Multistage Clonal Expansion Models Research Articles

Multistage carcinogenesis: Impact of age, genetic, and environmental factors on the incidence of malignant mesothelioma

The current paradigm of carcinogenesis as a cellular evolutionary process driven by mutations of a few critical driver genes has immediate logical implications for the epidemiology of cancer. These include the impact of age on cancer risk, the role played by inherited tumor predisposition syndromes, and the interaction of genetics and environmental exposures on cancer risk. In this paper, we explore the following logical epidemiological consequences of carcinogenesis as a clonal process of mutation accumulation, with special emphasis on asbestos-related cancers, specifically malignant mesothelioma:1 All cancers, including mesothelioma, can and do occur spontaneously, i.e., in the absence of exposure to any environmental carcinogens. 2. Age is an important determinant of cancer risk, with or without exposure to environmental carcinogens. 3. Genetic tumor predisposition syndromes, such as the BAP1 syndrome, increase enormously the risk of cancer even in the absence of exposure to environmental carcinogens. We illustrate these concepts by applying a multistage clonal expansion model to U.S. Surveillance, Epidemiology, and End Results cancer registry data for pleural and peritoneal malignant mesotheliomas in 1975–2018.

Case Studies of Gastric, Lung, and Oral Cancer Connect Etiologic Agent Prevalence to Cancer Incidence.

Obtaining detailed individual-level data on both exposure and cancer outcomes is challenging, and it is difficult to understand and characterize how temporal aspects of exposures translate into cancer risk. We show that, in lieu of individual-level information, population-level data on cancer incidence and etiologic agent prevalence can be leveraged to investigate cancer mechanisms and to better characterize and predict cancer trends. We use mechanistic carcinogenesis models [multistage clonal expansion (MSCE) models] and data on smoking, Helicobacter pylori (H. pylori), and HPV infection prevalence to investigate trends of lung, gastric, and HPV-related oropharyngeal cancers. MSCE models are based on the initiation-promotion-malignant conversion paradigm and allow for interpretation of trends in terms of general biological mechanisms. We assumed the rates of initiation depend on the prevalence of the corresponding risk factors. We performed two types of analysis, using the agent prevalence and cancer incidence data to estimate the model parameters and using cancer incidence data to infer the etiologic agent prevalence as well as the model parameters. By including risk factor prevalence, MSCE models with as few as three parameters closely reproduced 40 years of age-specific cancer incidence data. We recovered trends of H. pylori prevalence in the United States and demonstrated that cohort effects can explain the observed bimodal, age-specific pattern of oral HPV prevalence in men. Our results demonstrate the potential for joint analyses of population-level cancer and risk factor data through mechanistic modeling. This approach can be a first step in systematically testing relationships between exposures and cancer risk when individual-level data is lacking.Significance: Analysis of trends in risk-factor prevalence and cancer incidence can shed light on cancer mechanisms and the way that carcinogen exposure through time shapes the risk of cancer at different ages.Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/78/12/3386/F1.large.jpg Cancer Res; 78(12); 3386-96. ©2018 AACR.

Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis.

Many cancers are understood to be the product of multiple somatic mutations or other rate-limiting events. Multistage clonal expansion (MSCE) models are a class of continuous-time Markov chain models that capture the multi-hit initiation–promotion–malignant-conversion hypothesis of carcinogenesis. These models have been used broadly to investigate the epidemiology of many cancers, assess the impact of carcinogen exposures on cancer risk, and evaluate the potential impact of cancer prevention and control strategies on cancer rates. Structural identifiability (the analysis of the maximum parametric information available for a model given perfectly measured data) of certain MSCE models has been previously investigated. However, structural identifiability is a theoretical property and does not address the limitations of real data. In this study, we use pancreatic cancer as a case study to examine the practical identifiability of the two-, three-, and four-stage clonal expansion models given age-specific cancer incidence data using a numerical profile-likelihood approach. We demonstrate that, in the case of the three- and four-stage models, several parameters that are theoretically structurally identifiable, are, in practice, unidentifiable. This result means that key parameters such as the intermediate cell mutation rates are not individually identifiable from the data and that estimation of those parameters, even if structurally identifiable, will not be stable. We also show that products of these practically unidentifiable parameters are practically identifiable, and, based on this, we propose new reparameterizations of the model hazards that resolve the parameter estimation problems. Our results highlight the importance of identifiability to the interpretation of model parameter estimates.

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes.

