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. Author manuscript; available in PMC: 2018 Feb 22.
Published in final edited form as: Stat Med. 2015 Jul 30;34(29):3811–3830. doi: 10.1002/sim.6600

Table II.

Estimated AUC and its 95% confidence intervals. Multivariate normal distributions: μ0 = 0, μ1 = (0.1, ⋯, 0.6)T evenly spaced.

Mean AUC
Confidence interval
(n0, n1) p PW SW MM MVN LR Ridge LASSO PW SW MM MVN LR Ridge LASSO
             Σ0 = Σ1 = 0.85Ip×p + 0.15Jp×p (equal covariance in diseased and healthy groups)
(25,25) 2 0.6409 0.6409 0.6114 0.6453 0.6457 0.6458 0.6224 (0.470, 0.784) (0.470, 0.784) (0.469, 0.771) (0.461, 0.795) (0.470, 0.794) (0.469, 0.794) (0.490, 0.794)
4 0.6504 0.6476 0.6329 0.6536 0.6533 0.6616 0.6290 (0.483, 0.810) (0.470, 0.813) (0.474, 0.782) (0.482, 0.818) (0.482, 0.818) (0.478, 0.814) (0.475, 0.811)
6 0.6607 0.6506 0.6420 0.6558 0.6550 0.6739 0.6357 (0.481, 0.816) (0.477, 0.808) (0.472, 0.794) (0.466, 0.818) (0.466, 0.816) (0.477, 0.827) (0.488, 0.810)
10 0.6686 0.6489 0.6440 0.6513 0.6494 0.6830 0.6387 (0.490, 0.827) (0.470, 0.813) (0.467, 0.798) (0.469, 0.808) (0.472, 0.808) (0.499, 0.834) (0.490, 0.808)
20 0.7041 0.6605 0.6610 0.6549 0.6398 0.7160 0.6672 (0.533, 0.848) (0.490, 0.824) (0.478, 0.807) (0.474, 0.822) (0.467, 0.811) (0.549, 0.859) (0.488, 0.830)
50 0.7339 0.6529 0.6698 0.5850 0.5740 0.7499 0.6829 (0.558, 0.870) (0.469, 0.816) (0.482, 0.814) (0.454, 0.734) (0.464, 0.715) (0.608, 0.886) (0.500, 0.851)
(100,100) 2 0.6605 0.6605 0.6236 0.6612 0.6612 0.6612 0.6624 (0.584, 0.733) (0.584, 0.733) (0.537, 0.704) (0.585, 0.735) (0.584, 0.735) (0.584, 0.734) (0.585, 0.734)
4 0.6802 0.6790 0.6458 0.6814 0.6814 0.6826 0.6808 (0.601, 0.756) (0.602, 0.760) (0.558, 0.719) (0.604, 0.755) (0.604, 0.755) (0.604, 0.758) (0.600, 0.755)
6 0.6954 0.6918 0.6550 0.6952 0.6952 0.6979 0.6952 (0.612, 0.767) (0.606, 0.768) (0.575, 0.736) (0.615, 0.771) (0.615, 0.771) (0.618, 0.775) (0.611, 0.770)
10 0.7161 0.7064 0.6662 0.7112 0.7112 0.7176 0.7118 (0.642, 0.788) (0.623, 0.782) (0.588, 0.739) (0.633, 0.784) (0.634, 0.782) (0.644, 0.788) (0.633, 0.785)
20 0.7477 0.7270 0.6797 0.7377 0.7367 0.7515 0.7422 (0.676, 0.812) (0.641, 0.803) (0.601, 0.747) (0.658, 0.811) (0.657, 0.810) (0.673, 0.817) (0.662, 0.810)
50 0.7696 0.7310 0.6870 0.7617 0.7537 0.7930 0.7697 (0.706, 0.828) (0.644, 0.806) (0.615, 0.756) (0.683, 0.830) (0.674, 0.824) (0.729, 0.851) (0.698, 0.834)
100 0.7799 0.7308 0.6933 0.7630 0.7232 0.8350 0.7963 (0.710, 0.847) (0.637, 0.812) (0.615, 0.765) (0.681, 0.836) (0.636, 0.800) (0.771, 0.890) (0.723, 0.858)
150 0.7865 0.7293 0.6976 0.7168 0.6872 0.8627 0.8141 (0.718, 0.848) (0.637, 0.810) (0.622, 0.768) (0.618, 0.809) (0.585, 0.780) (0.805, 0.914) (0.740, 0.875)
200 0.7893 0.7301 0.7004 0.5739 0.5466 0.8865 0.8263 (0.723, 0.854) (0.636, 0.810) (0.626, 0.765) (0.478, 0.676) (0.476, 0.637) (0.831, 0.932) (0.752, 0.887)
