Question

In a recent survey of people aged 50-71 in the United States, during a follow-up period the annual probability of lung cancer occurrence was about 0.00023 for people who had never smoked and about 0.01284 for current smokers who smoked more than two packs per day. (a) Find and interpret the relevant difference in proportions. (b) Find and interpret the relevant relative risk. (c) Which measure would you say is more informative, and why? (d) For a different type of cancer, the relative risk for smokers vs. non-smokers is 3.10. Can we say this is a concerning increase in risk from a practical point of view? Explain why or why not.

Answer 1

a) difference in proportion = attributable risk

= 0.01284 - 0.00023 = 0.01261 or 1.26%

This is the risk difference that is the risk of having a lung cancer due to smoking only.

b) relative risk =( probabaility of lung cancer among smokers)/(probability of lung cancer among non smokers)

= 0.01284/0.00023 = 55.826

This tells that it is 55. 8 times highly likely for a smoker to have lung cancer than a non smoking person.

C) relative risk actually tells the magnitude of association in between the exposure condition and the disease

while risk difference or attributable risk only tells the number of cases of disease that could be caused due to the exposure only by removing the number of cases that could have been due to other causes.

So, relative risk appears to be more informative than the other one.

D) yes it is a concerning increase in risk as here it is thrice likely to be sick of cancer for a smoker person than a non smoker which is quite higher.

But if you compare it with the case of the lung cancer (a and b) you will be find that smoking is actually not that dangerous as it is in case of lung cancer .