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Table 5 Average number of non-zero coefficients and mean absolute error (MAE) of coefficient estimates over 100 simulations for scenario 3, 4, and 5

From: Gsslasso Cox: a Bayesian hierarchical model for predicting survival and detecting associated genes by incorporating pathway information

scenario 3: Group size
  4/4 4/20 4/50
Average Number MAE Average Number MAE Average Number MAE
gsslasso 9.09 0.58 (0.22) 9.26 0.64 (0.29) 9.27 0.69 (0.54)
lasso 53.75 3.90 (0.41) 54.58 3.94 (0.43) 53.96 3.93 (0.44)
grlasso 270.78 2.78 (1.22) 455.15 7.06 (1.69) 509.75 10.58 (1.71)
grMCP 13.40 0.57 (0.18) 40.00 3.50 (0.54) 84.50 10.09 (2.52)
grSCAD 56.16 0.85 (0.78) 53.85 3.62 (0.74) 100.00 7.86 (1.77)
cMCP 9.42 0.64 (0.29) 14.64 0.98 (0.33) 16.85 1.05 (0.38)
scenario 4: Number of non-null groups
  8/20 3/20 1/20
gsslasso 8.85 0.54 (0.19) 9.12 0.56 (0.19) 9.27 0.68 (0.26)
lasso 52.87 3.58 (0.44) 53.51 3.89 (0.43) 52.49 3.90 (0.41)
grlasso 757.1 19.84 (2.51) 610.25 13.91 (2.08) 461.25 7.64 (1.71)
grMCP 83.95 7.68 (0.60) 46.00 7.49 (1.51) 50.00 4.52 (0.67)
grSCAD 410.3 10.80 (0.82) 142.30 8.04 (0.74) 55.85 4.57 (0.74)
cMCP 13.22 0.83 (0.38) 15.74 0.96 (0.35) 14.81 1.03 (0.31)
scenario 5: Correlation coefficients within group
  r = 0 r = 0.5 r = 0.7
gsslasso 9.18 0.85 (0.72) 8.90 1.07 (0.99) 8.11 3.54 (0.54)
lasso 59.10 3.42 (0.35) 52.63 4.04 (0.49) 48.82 5.25 (0.50)
grlasso 557.00 10.27 (1.25) 490.50 11.88 (1.75) 465.90 13.61 (2.45)
grMCP 61.71 7.38 (0.89) 57.40 8.14 (1.29) 53.54 9.59 (0.83)
grSCAD 148.68 7.42 (0.67) 170.61 8.78 (1.16) 194.58 11.28 (1.28)
cMCP 16.72 0.98 (0.47) 14.32 0.98 (0.37) 21.51 3.53 (0.40)
  1. Notes: in scenario 3, group size “4/50” denotes that there are four none-zero coefficients embedded in a group with 50 predictors. The group size is 50. This is true for “4/20” and “4/4”. The optimal s0 = 0.02 for different group size settings. The slab scales, s1, are 1 in this scenario. In scenario 4 “8/20” denotes that there are 8 non-null groups among 20 groups. Each non-null group includs at least one non-zero coefficients. The optimal s0 = 0.02 for the three settings. In scenario 5, the optimal s0 are 0.02, 0.03, and 0.04 for different correlation coefficients, 0.0, 0.5, and 0.7 within group, respectively. The slab scales, s1, are 1 in this scenario 3, 4 and 5. Values in the parentheses are standard errors. “gsslasso” represents the proposed group spike-and-slab lasso cox