Age Effects and Temporal Trends in HPV-Related and HPV-Unrelated Oral Cancer in the United States: A Multistage Carcinogenesis Modeling Analysis.

Differences in prognosis in HPV-positive and HPV-negative oral (oropharyngeal and oral cavity) squamous cell carcinomas (OSCCs) and increasing incidence of HPV-related cancers have spurred interest in demographic and temporal trends in OSCC incidence. We leverage multistage clonal expansion (MSCE) models coupled with age—period—cohort (APC) epidemiological models to analyze OSCC data in the SEER cancer registry (1973–2012). MSCE models are based on the initiation—promotion—malignant conversion paradigm in carcinogenesis and allow for interpretation of trends in terms of biological mechanisms. APC models seek to differentiate between the temporal effects of age, period, and birth cohort on cancer risk. Previous studies have looked at the effect of period and cohort on tumor initiation, and we extend this to compare model fits of period and cohort effects on each of tumor initiation, promotion, and malignant conversion rates. HPV-related, HPV-unrelated except oral tongue, and HPV-unrelated oral tongue sites are best described by placing period and cohort effects on the initiation rate. HPV-related and non-oral-tongue HPV-unrelated cancers have similar promotion rates, suggesting similar tumorigenesis dynamics once initiated. Estimates of promotion rates at oral tongue sites are lower, corresponding to a longer sojourn time; this finding is consistent with the hypothesis of an etiology distinct from HPV or alcohol and tobacco use. Finally, for the three subsite groups, men have higher initiation rates than women of the same race, and black people have higher promotion than white people of the same sex. These differences explain part of the racial and sex differences in OSCC incidence.

Impact of Tumor Progression on Cancer Incidence Curves

Cancer arises through a multistage process, but it is not fully clear how this process influences the age-specific incidence curve. Studies of colorectal and pancreatic cancer using the multistage clonal expansion (MSCE) model have identified two phases of the incidence curves. One phase is linear, beginning about age of 60 years, suggesting that at least two rare rate-limiting mutations occur before clonal expansion of premalignant cells. A second phase is exponential, seen in early-onset cancers occurring before the age of 60 years that are associated with premalignant clonal expansion. Here, we extend the MSCE model to include clonal expansion of malignant cells, an advance that permits study of the effects of tumor growth and extinction on the incidence of colorectal, gastric, pancreatic, and esophageal adenocarcinomas in the digestive tract. After adjusting the age-specific incidence for birth-cohort and calendar-year trends, we found that initiating mutations and premalignant cell kinetics can explain the primary features of the incidence curve. However, we also found that the incidence data of these cancers harbored information on the kinetics of malignant clonal expansion before clinical detection, including tumor growth rates and extinction probabilities on three characteristic time scales for tumor progression. In addition, the data harbored information on the mean sojourn times for premalignant clones until occurrence of either the first malignant cell or the first persistent (surviving) malignant clone. Finally, the data also harbored information on the mean sojourn time of persistent malignant clones to the time of diagnosis. In conclusion, cancer incidence curves can harbor significant information about hidden processes of tumor initiation, premalignant clonal expansion, and malignant transformation, and even some limited information on tumor growth before clinical detection.

Number and Size Distribution of Colorectal Adenomas under the Multistage Clonal Expansion Model of Cancer

Colorectal cancer (CRC) is believed to arise from mutant stem cells in colonic crypts that undergo a well-characterized progression involving benign adenoma, the precursor to invasive carcinoma. Although a number of (epi)genetic events have been identified as drivers of this process, little is known about the dynamics involved in the stage-wise progression from the first appearance of an adenoma to its ultimate conversion to malignant cancer. By the time adenomas become endoscopically detectable (i.e., are in the range of 1–2 mm in diameter), adenomas are already comprised of hundreds of thousands of cells and may have been in existence for several years if not decades. Thus, a large fraction of adenomas may actually remain undetected during endoscopic screening and, at least in principle, could give rise to cancer before they are detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of when the colon is screened for neoplasia and as a function of the achievable detection limit. To this end, we have derived mathematical expressions for the detectable adenoma number and size distributions based on a recently developed stochastic model of CRC. Our results and illustrations using these expressions suggest (1) that screening efficacy is critically dependent on the detection threshold and implicit knowledge of the relevant stem cell fraction in adenomas, (2) that a large fraction of non-extinct adenomas remains likely undetected assuming plausible detection thresholds and cell division rates, and (3), under a realistic description of adenoma initiation, growth and progression to CRC, the empirical prevalence of adenomas is likely inflated with lesions that are not on the pathway to cancer.

