|
|
Group 1
|
Group 2
|
|
Negative
|
A
|
B
|
|
Positive
|
C
|
D
|
(Table page 316, Young 1997)
odds for the event in group 1 = C / A
odds for the event in group 2 = D / B
odds ratio for group 2 relative to group 1 =
= (odds group 2) / (odds group 1) =
= (A * D) / (B * C)
confidence interval for 95% =
= EXP( X +/- Y)
X =
= LN ((A * D) / (B * C))
Y =
= 1.96 * SQRT((1/A) + (1/B) + (1/C) + (1/D))
where:
• 1.96 is the value for Z from the standard normal distribution with F(Z) = 0.975
If the odds ratio is 1.0, then there is no difference between the two groups. If the 2 groups are comparing an intervention, then this is equivalent to a null hypothesis of no intervention difference.
Small Sample Sizes
If sample sizes are small (less than 10 or 20), then 0.5 is added to each of the factors.
odds ratio = (odds group 2) / (odds group 1) =
= ((A+0.5) * (D+0.5)) / ((B+0.5) * (C+0.5))
confidence interval for 95% =
= EXP( X +/- Y)
X =
= LN (((A+0.5) * (D+0.5)) / ((B+0.5) * (C+0.5)))
Y =
= 1.96 * SQRT((1/ (A+0.5)) + (1/ (B+0.5)) + (1/ (C+0.5)) + (1/ (D+0.5)))
NOTE: I am using sample size as (A + B + C + D).
