.292 (0.27)  
FPR 1 0.000 (0.00) 0.021 (0.02) 0.001 (0.00) 0.780 (0.06) 0.002 (0.01) 0.016 (0.02) 0.003 (0.01) 0.679 (0.07)
  2 0.001 (0.00) 0.011 (0.02) 0.001 (0.00)   0.003 (0.01) 0.009 (0.01) 0.001 (0.00)  
I–E interactions
TPR 1 1.000 (0.00) 0.924 (0.16) 0.691 (0.23) 0.926 (0.11) 0.998 (0.01) 0.823 (0.14) 0.543 (0.18) 0.908 (0.14)
  2 1.000 (0.00) 0.936 (0.11) 0.714 (0.23)   0.999 (0.01) 0.873 (0.14) 0.539 (0.18)  
FPR 1 0.006 (0.01) 0.053 (0.02) 0.020 (0.01) 0.784 (0.06) 0.022 (0.01) 0.052 (0.01) 0.025 (0.01) 0.704 (0.07)
  2 0.006 (0.01) 0.076 (0.02) 0.020 (0.01)   0.022 (0.01) 0.079 (0.01) 0.024 (0.01)  
Discrete E variables, a block-diagonal covariance matrix for I features
Inline graphic   2.000 (0.00)       2.000 (0.00)      
ARI   0.816 (0.06) 0.700 (0.10) 0.638 (0.25)   0.721 (0.06) 0.618 (0.07) 0.582 (0.16)  
Main I effects
TPR 1 1.000 (0.00) 0.932 (0.15) 0.636 (0.36) 0.934 (0.011) 0.998 (0.02) 0.802(0.21) 0.496 (0.29) 0.912 (0.13)
  2 1.000 (0.00) 0.886 (0.18) 0.548 (0.34)   1.000 (0.00) 0.736(0.20) 0.372 (0.27)  
FPR 1 0.001 (0.00) 0.020 (0.03) 0.003 (0.01) 0.811 (0.06) 0.003 (0.00) 0.017(0.02) 0.001 (0.01) 0.716 (0.08)
  2 0.001 (0.00) 0.009 (0.01) 0.002 (0.00)   0.002 (0.00) 0.010(0.02) 0.003 (0.06)  
I–E interactions
TPR 1 0.999 (0.01) 0.948 (0.12) 0.701 (0.32) 0.934 (0.11) 0.997 (0.02) 0.855 (0.13) 0.566 (0.20) 0.912 (0.13)
  2 1.000 (0.00) 0.948 (0.12) 0.720 (0.30)   1.000 (0.00) 0.892 (0.12) 0.586 (0.20)  
FPR 1 0.027 (0.01) 0.039 (0.02) 0.019 (0.01) 0.815(0.06) 0.031 (0.00) 0.038 (0.01) 0.022 (0.01) 0.722 (0.08)
  2 0.026 (0.01) 0.063 (0.02) 0.020 (0.01)   0.031 (0.00) 0.065 (0.01) 0.022 (0.01)  
Continuous E variables, a banded covariance matrix for I features
Inline graphic   2.000 (0.00)       2.000 (0.00)      
ARI   0.816 (0.05) 0.688 (0.08) 0.657 (0.15)   0.730 (0.06) 0.586 (0.11) 0.557(0.17)  
Main I effects
TPR 1 1.000 (0.00) 0.932 (0.17) 0.510 (0.29) 0.932 (0.11) 0.996 (0.04) 0.742 (0.25) 0.398 (0.26) 0.864 (0.15)
  2 1.000 (0.00) 0.890 (0.15) 0.490 (0.30)   1.000 (0.00) 0.722 (0.25) 0.316 (0.25)  
FPR 1 0.001 (0.00) 0.023 (0.03) 0.001 (0.01) 0.761 (0.07) 0.002 (0.01) 0.025 (0.03) 0.003 (0.01) 0.669 (0.073)
  2 0.001 (0.00) 0.011 (0.02) 0.001 (0.00)   0.002 (0.00) 0.013 (0.02) 0.002 (0.01)  
I–E interactions
TPR 1 1.000 (0.00) 0.929 (0.12) 0.688 (0.22) 0.932 (0.11) 0.985 (0.05) 0.797 (0.19) 0.528 (0.19) 0.864 (0.05)
  2 0.999 (0.01) 0.941 (0.09) 0.708 (0.22)   0.990 (0.04) 0.848 (0.17) 0.543 (0.22)  
FPR 1 0.006 (0.01) 0.054 (0.01) 0.021 (0.01) 0.766 (0.06) 0.019 (0.01) 0.056 (0.02) 0.024 (0.01) 0.675 (0.07)
  2 0.007 (0.01) 0.076 (0.01) 0.019 (0.01)   0.020 (0.01) 0.081 (0.01) 0.024 (0.01)  
Discrete E variables, a banded covariance matrix for I features
Inline graphic   2.000 (0.00)       2.000 (0.00)      
ARI   0.811 (0.06) 0.699 (0.07) 0.661 (0.20)   0.714 (0.06) 0.610 (0.06) 0.563 (0.18)  
Main I effects
TPR 1 1.000 (0.00) 0.948 (0.13) 0.674 (0.31) 0.932 (0.11) 1.000 (0.00) 0.832 (0.19) 0.496(0.29) 0.876(0.14)
  2 1.000 (0.00) 0.898 (0.15) 0.546 (0.30)   1.000 (0.00) 0.712 (0.21) 0.314(0.27)  
FPR 1 0.001 (0.00) 0.019 (0.02) 0.002 (0.00) 0.779 (0.06) 0.002 (0.01) 0.024 (0.03) 0.003(0.01) 0.689(0.08)
  2 0.002 (0.01) 0.010 (0.01) 0.002 (0.01)   0.001 (0.00) 0.012 (0.02) 0.003(0.01)  
I–E interactions
TPR 1 1.000 (0.00) 0.949 (0.09) 0.726 (0.26) 0.932 (0.11) 1.000 (0.00) 0.852 (0.13) 0.550(0.21) 0.876(0.14)
  2 1.000 (0.00) 0.961 (0.08) 0.743 (0.24)   1.000 (0.00) 0.903 (0.09) 0.562(0.22)  
FPR 1 0.027 (0.01) 0.037 (0.01) 0.019 (0.01) 0.784 (0.06) 0.031 (0.00) 0.039 (0.02) 0.023(0.01) 0.695(0.07)
  2 0.027 (0.01) 0.062 (0.01) 0.018 (0.01)   0.031 (0.00) 0.067 (0.01) 0.023(0.01)  

Inline graphic , estimated number of subgroups; ARI, adjusted rand index; TPR, true positive rate; FPR, false positive rate.