Evaluation of screening strategies for pre-malignant lesions using a biomathematical approach

We derive mathematical expressions for the size distribution of screen-detectable pre-malignant lesions, both conditional and unconditional on no prior detection of cancer in the tissue of interest, based on a general multistage clonal expansion model of carcinogenesis. We apply these expressions to simulate the natural history of colorectal cancer and to evaluate the effect of a screen for adenomatous polyps and concomitant intervention on cancer risk. Our approach allows the efficient simulation of multiple screens and interventions and determination of the optimal timing of the screens. We further demonstrate the utility of our approach by computing the benefits of up to two colonoscopies on the lifetime risk of colorectal cancer.

Systems biological and mechanistic modelling of radiation-induced cancer

This paper summarises the five presentations at the First International Workshop on Systems Radiation Biology that were concerned with mechanistic models for carcinogenesis. The mathematical description of various hypotheses about the carcinogenic process, and its comparison with available data is an example of systems biology. It promises better understanding of effects at the whole body level based on properties of cells and signalling mechanisms between them. Of these five presentations, three dealt with multistage carcinogenesis within the framework of stochastic multistage clonal expansion models, another presented a deterministic multistage model incorporating chromosomal aberrations and neoplastic transformation, and the last presented a model of DNA double-strand break repair pathways for second breast cancers following radiation therapy.

Symmetry, Identifiability, and Prediction Uncertainties in Multistage Clonal Expansion (MSCE) Models of Carcinogenesis

Many models of exposure-related carcinogenesis, including traditional linearized multistage models and more recent two-stage clonal expansion (TSCE) models, belong to a family of models in which cells progress between successive stages-possibly undergoing proliferation at some stages-at rates that may depend (usually linearly) on biologically effective doses. Biologically effective doses, in turn, may depend nonlinearly on administered doses, due to PBPK nonlinearities. This article provides an exact mathematical analysis of the expected number of cells in the last ("malignant") stage of such a "multistage clonal expansion" (MSCE) model as a function of dose rate and age. The solution displays symmetries such that several distinct sets of parameter values provide identical fits to all epidemiological data, make identical predictions about the effects on risk of changes in exposure levels or timing, and yet make significantly different predictions about the effects on risk of changes in the composition of exposure that affect the pharmacodynamic dose-response relation. Several different predictions for the effects of such an intervention (such as reducing carcinogenic constituents of an exposure) that acts on only one or a few stages of the carcinogenic process may be equally consistent with all preintervention epidemiological data. This is an example of nonunique identifiability of model parameters and predictions from data. The new results on nonunique model identifiability presented here show that the effects of an intervention on changing age-specific cancer risks in an MSCE model can be either large or small, but that which is the case cannot be predicted from preintervention epidemiological data and knowledge of biological effects of the intervention alone. Rather, biological data that identify which rate parameters hold for which specific stages are required to obtain unambiguous predictions. From epidemiological data alone, only a set of equally likely alternative predictions can be made for the effects on risk of such interventions.

Analysis of radiation effects using a combined cell cycle and multistage carcinogenesis model

Purpose To study radiation effects using a combined cell cycle and multistage clonal expansion model that includes processes of damage, repair, apoptosis, and mutation. The model includes endogenous and radiation induced damage causing progression of cells from normal, to damaged, to initiated, to initiated damage, to malignant status. We utilize complementary deterministic and stochastic versions of the model that share the same transition rates. The deterministic version is used to calibrate model rates for cell cycle progression, damage, checkpoint delay, repair, and apoptosis, and to implement tissue homeostasis. The stochastic version is used to predict the cancer hazard and survival. Results We calibrated transition rates in the deterministic version of the model to fit flow cytometry-based clonogenic survival data for Chinese hamster V79 cells and for HeLa × skin fibroblast human hybrid cells exposed to sparsely ionizing radiation during different phases of the cell cycle. We also calibrated repair and malignant transformation rates to fit neoplastic transformation data for HeLa × skin fibroblast human hybrid cells. We found that induced repair in G2 phase explained the low-dose hypersensitivity for survival in both cell lines, and a different induced repair process explained the neoplastic transformation data. Conclusion The shape of the induced repair curves for G2-phase survival and neoplastic transformation differ significantly, suggesting that these low-dose phenomena differ in regulation and, in fact, may be mechanistically unrelated.