A discrete latent factor model for smoking, cancer and mortality

- We use a general population survey to model smoking, onset of cancer and mortality.
- Selection on unobservable factors strongly influences differences in outcomes.
- Joint estimation of the model changes the results substantially.
- Estimated onset of cancer is 5.7 years earlier for heavy versus never-smokers.
- 93% of never- and 82% of heavy-smokers are expected to remain free of cancer by age 75.

This paper investigates the relationship between smoking and ill-health, with a focus on the onset of cancer. A discrete latent factor model for smoking and health outcomes, allowing for these to be commonly affected by unobserved factors, is jointly estimated, using the British Health and Lifestyle Survey (HALS) dataset. Post-estimation predictions suggest the reduction in time-to-cancer to be 5.7 years for those with an exposure of 30 pack-years, compared to never-smokers. Estimation of posterior probabilities for class membership shows that individuals in certain classes exhibit similar observables but highly divergent health outcomes, suggesting that unobserved factors influence outcomes. The use of a joint model changes the results substantially. The results show that failure to account for unobserved heterogeneity leads to differences in survival times between those with different smoking exposures to be overestimated by more than 50% (males, with 30 pack-years of exposure).