New stochastic carcinogenesis model with covariates: an approach involving intracellular barrier mechanisms

Abstract

In this paper we present a new multiple-pathway stochastic model of carcinogenesis with potential of predicting individual incidence risks on the basis of biomedical measurements. The model incorporates the concept of intracellular barrier mechanisms in which cell malignization occurs due to an inefficient operation of barrier cell mechanisms, such as antioxidant defense, repair systems, and apoptosis. Mathematical formalism combines methodological innovations of mechanistic carcinogenesis models and stochastic process models widely used in studying biodemography of aging and longevity. An advantage of the modeling approach is in the natural combining of two types of measures expressed in terms of model parameters: age-specific hazard rate and means of barrier states. Results of simulation studies allow us to conclude that the model parameters can be estimated in joint analyses of epidemiological data and newly collected data on individual biomolecular measurements of barrier states. Respective experimental designs for such measurements are suggested and discussed. An analytical solution is obtained for the simplest design when only age-specific incidence rates are observed. Detailed comparison with TSCE model reveals advantages of the approach such as the possibility to describe decline in risk at advanced ages, possibilities to describe heterogeneous system of intermediate cells, and perspectives for individual prognoses of cancer risks. Application of the results to fit the SEER data on cancer risks demonstrates a strong predictive power of the model. Further generalizations of the model, opportunities to measure barrier systems, biomedical and mathematical aspects of the new model are discussed.

Figure 1

Two Stage Clonal Expansion model.

Figure 2

Scheme of the compartmental model of sequential breaking of barrier mechanisms. Transfers correspond to the failure of a specific barrier.

Figure 3. Typical shape of age dependence of cancer risk provided by the TSCE model a) and two versions of BBM models, i.e., the minimal and reduced models given by eqs (4.3) and (4.4)

Figure 4

Age-patterns of cancer incidence rates (dots and standard error bars) calculated using SEER data and BBM model prediction (solid lines) for age patterns of 15 cancer sites.

Figure 5

Lymphoid Leukemia incidence rate (dots and error bars) and predictions by the extended BBM model (solid lines).