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Table 1 The average and the empirical standard error (ESE) of the AUC at 5 years in alternative scenarios for the simulations (a) with n=500 patients, p=1000 biomarkers and R=20 biomarker groups of equal size. Average quantities across 500 replications

From: Accounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models

Methods Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 Scenario 8
  (l = 1; q = 8) (l = 2; q = 8) (l = 1;q = 32) (l = 2;q = 32) (l = 2;q = 16) (l = 2;q = 8)
  HR U(0.65,0.75)   HR U(0.85,0.95)    
Standard Lasso 0.88 (0.02) 0.87 (0.03) 0.75 (0.04) 0.75 (0.04) 0.67 (0.05) 0.61 (0.05)
Adaptive lasso       
AC 0.88 (0.02) 0.88 (0.03) 0.78 (0.04) 0.77 (0.04) 0.68 (0.05) 0.61 (0.05)
PCA 0.87 (0.06) 0.85 (0.05) 0.74 (0.09) 0.73 (0.07) 0.64 (0.07) 0.58 (0.06)
Lasso+PCA 0.88 (0.04) 0.86 (0.05) 0.74 (0.08) 0.73 (0.06) 0.66 (0.06) 0.61 (0.06)
SW 0.88 (0.02) 0.88 (0.03) 0.75 (0.04) 0.75 (0.04) 0.65 (0.05) 0.59 (0.05)
ASW 0.88 (0.02) 0.88 (0.03) 0.78 (0.03) 0.77 (0.04) 0.68 (0.05) 0.61 (0.05)
ASW*SW 0.89 (0.02) 0.88 (0.02) 0.78 (0.04) 0.77 (0.04) 0.66 (0.05) 0.59 (0.05)
MSW 0.88 (0.02) 0.88 (0.02) 0.78 (0.04) 0.77 (0.04) 0.68 (0.05) 0.62 (0.05)
MSW*SW 0.89 (0.02) 0.88 (0.02) 0.77 (0.04) 0.76 (0.04) 0.67 (0.05) 0.60 (0.05)
cMCP 0.87 (0.03) 0.86 (0.03) 0.75 (0.04) 0.74 (0.04) 0.67 (0.05) 0.61 (0.06)
gel 0.88 (0.02) 0.88 (0.02) 0.74 (0.08) 0.60 (0.08) 0.58 (0.07) 0.57 (0.06)
SGL 0.88 (0.02) 0.88 (0.02) 0.77 (0.04) 0.76 (0.04) 0.69 (0.05) 0.62 (0.06)
IPF-Lasso       
IPF-Lasso1 0.88 (0.02) 0.88 (0.03) 0.78 (0.04) 0.77 (0.04) 0.69 (0.05) 0.63 (0.05)
IPF-Lasso2 0.88 (0.02) 0.88 (0.03) 0.76 (0.04) 0.75 (0.04) 0.68 (0.05) 0.62 (0.06)
  1. Abbreviations: l, number of active groups; q, number of active biomarkers; AC: Average Coefficients; SW: Single Wald; ASW: Average Single Wald; ASW*SW: Average Single Wald product Single Wald; MSW: Max Single Wald; MSW*SW: Max Single Wald product Single Wald.
  2. IPF-Lasso1: pflist1 = list(c(1,rep(2,19)), c(2,1,rep(2,18)), c(rep(2,10),1,rep(2,9)), c(1,1,rep(2,18)), c(1,rep(2,9),1,rep(2,9)), c(2,1,rep(2,8),1,rep(2,9)), c(1,1,rep(2,8),1,rep(2,9))).
  3. IPF-Lasso2: pflist2 = list(c(2,rep(1,19)), c(1,2,rep(1,18)), c(rep(1,10),2,rep(1,9)), c(2,2,rep(1,18)), c(2,rep(1,9),2,rep(1,9)), c(1,2,rep(1,8),2,rep(1,9)), c(2,2,rep(1,8),2,rep(1,9)))