We rely on a recent French matched case-control study to investigate the effect of occupational exposure to asbestos on the occurrence of lung cancer. 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 is made possible because the conditional distribution of being a case given the matching variable and the marginal distribution of the matching variable can be computed beforehand based on two studies independent from our dataset. The implications of the fitted model in terms of expected years of life free of lung cancer lost due to the occupational exposure to asbestos are discussed.