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. Author manuscript; available in PMC: 2011 Nov 9.
Published in final edited form as: Ann Appl Stat. 2011 Sep 1;5(3):2003–2023. doi: 10.1214/11-aoas458

Table 2.

Simulation results for evaluating feature selection and prediction performance based on 400 Monte Carlo data sets, where n = 125 and d = 8. Lasso-PL, Lasso partly linear AFT model; Lasso-SK, Lasso stratified model with K strata; Lasso-L, Lasso linear AFT model assuming a linear effect for both Xi and Zi; Lasso-Cox, Lasso linear Cox model assuming a linear effect for both Xi and Zi; AFT, standard AFT model assuming linear effects for both Xi and Zi without regularization; and Oracle, oracle partly linear model with zero coefficients being set to 0. Δ, effect size; SSE, sum of squared errors for ϑ̂; PC, proportion of zero coefficients being set to zero; PI, proportion of nonzero coefficients being set to zero; MSPE1, squared prediction error using both nonlinear and linear components; and MSPE2, squared prediction error using only linear components. Range of SEs, range of SEs for the corresponding performance measure in each column. NA, a performance measure is not applicable for an estimator. All numbers are multiplied by 1000.

Δ = 1 Δ = 0.5
SSE PC PI MSPE1 MSPE2 SSE PC PI MSPE1 MSPE2
ρ= 0
Lasso-PL 8 734 0 244 67 8 724 0 237 67
Lasso-S2 23 482 0 NA 186 23 453 1 NA 185
Lasso-S4 16 582 0 NA 127 15 565 2 NA 122
Lasso-S8 20 424 0 NA 161 20 438 8 NA 159
Lasso-L 12 639 0 997 100 12 611 0 990 99
Lasso-Cox NA 488 0 NA NA NA 543 17 NA NA
AFT 18 0 0 982 142 18 0 0 982 143
Oracle 4 1000 0 153 29 4 1000 0 207 30
ρ = 0.5
Lasso-PL 11 767 0 225 74 11 777 2 296 75
Lasso-S2 38 403 0 NA 341 40 412 8 NA 353
Lasso-S4 21 569 0 NA 171 20 599 5 NA 146
Lasso-S8 26 540 0 NA 218 26 594 15 NA 204
Lasso-L 19 720 0 2894 126 19 748 16 2943 121
Lasso-Cox NA 562 0 NA NA NA 612 14 NA NA
AFT 33 0 0 2839 212 32 0 0 2878 202
Oracle 5 1000 0 175 31 5 1000 0 248 32
ρ = 0.9
Lasso-PL 45 739 2 373 118 39 758 113 337 130
Lasso-S2 126 502 16 NA 592 106 500 152 NA 595
Lasso-S4 77 582 4 NA 184 60 596 124 NA 170
Lasso-S8 118 236 6 NA 338 96 424 135 NA 390
Lasso-L 92 751 31 6571 245 65 778 270 6738 262
Lasso-Cox NA 596 8 NA NA NA 651 153 NA NA
AFT 224 0 0 6483 337 226 0 0 6612 354
Oracle 17 1000 0 320 55 17 1000 0 288 54
Range of SEs 0.1-8 0-24 0-5 8-76 1-23 0.2-8 0-26 0-13 10-81 1-25