Incorporation of inter-individual heterogeneity into the multistage carcinogenesis model: approach to the analysis of cancer incidence data

We investigate a multistage carcinogenesis frailty model to incorporate inter-individual heterogeneity into carcinogenic response. Attention is focused on inference concerning the effects of different sources of population heterogeneity on cancer rates. The authors consider unobserved variability arising from either carcinogen exposure or background characteristics. Gamma and Inverse-Gaussian distributions are selected for frailty models, and the baseline hazard function is the generalized Armitage-Doll model (i.e. non-frailty model) in which exposure effects shift the age scale instead of acting multiplicatively on cancer rates. For illustration, we apply the method to solid cancer data from a cohort of atomic bomb survivors to examine some features of proposed models. The results show that the Gamma frailty model for the heterogeneity of baseline rates provides the best goodness-of-fit of the model and a non-zero frailty variance. Parameter estimates are, for the most part, comparable between the Gamma and Inverse-Gaussian frailty models. In a heterogeneous population the exposure effects on young adulthood cancer rates might be underestimated for the non-frailty model. Meaningful information regarding each source of heterogeneity has been provided by the proposed method. Therefore, the multistage carcinogenesis frailty model approach is useful for analyses of epidemiological cancer data to assess population heterogeneity and heterogeneity-influenced exposure effects.     

Heterogeneity in multistage carcinogenesis and mixture modeling

Carcinogenesis is commonly described as a multistage process, in which stem cells are transformed into cancer cells via a series of mutations. In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way. We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts. Maximum likelihood estimation does not perform well in this application due to the heavy censoring in our data. We thus use analytic graduation instead. Very good fits are achieved for models that combine a small high risk group with a large group that is quasi immune.     

Optimal Designs for Estimating the Percentiles of the Risk in Multistage Models of Carcinogenesis

The multistage carcinogenesis models describe a process by which a normal cell becomes malignant and gives rise to a tumor. This paper aims at evaluating the percentiles of the risk function derived as dose-response relationship in a multi-stage model. These percentiles have been known as “virtual safe dose” levels or risk specific dose levels. The optimal design theory is applied to estimate the appropriate percentile and the sequential approach of design is adopted through a stochastic approximation scheme. If the initial design is D-optimal the limit design is D-optimal as well and it is the one with the minimum entropy.     

A stochastic carcinogenesis model incorporating multiple types of genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.     

Modeling progression in radiation-induced lung adenocarcinomas

Quantitative multistage carcinogenesis models are used in radiobiology to estimate cancer risks and latency periods (time from exposure to clinical cancer). Steps such as initiation, promotion and transformation have been modeled in detail. However, progression, a later step during which malignant cells can develop into clinical symptomatic cancer, has often been approximated simply as a fixed lag time. This approach discounts important stochastic mechanisms in progression and evidence on the high prevalence of dormant tumors. Modeling progression more accurately is therefore important for risk assessment. Unlike models of earlier steps, progression models can readily utilize not only experimental and epidemiological data but also clinical data such as the results of modern screening and imaging. Here, a stochastic progression model is presented. We describe, with minimal parameterization: the initial growth or extinction of a malignant clone after formation of a malignant cell; the likely dormancy caused, for example, by nutrient and oxygen deprivation; and possible escape from dormancy resulting in a clinical cancer. It is shown, using cohort simulations with parameters appropriate for lung adenocarcinomas, that incorporating such processes can dramatically lengthen predicted latency periods. Such long latency periods together with data on timing of radiation-induced cancers suggest that radiation may influence progression itself.     

Spatial Stochastic Models for Cancer Initiation and Progression

The multistage carcinogenesis hypothesis has been formulated by a number of authors as a stochastic process. However, most previous models assumed “perfect mixing” in the population of cells, and included no information about spatial locations. In this work, we studied the role of spatial dynamics in carcinogenesis. We formulated a 1D spatial generalization of a constant population (Moran) birth–death process, and described the dynamics analytically. We found that in the spatial model, the probability of fixation of advantageous and disadvantageous mutants is lower, and the rate of generation of double-hit mutants (the so-called tunneling rate) is higher, compared to those for the space-free model. This means that the results previously obtained for space-free models give an underestimation for rates of cancer initiation in the case where the first event is the generation of a double-hit mutant, e.g. the inactivation of a tumor-suppressor gene.     

Integration of positive and negative growth signals during ras pathway activation in vivo

Expression of RAS proteins can have either positive or negative effects on cell growth, differentiation and death. New technologies are being developed for the generation of animal models to address the questions of where, when and how much Ras is expressed during tumorigenesis, and how these disparate signals are integrated during multistage carcinogenesis.     

Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.     

