In a certain noisy factory, workers are provided with earplugs and are expected
ID: 3298040 • Letter: I
Question
In a certain noisy factory, workers are provided with earplugs and are expected to wear them. An industrial hygienist inspecting the plant found that 100 of the 500 workers in the factory were not wearing their earplugs because they regarded them as uncomfortable and a nuisance. When all the workers were given a hearing test, it was found that 16 of the earplug wearers and 40 of the nonwearers had developed significant hearing loss. All had had normal hearing at their preemployment examinations 4 years earlier, when the plant opened
What was the cumulative incidence rate of hearing loss in workers who did not wear earplugs?
What was the relative risk of hearing loss in workers who did not wear earplugs, compared with those who did?
What was the risk of hearing loss attributable to not wearing earplugs? (i.e., what was the risk difference?)
What proportion of hearing loss in the nonwearers was attributable to not wearing earplugs?
What proportion of the hearing loss in all the workers was attributable to not wearing earplugs?
Explanation / Answer
Solution:
1. What was the cumulative incidence rate of hearing loss in workers who did not wear earplugs?
Cumulative incidence rate = (40 / 100) / (16 / 400) = 10
Thus, not wearing earplugs increase the risk of hearing loss 10 times.
2. What was the relative risk of hearing loss in workers who did not wear earplugs, compared with those who did?
Event A: getting ear damage
Event B: not wearing plugs
P (B) = 100/500=1/5
P (not B) = 1-1/5 = 4/5
P (A|B) =10/500= 1/50 = P (A and B)/P (B)
P (A and B) = 1/50 *1/5 = 1/250
P (A| not B) = 4/500= 1/125 = P (A and not B)/P (not B)
P (A and not B) = 1/125 * 4/5 = 4/625
P(A) = P(A and B) + P( A and not B) = 1/250 +4/625= 26/2500
3. What was the risk of hearing loss attributable to not wearing earplugs? (i.e., what was the risk difference?)
The risk difference (attributable risk), i.e., the risk in the exposed - the risk in the unexposed is the risk associated with exposure.
Risk difference = (40 / 100) - (16 / 400) = 0.36
Thus, not wearing earplugs increase the risk of hearing loss by 36%.
4. What proportion of hearing loss in the non wearers was attributable to not wearing earplugs?
Required Proportion = (Number of hearing loss in non wearers)/ ( Number of non – wearer) = 10/100 = 0.1
5. What proportion of the hearing loss in all the workers was attributable to not wearing earplugs?
Required Proportion = (Number of hearing loss in non wearers)/ ( Number of workers) = 10/500 = 0.02