IUDs and infertility A casecontrol study found a history of

IUDs and infertility. A case-control study found a history of intrauterine device use in 89 of 283 infertile women. In contrast, 640 of the 3833 controls had used IUDs.   Calculate the odds ratio and its 95% confidence interval for IUD use and infertility. (Note: Data must first be put into a two-by-two table before the odds ratio is calculated.) Interpret the results.

Solution

a)
ODDS RATIO = 89 : 283 :: 640: 3833 = 89*3833 : 283*640 = 341137 : 181120
b)
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
Probability Succuses( X1 )=89
No.Of Observed (n1)=283
P1= X1/n1=0.314
Proportion 2
Probability Succuses(X2)=640
No.Of Observed (n2)=3833
P2= X2/n2=0.167
C.I = (0.314-0.167) ±Z a/2 * Sqrt( (0.314*0.686/283) + (0.167*0.833/3833) )
=(0.314-0.167) ± 1.96* Sqrt(0.001)
=0.148-0.055,0.148+0.055
=[0.092,0.203]