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Table 2 Bisection procedure to determine log-odds ratio for treatment in a logistic regression model to produce a binary outcome with a given relative risk (target relative risk: 0.80)

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

Iteration

Target relative risk

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

Empirical relative risk

1

0.8

0

1

2

0.8

-5

0.010792

3

0.8

-2.5

0.12165

4

0.8

-1.25

0.371719

5

0.8

-0.625

0.621492

6

0.8

-0.3125

0.792433

7

0.8

-0.15625

0.891377

8

0.8

-0.23438

0.840727

9

0.8

-0.27344

0.81629

10

0.8

-0.29297

0.804289

11

0.8

-0.30273

0.798343

12

0.8

-0.29785

0.801312

13

0.8

-0.30029

0.799827

14

0.8

-0.29907

0.800569

15

0.8

-0.29968

0.800198

16

0.8

-0.29999

0.800012