Threshold Regression Models Adapted to Case-Control Studies, and the Risk of Lung Cancer Due to Occupational Exposure to Asbestos in France

Asbestos has been known for many years as a powerful carcinogen. Our purpose is quantify the relationship between an occupational exposure to asbestos and an increase of the risk of lung cancer. Furthermore, we wish to tackle the very delicate question of the evaluation, in subjects suffering from a lung cancer, of how much the amount of exposure to asbestos explains the occurrence of the cancer. For this purpose, we rely on a recent French case-control study. We build a large collection of threshold regression models, data-adaptively select a better model in it by multi-fold likelihood-based cross-validation, then fit the resulting better model by maximum likelihood. A necessary preliminary step to eliminate the bias due to the case-control sampling design is made possible because the probability distribution of being a case can be computed beforehand based on an independent study. The implications of the fitted model in terms of a notion of maximum number of years of life guaranteed free of lung cancer are discussed