Use of multistage models to infer stage affected by carcinogenic exposure: Example of lung cancer and cigarette smoking

Abstract

Statistical methods based on the Armitage-Doll mathematical model of the carcinogenic process are presented for analyzing epidemiologic case-control studies of cancer. These methods are proposed to provide inferences regarding the stage(s) in the cancer process at which the exposure of interest acts. An example of these methods is given which shows evidence that carcinogens in cigarette smoke appear to affect the transition rates for two separate stages in the development of lung cancer, and the relative magnitudes of these effects are estimated. The data for this analysis came from a European multi-center case-control study of lung cancer.

The results of the analysis show that: (1) the relative risk of lung cancer among continuing smokers compared to nonsmokers of the same age decreases as the age started smoking increases, while the rate of smoking stays fixed, a result which indicates a carcinogenic effect on an early stage in the process; and (2) the relative risk among ex-smokers compared to continuing smokers having the same duration and rate of smoking decreases with time since smoking stopped, a result which indicates a carcinogenic effect on a late stage in the process. Both results are shown to be best described by the hypothesis that cigarette smoking affects two stages. The estimated relative magnitudes of cigarettes' carcinogenic effects on the two stages indicate that the largest proportion of the total lifetime lung cancer risk among continuing smokers is due to its late stage effect, and that the proportion of risk due to causes other than smoking varies from 23% among men smoking 1–10 cigarettes per day to 6% among those smoking greater than 30 cigarettes per day. These findings imply that preventive measures directed toward inducing smokers to stop would have a potentially substantial payoff in reducing future lung cancer mortality.