The Yale Lung Cancer Model for Population Rates (YLCM) is a macro-level population model that directly uses the population distribution of smoking history parameters and a carcinogenesis model for lung cancer, which specifies the relationship between smoking history and disease risk. This provides a flexible platform that can be used with alternative carcinogenesis models for the effect of cigarette smoking, e.g., Two Stage Clonal Expansion (TSCE) (1) and Knoke (2) models. By specifying changes in smoking history parameters that would be expected from tobacco control, the model estimates the impact on lung cancer deaths.
Calibration is used to scale rates generated by a carcinogenesis model so that predicted rates conform to what is observed in the population; but calibration can also be used to introduce temporal factors that correct for temporal effects that are not identified either by the carcinogenesis model or by the smoking history for the population. Calibrated results are realized by model fitting to obtain maximum likelihood estimates of calibration parameters; to do this, a log-linear Poisson regression is used for the multiplicative calibration factor for the rates from the carcinogenesis model. The flexible approach allows it to be readily adapted for quantifying impact of change in smoking behavior on other health outcomes, including all-cause mortality (3), years of life lost due to early deaths from cigarette smoking, and measures of the tobacco exposure burden in the population, e.g., mean pack-years exposure.
Single year of age and birth cohort elements of smoking histories employed by the YLCM are: (a) initiation and cessation probabilities; (b) prevalence of current, former, and never smokers, which can also be derived from (a); and (c) distribution of smoking intensity categories [cigarettes per day (CPD): CPD≤5, 5<CPD≤15, 15<CPD≤25, 25<CPD≤35, 35<CPD≤45, 45<CPD].
Lung cancer mortality among never smokers depends only on age. For current smokers, a carcinogenesis model expresses lung cancer death rates as a function of age at initiation, current age, and smoking intensity, which we represent by a midpoint of a smoking intensity category. We determine the cumulative distribution function of time to initiation from the initiation probabilities, which are the conditional probability that a never smoker at the start of a year becomes a smoker by the end of that year. This is used to determine the probability distribution for age started to smoke given that an individual is a never smoker. For a given smoking intensity category, the probability that an individual smokes with that intensity is one of the smoking history generator (SHG) input parameters. We assume that the distribution of initiation age and intensity are independent. Thus, the lung cancer mortality rate for current smokers at a given age is obtained by combining over the mixture of initiation and intensity distribution in the population.
The lung cancer mortality rate for former smokers depends not only on age at smoking initiation, current age and smoking intensity, but also age at quit smoking. Cessation probabilities are conditional probabilities of quitting at a given age, which yields the distribution of age of cessation given age at initiation and current age of the subject. The lung cancer mortality rate for former smokers is thus obtained by combining this mixture of ages of cessation, initiation and smoking intensity.
Finally, the prevalence of never smokers at a given age, current smokers, and former smokers are combined to yield the overall lung cancer mortality rate.
The lung cancer mortality rate in a population and the rate implied by a carcinogenesis model are related by a multiplicative calibration factor which can depend on age, period and cohort. We employ a log-linear calibration model similar to that used by Luebeck et al.(4), and in this specific instance we only adjust for period and cohort.
The intercept scales rates so that the estimate from the model corresponds to those observed in the population. Temporal elements provide corresponding temporal calibration for the corresponding elements in the carcinogenesis model that do not fit well to the population mortality estimate using only the carcinogenesis model.
References
- Hazelton WD, Jeon J, Meza R, Moolgavkar SH. The FHCRC lung cancer model. Risk Analysis. 2012;32(S1):s99-s116.
- Knoke JD, Shanks TG, Vaughn JW, M.J. T, Burns DM. Lung cancer mortality is related to age in addition to duration and intensity of cigarette smoking: an analysis of CPS-I data. Cancer Epidemiol Biomarkers Prev. 2004;13(6):949-957.
- Holford TR, Meza R, Warner KE, et al. Tobacco control and the reduction in smoking-related premature deaths in the united states, 1964-2012. JAMA. 2014;311(2):164-171.
- Luebeck EG, Moolgavkar SH. Multistage carcinogenesis and the incidence of colorectal cancer. Proc Natl Acad Sci U S A. Nov 12 2002;99(23):15095-15100.
