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. Author manuscript; available in PMC: 2011 Apr 10.
Published in final edited form as: Biometrics. 2009 Jun;65(2):394–404. doi: 10.1111/j.1541-0420.2008.01074.x

Table 3.

Simulation study: Mean squared prediction error, proportion of zero coefficients being set to zero (P0+) and proportion of nonzero coefficient being set to zero (P0−) of model selection results based on the Orcale estimator, the standard unregularized estimator, the LASSO estimator and the Adaptive LASSO (ALASSO) estimator using Gehan’s rank based, BJ (BJ) iterative and IPW procedures, for βo = (0.7,0.7,0,0,0,0.7,0,0,0)′.

ρ = 0
 ρ = 0.5
 ρ = 0.9
MSE
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 0.19 0.23 0.31 0.21 0.24 0.41 0.23 0.25 0.68
50 Regular 0.70 0.72 0.60 0.75 0.75 0.70 0.76 0.78 0.97
LASSO 0.49 0.49 0.64 0.45 0.48 0.73 0.34 0.41 0.84
ALASSO 0.49 0.48 0.61 0.51 0.52 0.70 0.42 0.45 0.88
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 0.08 0.08 0.23 0.09 0.09 0.32 0.09 0.09 0.60
100 Regular 0.25 0.26 0.33 0.26 0.27 0.43 0.27 0.28 0.72
LASSO 0.18 0.18 0.40 0.17 0.18 0.49 0.14 0.18 0.72
ALASSO 0.14 0.14 0.34 0.17 0.17 0.45 0.19 0.21 0.73
P 0+
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 1 1 1 1 1 1 1 1 1
50 Regular 0 0 0 0 0 0 0 0 0
LASSO 0.56 0.61 0.65 0.60 0.64 0.66 0.63 0.63 0.68
ALASSO 0.70 0.75 0.77 0.70 0.73 0.74 0.68 0.72 0.75
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 1 1 1 1 1 1 1 1 1
100 Regular 0 0 0 0 0 0 0 0 0
LASSO 0.48 0.70 0.58 0.54 0.70 0.67 0.62 0.70 0.66
ALASSO 0.70 0.85 0.80 0.75 0.84 0.79 0.73 0.81 0.77
P 0−
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 0 0 0 0 0 0 0 0 0
50 Regular 0 0 0 0 0 0 0 0 0
LASSO 0.06 0.07 0.13 0.07 0.10 0.16 0.23 0.28 0.36
ALASSO 0.07 0.08 0.18 0.11 0.15 0.24 0.41 0.45 0.54
Gehan BJ IPW Gehan BJ IPW Gehan BJ IPW
Oracle 0 0 0 0 0 0 0 0 0
100 Regular 0 0 0 0 0 0 0 0 0
LASSO 0 0 0.01 0 0 0.01 0.09 0.12 0.23
ALASSO 0 0 0.01 0.01 0.02 0.05 0.24 0.33 0.42