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)?
RR=1.89; OR=2.05 RR=2.05; OR=1.89 RR=0.40; OR=0.30 RR=0.30; OR=0.40 RR=2.05; OR=3.0
RR=1.89; OR=2.05
To calculate the observed risk ratio (RR) and odds ratio (OR), we need to understand the number of women who were recalled for further evaluation in both the exposed (U.S. women) and unexposed (U.K. women) groups.
Let's denote:
- R1 as the number of U.S. women recalled for further evaluation
- R2 as the number of U.K. women recalled for further evaluation
- N1 as the total number of U.S. women in the sample
- N2 as the total number of U.K. women in the sample
The observed risk ratio (RR) is calculated as the ratio of the risk of being recalled for further evaluation in the exposed group (R1/N1) to the risk in the unexposed group (R2/N2):
RR = (R1/N1) / (R2/N2)
Similarly, the observed odds ratio (OR) is calculated as the ratio of the odds of being recalled for further evaluation in the exposed group (R1/(N1-R1)) to the odds in the unexposed group (R2/(N2-R2)):
OR = (R1/(N1-R1)) / (R2/(N2-R2))
Let's calculate the observed risk ratio (RR) first:
RR = (14.4%/100) / (7.6%/100)
= 0.144 / 0.076
≈ 1.8947 (rounded to 2 decimal places)
Therefore, the observed risk ratio (RR) is approximately 1.89.
Now, let's calculate the observed odds ratio (OR):
OR = (14.4%/(100-14.4%)) / (7.6%/(100-7.6%))
= 0.144 / 0.076
≈ 1.8947 (rounded to 2 decimal places)
Therefore, the observed odds ratio (OR) is approximately 1.89.
Hence, the correct answer would be: RR=1.89; OR=1.89.