Age-specific incidence of cancer: Phases, transitions, and biological implications

Common hepatic artery lymph node metastasis in pancreatic ductal adenocarcinoma: an analysis of actual survival

BACKGROUND

The common hepatic artery lymph node (CHALN) represents a second-echelon node for tumors in the head of the pancreas. Although early studies suggested survival was comparable between the CHALN and remote metastasis in pancreatic ductal adenocarcinoma (PDAC), whether the lymph node is associated with adverse survival remains equivocal. Here, we examined a prospective cohort of patients calculating actual survival to better understand implications of this specific lymph node metastasis.

METHODS

We studied 215 patients with pancreatic head PDAC, who underwent pancreaticoduodenectomies at a single institution between 2010 and 2017, wherein the CHALNs were excised. We performed actual and actuarial overall survival and disease-free survival (DFS) analyses, with subsequent univariate and multivariate analyses in node-positive patients.

RESULTS

Of this cohort, 7.3% of patients had involvement of the CHALN, and all of them had metastatic spread to first-echelon nodes. Actual median survival of patients with no lymph node involvement was 49 months. In patients with any nodal involvement, the survival was no different when comparing the lymph node positive and negative (13 and 20 months, respectively). Univariate and multivariate analyses likewise attached no significance to the lymph node metastasis, while demonstrating worse survival with positive margin status and poorly differentiated histology. Our DFS analyses yielded similar results.

CONCLUSION

We found no difference in actual survival in node-positive patients regardless of the CHALN involvement and recommended against its assessment in prognosticating survival or guiding surgical treatment.

Mathematical modeling the gene mechanism of colorectal cancer and the effect of radiation exposure

Cancer is the result of continuous accumulation of gene mutations in normal cells. The number of mutations is different in different types of cancer and even in different patients with the same type of cancer. Therefore, studying all possible numbers of gene mutations in malignant cells is of great value for the understanding of tumorigenesis and the treatment of cancer. To this end, we applied a stochastic mathematical model considering the clonal expansion of any premalignant cells with different mutations to analyze the number of gene mutations in colorectal cancer. The age-specific colorectal cancer incidence rates from the Surveillance, Epidemiology and End Results (SEER) registry in the United States and the Life Span Study (LSS) in Nagasaki and Hiroshima, Japan are chosen to test the reasonableness of the model. Our fitting results indicate that the transformation from normal cells to malignant cells may undergo two to five driver mutations for colorectal cancer patients without radiation-exposed environment, two to four driver mutations for colorectal cancer patients with low level radiation-exposure, and two to three driver mutations for colorectal cancer patients with high level radiation-exposure. Furthermore, the net growth rate of the mutated cells with radiation-exposure was is higher than that of the mutated cells without radiation-exposure for the models with two to five driver mutations. These results suggest that radiation environment may affect the clonal expansion of cells and significantly affect the development of tumors.

The Natural Disease Course of Pancreatic Cyst-Associated Neoplasia, Dysplasia, and Ductal Adenocarcinoma: Results of a Microsimulation Model

BACKGROUND & AIMS

Estimates on the progression of precursor lesions to pancreatic cancer (PC) are scarce. We used microsimulation modeling to gain insight into the natural disease course of PC and its precursors. This information is pivotal to explore the efficacy of PC screening.

METHODS

A Microsimulation Screening Analysis model was developed in which pancreatic intraepithelial neoplasms and cysts can evolve from low-grade dysplasia (LGD) to high-grade dysplasia (HGD) to PC. The model was calibrated to Dutch PC incidence data and Japanese precursor prevalence data (autopsy cases without PC) and provides estimates of PC progression (precursor lesion onset and stage duration).

RESULTS

Mean LGD state durations of cysts and pancreatic intraepithelial neoplasms were 15.8 years and 17.1 years, respectively. Mean HGD state duration was 5.8 years. For lesions that progress to PC, the mean duration was 4.8-4.9 years for LGD lesions and 4.0-4.1 years for HGD lesions. In 13.7% of individuals who developed PC, the HGD state lasted less than 1 year. The probability that an individual at age 50 years developed PC in the next 20 years was estimated to be 1.8% in the presence of any cyst and 6.1% in case of an LGD mucinous cyst. This 20-year PC risk was estimated to be 5.1% for individuals with an LGD pancreatic intraepithelial neoplasm.

