Question

Researchers reported that in a sample of U.S. women aged 50 to 54 who underwent mammography, 14.4% were recalled for further evaluation; however, in a similar sample of women undergoing mammography in the United Kingdom, only 7.6% were recalled for further evaluation. What are the observed risk and odds ratios for the association between living in the United States (“exposed”) vs. the United Kingdom (“unexposed”) and being recalled for further evaluation following mammography (outcome)?

Answer 1

The 'odds ratio' can be used for sample based estimates of the ratio of an event occurring in one group to the odds of it occurring in another group. let p1 be the probability of a recall in the US and let p2 be the probability of a recall in the UK. The odds ratio is given by:
\[\large OR=\frac{\frac{p _{1}}{1-p _{1}}}{{\frac{p _{2}}{1-p _{2}}}}\ ........(1)\]
Substituting the given values into (1) gives:
\[\large OR=\frac{0.144\times (1-0.076)}{0.076\times (1-0.144)}=you\ can\ calculate\]