We analyze the effect of occupational exposure to asbestos on the occurrence of lung cancer based on a recent French case–control (CC) study. We build a large collection of threshold regression models, dataadaptively select a better model by CC-weighted likelihood-based cross-validation and then fit this better model by CC-weighted maximum likelihood. The CC-weighting allows us to draw valid inferences from CC data without relying on a logistic regression. This is possible because the joint distribution of the indicator of being a case and matching variable is available beforehand owing to two studies independent from our data set. The implications of the fitted model in terms of years of life free of lung cancer lost due to the exposure to asbestos are discussed.