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 7.3.4). Interpret.
TABLE 2.11 Data for Problem 2.18
Number of Cigarettes
Source: Reprinted with permission from R. Doll and A. B. Hill, British Med. J. 2: 1271-1286(1952.