             Σ0 = 0.9Ip×p + 0.1Jp×p and Σ1 = 0.85Ip×p + 0.15Jp×p (unequal covariance)
(25,25) 2 0.6421 0.6421 0.6119 0.6458 0.6460 0.6458 0.6231 (0.472, 0.790) (0.472, 0.790) (0.470, 0.776) (0.470, 0.794) (0.475, 0.794) (0.464, 0.795) (0.490, 0.792)
4 0.6489 0.6476 0.6296 0.6500 0.6498 0.6586 0.6281 (0.466, 0.811) (0.474, 0.806) (0.474, 0.786) (0.466, 0.806) (0.467, 0.805) (0.480, 0.811) (0.461, 0.802)
6 0.6668 0.6576 0.6443 0.6635 0.6632 0.6792 0.6410 (0.470, 0.827) (0.483, 0.822) (0.467, 0.794) (0.486, 0.829) (0.472, 0.829) (0.504, 0.834) (0.488, 0.827)
10 0.6784 0.6587 0.6487 0.6620 0.6607 0.6913 0.6455 (0.488, 0.830) (0.474, 0.818) (0.470, 0.810) (0.483, 0.827) (0.501, 0.826) (0.512, 0.838) (0.490, 0.819)
20 0.7127 0.6683 0.6677 0.6576 0.6413 0.7265 0.6752 (0.531, 0.853) (0.481, 0.819) (0.485, 0.811) (0.467, 0.810) (0.472, 0.803) (0.571, 0.854) (0.494, 0.834)
50 0.7486 0.6602 0.6839 0.5865 0.5740 0.7606 0.6947 (0.581, 0.885) (0.474, 0.829) (0.504, 0.827) (0.458, 0.746) (0.461, 0.715) (0.624, 0.882) (0.500, 0.845)
(100,100) 2 0.6607 0.6607 0.6234 0.6614 0.6614 0.6614 0.6625 (0.583, 0.735) (0.583, 0.735) (0.535, 0.703) (0.585, 0.735) (0.585, 0.735) (0.584, 0.735) (0.585, 0.735)
4 0.6828 0.6816 0.6474 0.6838 0.6838 0.6849 0.6826 (0.602, 0.756) (0.600, 0.757) (0.559, 0.723) (0.601, 0.756) (0.603, 0.755) (0.605, 0.757) (0.598, 0.756)
6 0.7003 0.6967 0.6597 0.6993 0.6992 0.7017 0.6987 (0.621, 0.775) (0.614, 0.772) (0.578, 0.735) (0.622, 0.775) (0.622, 0.776) (0.625, 0.778) (0.621, 0.774)
10 0.7228 0.7121 0.6713 0.7165 0.7164 0.7230 0.7174 (0.647, 0.793) (0.631, 0.786) (0.593, 0.743) (0.636, 0.788) (0.638, 0.788) (0.645, 0.792) (0.638, 0.787)
20 0.7586 0.7399 0.6876 0.7470 0.7464 0.7606 0.7513 (0.686, 0.825) (0.660, 0.813) (0.608, 0.766) (0.672, 0.820) (0.670, 0.820) (0.686, 0.828) (0.677, 0.822)
50 0.7830 0.7466 0.6976 0.7676 0.7587 0.8011 0.7809 (0.719, 0.842) (0.663, 0.819) (0.627, 0.769) (0.692, 0.837) (0.681, 0.831) (0.735, 0.858) (0.713, 0.843)
100 0.7951 0.7464 0.7042 0.7641 0.7244 0.8397 0.8037 (0.726, 0.858) (0.665, 0.827) (0.630, 0.770) (0.685, 0.834) (0.635, 0.806) (0.778, 0.892) (0.731, 0.866)
150 0.8019 0.7482 0.7099 0.7171 0.6889 0.8677 0.8206 (0.739, 0.860) (0.656, 0.832) (0.636, 0.775) (0.627, 0.802) (0.591, 0.778) (0.811, 0.917) (0.755, 0.883)
200 0.8044 0.7488 0.7122 0.5718 0.5466 0.8877 0.8312 (0.739, 0.863) (0.663, 0.823) (0.642, 0.780) (0.485, 0.680) (0.476, 0.634) (0.838, 0.933) (0.763, 0.890)

AUC, area under the receiver operating characteristic curve; PW, pairwise; SW, stepwise; MM, min–max; MVN, multivariate normal; LR, logistic regression; LASSO, Least Absolute Shrinkage and Selection Operator.

(n0, n1), sample sizes in healthy/diseased groups.

p, the number of markers.