Evidence of an increased risk of lung cancer associated with cigarette smoking was sought by Doll and Hill. In one study, 649 lung cancer cases were matched by age, and gender to 649 controls; 647 of the cases and 622 of the control had a history of smoking cigarettes.
a. Name the type of study.
b. Create the appropriate 2X2 table for the study.
Lung Cancer Controls
Smokers 647 622
Nonsmokers 2 27
Total 649 649
c. Calculate the appropriate measure of association for the study.
d. Interpret the results.
a. Matched pairs
c. Use the Chi-square (X^2) method.
X^2 = ∑ (O-E)^2/E, where O = observed frequency and E = expected frequency.
∑ = sum of all the cells.
E = (column total * row total)/grand total
df = n - 1, where n = number of cells
Look up value in X^2 table in the back of your textbook.
d. I'll let you come to your own conclusions.
a. The type of study conducted by Doll and Hill is a matched case-control study.
b. The appropriate 2x2 table for the study would look like this:
Lung Cancer Controls
Smokers 647 622
Non-smokers 2 27
Total 649 649
c. To calculate the appropriate measure of association for the study, we can use the odds ratio. The formula for odds ratio is:
Odds Ratio = (ad)/(bc)
where a = number of exposed cases (smokers with lung cancer),
b = number of unexposed controls (non-smokers without lung cancer),
c = number of unexposed cases (non-smokers with lung cancer),
d = number of exposed controls (smokers without lung cancer).
In this case, a = 647, b = 622, c = 2, and d = 27.
Odds Ratio = (647 * 27) / (2 * 622) = 52769 / 1244 = 42.39 (rounded to two decimal places)
Therefore, the odds ratio is 42.39.
d. The interpretation of the results is that there is a strong positive association between smoking cigarettes and the risk of developing lung cancer. The odds ratio of 42.39 indicates that smokers are 42.39 times more likely to develop lung cancer compared to non-smokers. This suggests a strong link between smoking and lung cancer.