Bayesian area–age–period–cohort model with carcinogenesis age effects in estimating cancer mortality

Objective: Area–age–period–cohort (AAPC) model has been widely used in studying the spatial and temporal pattern of disease incidence and mortality rates. However, lack of biological plausibility and ease of interpretability on temporal components especially for age effects are generally the weakness of AAPC models. We develop a Bayesian AAPC model where carcinogenesis age effect is incorporated to explain age effects from the underlying disease process. An autoregressive prior structure and an arbitrary linear constraint are used to solve the nonidentifiability issues. Methods: Two multistage carcinogenesis models are employed to derive the hazard functions to substitute the age effects in the AAPC models. The Iowa county-wide lung cancer mortality data are used for the model fitting and Deviance Information Criteria (DIC) is used for model comparison. Results: Our study shows that conventional AAPC model (DIC = 19,231.30), AAPC model with Armitage–Doll age effect (DIC = 19,233.00) and with two-stage clonal expansion (TSCE) age effect (DIC = 19,234.70) achieved the similar DIC values which indicated consistent model fitting among three models. The spatial pattern shows that the high spatial effects are clustered in the south of Iowa and also in largely populated areas. The lung cancer mortality rate is continuously declining by birth cohorts while increasing by the calendar period until 2000–2004. The age effects show an increasing pattern over time which can be easily explained by Armitage–Doll carcinogenesis model since we assume a log-linear relationship between age and hazard function. Conclusions: Our finding suggests that the proposed Bayesian AAPC model can be used to replace the conventional AAPC model without affecting model performance while providing a more biological sound approach from the underlining disease process.     

Paracrine effect of TGF-beta1 on downregulation of gap junctional intercellular communication between human dermal fibroblasts

Disruption of gap junctional intercellular communication (GJIC) is associated with tumor progression during multistage carcinogenesis. A coordinated interaction of epithelial tumor cells with the stromal environment via growth factors is a prerequisite for tumor invasion. Here, the involvement of growth factors in downregulation of homologous GJIC of dermal fibroblasts, used as model for stromal cells, was examined. Tumor cell derived transforming growth factor-beta1 (TGF-beta1), having oncogenic activities at late stages of carcinogenesis, was identified as being responsible for downregulation of GJIC via an increase in the level of reactive oxygen species in stromal fibroblasts. Lowering the level of reactive oxygen species by antioxidants, such as the cell-permeable N-acetyl-L-cysteine, prevented TGF-beta1-mediated downregulation of intercellular communication between confluent fibroblasts.     

Experimental gastric carcinogenesis in Cebus apella nonhuman primates

The evolution of gastric carcinogenesis remains largely unknown. We established two gastric carcinogenesis models in New-World nonhuman primates. In the first model, ACP03 gastric cancer cell line was inoculated in 18 animals. In the second model, we treated 6 animals with N-methyl-nitrosourea (MNU). Animals with gastric cancer were also treated with Canova immunomodulator. Clinical, hematologic, and biochemical, including C-reactive protein, folic acid, and homocysteine, analyses were performed in this study. MYC expression and copy number was also evaluated. We observed that all animals inoculated with ACP03 developed gastric cancer on the 9(th) day though on the 14(th) day presented total tumor remission. In the second model, all animals developed pre-neoplastic lesions and five died of drug intoxication before the development of cancer. The last surviving MNU-treated animal developed intestinal-type gastric adenocarcinoma observed by endoscopy on the 940(th) day. The level of C-reactive protein level and homocysteine concentration increased while the level of folic acid decreased with the presence of tumors in ACP03-inoculated animals and MNU treatment. ACP03 inoculation also led to anemia and leukocytosis. The hematologic and biochemical results corroborate those observed in patients with gastric cancer, supporting that our in vivo models are potentially useful to study this neoplasia. In cell line inoculated animals, we detected MYC immunoreactivity, mRNA overexpression, and amplification, as previously observed in vitro. In MNU-treated animals, mRNA expression and MYC copy number increased during the sequential steps of intestinal-type gastric carcinogenesis and immunoreactivity was only observed in intestinal metaplasia and gastric cancer. Thus, MYC deregulation supports the gastric carcinogenesis process. Canova immunomodulator restored several hematologic measurements and therefore, can be applied during/after chemotherapy to increase the tolerability and duration of anticancer treatments.     

The application of a multistage model that incorporates DNA damage and repair to the analysis of initiation/promotion experiments.

In a previous article, a multistage model of carcinogenesis was introduced that takes into account the role of DNA damage, DNA repair, and cell replication on the incidence of malignancies. For this model the number of detectable clones of initiated cells is derived and model parameters are estimated using data arising from a two-stage skin-painting experiment in mice. The data from this experiment are interpretable in terms of the cellular events involved in initiation and promotion.     

