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Table 1 Performance of optimal and linear classifiers

From: Determination of sample size for a multi-class classifier based on single-nucleotide polymorphisms: a volume under the surface approach

  D = 3
h m n VUS ( ) ̂ VUS ( n ) ̂ VUS ( n ) MC ̂ Bias ̂
0.02 50 50 0.3013 0.1772 0.1657 -0.0116
0.02 50 100 0.3015 0.1793 0.1742 -0.0052
0.02 100 50 0.3662 0.1807 0.1874 0.0067
0.02 100 100 0.366 0.1837 0.1974 0.0136
0.05 50 50 0.5469 0.2229 0.2442 0.0213
0.05 50 100 0.5467 0.2517 0.2845 0.0328
0.05 100 50 0.6988 0.2448 0.2912 0.0463
0.05 100 100 0.6987 0.2848 0.3377 0.0529
0.1 50 50 0.8686 0.4179 0.4675 0.0496
0.1 50 100 0.8687 0.4958 0.55 0.0542
0.1 100 50 0.9667 0.4776 0.5342 0.0566
0.1 100 100 0.9667 0.5692 0.6341 0.0649
  D = 4
h m n VUS ( ) ̂ VUS ( n ) ̂ VUS ( n ) MC ̂ Bias ̂
0.02 50 50 0.1319 0.048 0.0462 -0.0018
0.02 50 100 0.1318 0.05 0.0512 0.0013
0.02 100 50 0.1892 0.0503 0.057 0.0068
0.02 100 100 0.189 0.0531 0.0614 0.0082
0.05 50 50 0.3891 0.0893 0.0923 0.003
0.05 50 100 0.3893 0.1175 0.1144 -0.0032
0.05 100 50 0.5832 0.1092 0.1127 0.0034
0.05 100 100 0.5831 0.1458 0.1285 -0.0174
0.1 50 50 0.8376 0.2933 0.2705 -0.0228
0.1 50 100 0.8378 0.4059 0.3517 -0.0542
0.1 100 50 0.9623 0.3653 0.3119 -0.0534
0.1 100 100 0.9626 0.4962 0.4085 -0.0877
  1. Here, D = 3 and 4, θ 1 = ( θ 1 , 1 , , θ 1 , m ) , let θ1,jU(0.4,0.49),j=1,…,m; for a specified scalar value h, let h 1 , h 2 , h 3 be such that their components hi,jU (h−0.002,h+0.002),j=1,…,m; and let θ i + 1 = θ i h i ,i=1,2,3; n is the sample size for each class; m is the number of independent SNPs, α=0.01 is the significant level for Wald tests; and ρ=1 is the percentage of the significant SNPs.