Question: Use of Oral Contraceptives and Thromboembolism

In their paper “Thromboembolism and Oral Contraceptives: an Epidemiologic Case-Control Study” Sartwell et al. (1969) conducted a case-control study to examine the potential relationship between thromboembolism and oral contraceptive use. The cases were 175 women of reproductive age (15 – 44), discharged alive from 43 hospitals in five cities after initial attacks of idiopathic (i.e. of unknown cause) thrombophlebitis, pulmonary embolism, or cerebral thrombosis or embolism. The controls were matched with their cases for hospital, residence, time of hospitalization, race, age, marital status, parity, and pay status. More specifically, the controls were female patients from the same hospital during the same 6-month interval. The controls were within 5 years of age and matched on parity (0, 1, 2, 3, or more prior pregnancies). The hospital pay status (ward, semi-private, or private) was the same. The data for oral contraceptive use are presented in the table below:

a) Do these data provide evidence that the population proportion of oral contraceptive use amongst cases is greater than the population proportion of oral contraceptive use amongst similar controls? (4 pts.)

b) OR for Dependent Samples or Matched-Pair Data
(This is NOT in Powerpoint, you are seeing it here for the first time)

The estimated odds ratio (OR) from matched-pair data is given by

Note: b and c are as defined in the Powerpoint on Comparing Two Population Proportions Using Dependent Samples

\[\text{Estimated }OR=\frac{b}{c}\]

and one form of the 95% CI for the OR is as follows:

\[OR\pm 1.96\cdot \left( 1+\frac{b}{c} \right)\sqrt{\frac{b}{c(b+c)}}\]

Find a 95% CI for the OR in this study and interpret. (4 pts.)