Question

g (15 points) Suppose 42 out of 600 rats exposed to a potential carcinogen develop tumors. A control group of 350 rats not exposed to the carcinogen develops 13 tumors. Based on these data, computed (a) the relative risk, (b) the attributable risk, and (c) the odds ratio. Do these indicators suggest that there is a relationship between exposure and tumor risk

Answer 1

a) The relative risk is 1.8
`\overline{846153}`

b) The attributable risk is
`0.69 \overline{047619}`

c) There is a relationship between exposure and tumor risk

Explanation:

The number of exposed rats that develop tumors, a = 42

The number of rats exposed to the carcinogen = 600 rats

The number of exposed rats that did not develop tumors, b = 600 - 42 = 558

The number of not exposed rats in the control group = 350 rats

The number of rats that develop tumors in the control group, c = 13 tumors

The number of not exposed rats that did not develop tumors, d = 350 - 13 = 337 rats

a) The relative risk, RR = a/(a + b)/(c/(c + d))

∴ RR = (42/(42 + 558))/(13/(13 + 337)) = 49/26 = 1.8
`\overline{846153}`

b) The attributable risk = (a - c)/a

∴ The attributable risk = (42 - 13)/42 =
`0.69 \overline{047619}`

c) The odds ratio = (a·b)/(c·d)

∴ The odds ratio = 42 × 558/(13 × 337) = 23439/4381 ≈ 5.35

Given that the result of attributable risk is positive, there is an indication that there is a higher probability to develop tumor when exposed to the potential carcinogen, therefore, there is a relationship between exposure and tumor risk