Table 3 Regression coefficients (standardized regression coefficients) for scenarios with K ∈ {2, 5, 10} and a ∈ {0.5, 1}, where K is the number of true predictors in the data-generating mechanism and a is the effect multiplier. Regression coefficients of X7, …, X10 were chosen such that the log odds ratio between the first and the fifth sextile of the corresponding distribution was equal to 0.69. The last row shows the approximate true c-indices for those scenarios
From: To tune or not to tune, a case study of ridge logistic regression in small or sparse datasets
K = 2 | K = 5 | K = 10 | |||||
|---|---|---|---|---|---|---|---|
a = 1 | a = 0.5 | a = 1 | a = 0.5 | a = 1 | a = 0.5 | ||
(Standardized) regression coefficients of true predictors | X1 | 2.08 (0.83) | 1.04 (0.42) | 2.08 (0.83) | 1.04 (0.42) | 2.08 (0.83) | 1.04 (0.42) |
X2 | 1.39 (0.67) | 0.69 (0.33) | 1.39 (0.67) | 0.69 (0.33) | 1.39 (0.67) | 0.69 (0.33) | |
X3 | – | – | 0.69 (0.35) | 0.35 (0.17) | 0.69 (0.35) | 0.35 (0.17) | |
X4 | – | – | 0.69 (0.35) | 0.35 (0.17) | 0.69 (0.35) | 0.35 (0.17) | |
X5 | – | – | 0.35 (0.2) | 0.17 (0.10) | 0.35 (0.2) | 0.17 (0.10) | |
X6 | – | – | – | – | 0.35 (0.21) | 0.17 (0.11) | |
X7 | – | – | – | – | 0.036 (0.37) | 0.018 (0.18) | |
X8 | – | – | – | – | 0.003 (0.67) | 0.002 (0.33) | |
X9 | – | – | – | – | 0.004 (0.66) | 0.002 (0.33) | |
X10 | – | – | – | – | 0.036 (0.36) | 0.018 (0.18) | |
Noise | X11, …, X15 | 0 | 0 | 0 | 0 | 0 | 0 |
True c-index | 0.73 | 0.64 | 0.76 | 0.66 | 0.84 | 0.71 | |