In a clinical trial of 2165 subjects treated with a certain drug, 21 reported headaches. In a control group of 1718 subjects gi
ven a placebo, 23 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control (placebo) group by pc, the relative risk is pt/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating StartFraction p Subscript t Baseline divided by (1 minus p Subscript t Baseline )Over p Subscript c Baseline divided by (1 minus p Subscript c Baseline )EndFraction . The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug treatment?
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Explanation
Let's first graph the elements:
Using the distance formula we get:
