Table 1 Minimum detectable OR from J controls/case, for example minimum detectable OR for 1 control/case, based on a derivation valid for small associations (see Supplement). Note that the percent reduction in the OR only depends on the number of controls per case, subsuming power, α, number of cases, or control marker frequency

1

1.05

1.1

1.2

1.3

1.5

1.75

2

0.0%

-26.5%

2

1.043

1.087

1.17

1.26

1.43

1.65

1.87

13.4%

-9.5%

3

1.041

1.082

1.16

1.25

1.41

1.61

1.82

18.4%

-3.3%

4

1.04

1.079

1.16

1.24

1.40

1.59

1.79

20.9%

0.0%

5

1.039

1.077

1.16

1.23

1.39

1.58

1.78

22.5%

2.0%

10

1.037

1.074

1.15

1.22

1.37

1.56

1.74

25.8%

6.2%

20

1.036

1.072

1.15

1.22

1.36

1.54

1.73

27.5%

8.3%

50

1.036

1.071

1.14

1.21

1.36

1.54

1.71

28.6%

9.7%

100

1.036

1.071

1.14

1.21

1.36

1.53

1.71

28.9%

10.1%

1000

1.035

1.071

1.14

1.21

1.35

1.53

1.71

29.3%

10.5%