To account for the dynamic aspects of carcinogenesis, we propose a compartmental hidden Markov model in which individuals are either healthy, asymptomatically affected, diagnosed, or deceased. Our model is illustrated using the example of smoking-induced lung cancer.
The model was fitted on a case control study nested in the European Prospective Investigation into Cancer and Nutrition study including 757 incident cases and 1524 matched controls. Model estimation was done through a Markov Chain Monte Carlo algorithm, and predictive abilities of the model were assessed through a simulation study based on the posterior estimates of the model parameters. We considered a logistic function for the risk of entering carcinogenesis. Sensitivity analyses to assess the role of each of model parameters was performed by comparing sub-models on the basis of their (simulated) predictive performances.
We found that once adjusted on its impact on exposure duration, age does not independently drive the risk of lung carcinogenesis, while age at starting smoking in ever smokers, and time since cessation in former smokers were found influential. We estimated the time between onset of malignancy and clinical diagnosis to range from 2 to 4 years. Our approach yielded good performances in reconstructing individual trajectories in both cases (sensitivity >90%) and controls (sensitivity >80%). Results also showed that our data did no support an age-dependent time to diagnosis.
The flexible and general formulation of our compartmental model enables the future incorporation of disease states measured by intermediate markers into the modelling of the natural history of cancer. Together with its ability to elucidate temporal effects of exposure on disease risk, this suggests a large range of applications in chronic disease epidemiology.
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