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. Author manuscript; available in PMC: 2023 Mar 1.
Published in final edited form as: Stat Med. 2021 Feb 2;40(7):1767–1789. doi: 10.1002/sim.8869

Table 1.

Attained lower and upper bounds of the AUC for some given values of the length.

length lower bound of AUC upper bound of the AUC
2 0.50000 0.50000
1.65 0.77788 0.85729
1.75 0.85417 0.92719
1.85 0.91838 0.97379
1.95 0.97434 0.99709
2.00 1.00000 1.00000