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Table 3 Bisection procedure to determine \(\sigma\) for multiplying the coefficients of a logistic regression model to produce a binary outcome such that the outcomes model has a given c-statistic (target c-statistic: 0.80)

From: The iterative bisection procedure: a useful tool for determining parameter values in data-generating processes in Monte Carlo simulations

Iteration

Target c-statistic

\(\sigma_{{}}^{{{\text{midpoint}}}}\)

Empirical c-statistic \({\text{(AUC}}^{{\sigma^{{{\text{midpoint}}}} }} )\)

1

0.8

5

0.983782

2

0.8

2.5

0.944541

3

0.8

1.25

0.868001

4

0.8

0.625

0.742962

5

0.8

0.9375

0.821941

6

0.8

0.78125

0.788305

7

0.8

0.859375

0.805549

8

0.8

0.820313

0.79756

9

0.8

0.839844

0.801353

10

0.8

0.830078

0.798494

11

0.8

0.834961

0.800622