Incorporation of biological information in cancer risk assessment: Example — Vinyl chloride

Vinyl chloride (VC) is used as an example to demonstrate how biological information can be incorporated into quantitative risk assessment. The information included is the pharmacokinetics of VC in animals and humans and the data-generated hypothesis that VC primarily affects the initiation stage of the multistage carcinogenesis. The emphasis in this paper is on the improvement of risk assessment methodology rather than the risk assessment of VC per se.Sufficient data are available to construct physiologically-based pharmacokinetic models for both animals and humans. These models are used to calculate the metabolized dose corresponding to exposure scenarios in animals and in humans.On the basis of the data on liver angiosarcomas and carcinomas in rats, the cancer risk per unit of metabolized dose is comparable, irrespective of routes (oral or inhalation) of exposure. The tumor response from an intermittent/partial lifetime exposure is shown to be consistent with that from a lifetime exposure when VC is assumed to affect the first (initiation) stage of the multistage carcinogenic process. Furthermore, the risk estimates calculated on the basis of animal data are shown to be consistent with the human experience.     

Palytoxin: exploiting a novel skin tumor promoter to explore signal transduction and carcinogenesis

Palytoxin is a novel skin tumor promoter, which has been used to help probe the role of different types of signaling mechanisms in carcinogenesis. The multistage mouse skin model indicates that tumor promotion is an early, prolonged, and reversible phase of carcinogenesis. Understanding the molecular mechanisms underlying tumor promotion is therefore important for developing strategies to prevent and treat cancer. Naturally occurring tumor promoters that bind to specific cellular receptors have proven to be useful tools for investigating important biochemical events in multistage carcinogenesis. For example, the identification of protein kinase C as the receptor for the prototypical skin tumor promoter 12-O-tetradecanoylphorbol-13-acetate (TPA) (also called phorbol 12-myristate 13-acetate, PMA) provided key evidence that tumor promotion involves the aberrant modulation of signaling cascades that govern cell fate and function. The subsequent discovery that palytoxin, a marine toxin isolated from zoanthids (genus Palythoa), is a potent skin tumor promoter yet does not activate protein kinase C indicated that investigating palytoxin action could help reveal new aspects of tumor promotion. Interestingly, the putative receptor for palytoxin is the Na⁺,K⁺-ATPase. This review focuses on palytoxin-stimulated signaling and how palytoxin has been used to investigate alternate biochemical mechanisms by which important targets in carcinogenesis can be modulated. mitogen-activated protein kinase; dual-specificity phosphatase; prostaglandins; sodium, potassium adenosinetriphosphatase     

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.     

Monitoring futility and efficacy in phase II trials with Bayesian posterior distributions—A calibration approach

A multistage single arm phase II trial with binary endpoint is considered. Bayesian posterior probabilities are used to monitor futility in interim analyses and efficacy in the final analysis. For a beta‐binomial model, decision rules based on Bayesian posterior probabilities are converted to “traditional” decision rules in terms of number of responders among patients observed so far. Analytical derivations are given for the probability of stopping for futility and for the probability to declare efficacy. A workflow is presented on how to select the parameters specifying the Bayesian design, and the operating characteristics of the design are investigated. It is outlined how the presented approach can be transferred to statistical models other than the beta‐binomial model.     

Statistical models for low dose exposure

Extrapolation of health risks from high to low doses has received a considerable amount of attention in carcinogenic risk assessment over decades. Fitting statistical dose-response models to experimental data collected at high doses and use of the fitted model for estimating effects at low doses lead to quite different risk predictions. Dissatisfaction with this procedure was formulated both by toxicologists who saw a deficit of biological knowledge in the models as well as by risk modelers who saw the need of mechanistically-based stochastic modeling. This contribution summarizes the present status of low dose modeling and the determination of the shape of dose-response curves. We will address the controversial issues of the appropriateness of threshold models, the estimation of no observed adverse effect levels (NOAEL), and their relevance for low dose modeling. We will distinguish between quantal dose-response models for tumor incidence and models of the more informative age/time dependent tumor incidence. The multistage model and the two-stage model of clonal expansion are considered as dose-response models accounting for biological mechanisms. Problems of the identifiability of mechanisms are addressed, the relation between administered dose and effective target dose is illustrated by examples, and the recently proposed Benchmark Dose concept for risk assessment is presented with its consequences for mechanistic modeling and statistical estimation.     

Biodynamic modeling and simulation of multistage cell mutations

The aim of this study is to present a mathematical computer simulation model for multistage carcinogenesis. The population genetic model is developed based on the reaction diffusion, logistic behavior, and Hollings Type II interactions between normal, benign, and premalignant cells. The simple form of the Fisher-Haldane-Wright equation of the genetic model of tumor suppressor gene and oncogenes is used to describe this type of interaction. Through computer simulation, we observe the behavior, stability, and traveling wave solution of the premalignant stage mutation as well as its survival under natural selection pressure. As a simple case of this model, the interaction between normal and tumor cells with one or two stages of mutations is analyzed.