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Table 2.11 refers to a retrospective study of lung cancer and tobacco smoking among patients in several English hospitals. The table com­pares male lung cancer patients with control patients having...

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Table 2.11 refers to a retrospective study of lung cancer and tobacco smoking among patients in several English hospitals. The table com­pares male lung cancer patients with control patients having other diseases, according to the average number of cigarettes smoked daily over a 10-year period preceding the onset of the disease.

a. Find the sample odds of lung cancer at each smoking level and the five odds ratios that pair each level of smoking with no smoking. As smoking increases, is there a trend? Interpret.

b. If the log odds of lung cancer is linearly related to smoking level, the log odds in row i satisfies log(oddsi)= α -βi. Show that this implies that the local odds ratios are identical.

c. Using these data, can you estimate the probability of lung cancer at each level of smoking? Are the estimated odds ratios in part (a) meaningful? Explain.

d. Show that the disease groups are stochastically ordered with respect to their distributions on smoking of cigarettes (see Problem 2.34 and Section XXXXXXXXXXInterpret.

TABLE 2.11 Data for Problem 2.18

 

Disease Group

Daily Average

Lung Cancer

Control

Number of Cigarettes

Patients

Patients

None

7

61

<5

55

129

5-14

489

570

15-24

475

431

25-49

293

154

50 +

38

12

    

Source: Reprinted with permission from R. Doll and A. B. Hill, British MedJ2: XXXXXXXXXX.

Answered Same DayDec 29, 2021

Solution

David answered on Dec 29 2021
55 Votes
2.18. Table 2.11 refers to a retrospective study of lung cancer and tobacco smoking among
patients in several English hospitals. The table compares male lung cancer patients with control
patients having other diseases, according to the average number of cigarettes smoked daily over
a 10-year period preceding the onset of the disease. The lung cancer group has n = 1357, and the
control group has n = 1357.
a) Find the sample odds of lung cancer at each smoking level and the five odds ratios that pair
each level of smoking with no smoking. As smoking increases, is there a trend? Interpret.
Daily Avg. No. of Cigarettes Odds of Lung Cancer Ln(Odds)
None 0.114754 -2.164964
5 0.426357 -0.852479
5 – 14 0.857895 -0.153274
15 – 24 1.102088 0.097207
25 – 49 1.902597 0.643220
50 + 3.166667 1.152680
The odds ratios are:
For < 5 v. None, the odds ratio is
7154.3
2112
2211 
nn
nn
 .
For 5 – 14 v. None, the odds ratio is
4759.7
2112
2211 
nn
nn
 .
For 15 – 24 v. None, the odds ratio is
6039.9
2112
2211 
nn
nn
 .
For 25 – 49 v. None, the odds ratio is
5798.16
2112
2211 
nn
nn
 .
For 50 + v. None, the odds ratio is
5953.27
2112
|2211

nn
nn
 .
These odds ratios must be interpreted carefully, due to the retrospective nature of the study.
Consider the random...
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