Question

In a clinical trial of

20922092

subjects treated with a certain​ drug,

2626

reported headaches. In a control group of

17551755

subjects given a​ placebo,

2424

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 left parenthesis 1 minus p Subscript t Baseline right parenthesis Over p Subscript c Baseline divided by left parenthesis 1 minus p Subscript c Baseline right parenthesis EndFractionpt/1−ptpc/1−pc.

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?

Find the relative risk for the headache data.

The relative

riskequals=0.909 0.909

​(Round to three decimal places as​ needed.)

Find the odds ratio for the headache data.

The odds

ratio

Answer 1

	Headache
	Yes	No	Total
Cases	26	2066	2092
Control	24	1731	1755
Total	50	3797	3847

Odds Ratio = (a/c)/(b/d) = (26/24)/(2066/1731) = 0.91

The odds are 0.91 times higher that People will have headache in Treatment than those in the control group.