Question

21. in a clinical trial of 2038 subjects treated with a certain​ drug, 22 reported headaches. In a control group of 1588 subjects given a​ placebo, 25 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

Pt/(1-Pt)/

Pc/(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 risk=____

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

Find the Odds ratio for the headache data

The odds ration_____

(Round to three decimal places as​ needed.)

Answer 1

	Event	No Event
Treatment	a	b
Control	c	d

Relative risk = risk in treatment group / risk in control group

= (a/(a+b)) / (c/(c+d))

Odds ratio

= odds in treatment group/ odds in control group

= (a/b) /(c/d) = ad/bc

Now ,

here a = 22, b = 2038-22 = 2016

c = 25 d = 1588 -25 = 1563

Thus, relative risk = (22/2028) / (25/1588)

= 22*1588 / 2028*25

= 0.689

Odds ratio = 22*1563 / 2016*25

= 0.682