CONCLUSIONS

Mean duration of HGD lesions before development of PC was estimated to be 4.0 years. This implies a window of opportunity for screening, presuming the availability of a reliable diagnostic test. The probability that an LGD cyst will progress to cancer was predicted to be low.

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.

Autoimmune alleles at the major histocompatibility locus modify melanoma susceptibility

Autoimmunity and cancer represent two different aspects of immune dysfunction. Autoimmunity is characterized by breakdowns in immune self-tolerance, while impaired immune surveillance can allow for tumorigenesis. The class I major histocompatibility complex (MHC-I), which displays derivatives of the cellular peptidome for immune surveillance by CD8+ T cells, serves as a common genetic link between these conditions. As melanoma-specific CD8+ T cells have been shown to target melanocyte-specific peptide antigens more often than melanoma-specific antigens, we investigated whether vitiligo- and psoriasis-predisposing MHC-I alleles conferred a melanoma-protective effect. In individuals with cutaneous melanoma from both The Cancer Genome Atlas (n = 451) and an independent validation set (n = 586), MHC-I autoimmune-allele carrier status was significantly associated with a later age of melanoma diagnosis. Furthermore, MHC-I autoimmune-allele carriers were significantly associated with decreased risk of developing melanoma in the Million Veteran Program (OR = 0.962, p = 0.024). Existing melanoma polygenic risk scores (PRSs) did not predict autoimmune-allele carrier status, suggesting these alleles provide orthogonal risk-relevant information. Mechanisms of autoimmune protection were neither associated with improved melanoma-driver mutation association nor improved gene-level conserved antigen presentation relative to common alleles. However, autoimmune alleles showed higher affinity relative to common alleles for particular windows of melanocyte-conserved antigens and loss of heterozygosity of autoimmune alleles caused the greatest reduction in presentation for several conserved antigens across individuals with loss of HLA alleles. Overall, this study presents evidence that MHC-I autoimmune-risk alleles modulate melanoma risk unaccounted for by current PRSs.

Mathematical modeling the order of driver gene mutations in colorectal cancer

Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973-2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation order with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53 explain the age-specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53.

Waiting times in a branching process model of colorectal cancer initiation

We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.

Mechanisms and shapes of causal exposure-response functions for asbestos in mesotheliomas and lung cancers

This paper summarizes recent insights into causal biological mechanisms underlying the carcinogenicity of asbestos. It addresses their implications for the shapes of exposure-response curves and considers recent epidemiologic trends in malignant mesotheliomas (MMs) and lung fiber burden studies. Since the commercial amphiboles crocidolite and amosite pose the highest risk of MMs and contain high levels of iron, endogenous and exogenous pathways of iron injury and repair are discussed. Some practical implications of recent developments are that: (1) Asbestos-cancer exposure-response relationships should be expected to have non-zero background rates; (2) Evidence from inflammation biology and other sources suggests that there are exposure concentration thresholds below which exposures do not increase inflammasome-mediated inflammation or resulting inflammation-mediated cancer risks above background risk rates; and (3) The size of the suggested exposure concentration threshold depends on both the detailed time patterns of exposure on a time scale of hours to days and also on the composition of asbestos fibers in terms of their physiochemical properties. These conclusions are supported by complementary strands of evidence including biomathematical modeling, cell biology and biochemistry of asbestos-cell interactions in vitro and in vivo, lung fiber burden analyses and epidemiology showing trends in human exposures and MM rates.

Concepts of association between cancer and ionising radiation: accounting for specific biological mechanisms

The probability that an observed cancer was caused by radiation exposure is usually estimated using cancer rates and risk models from radioepidemiological cohorts and is called assigned share (AS). This definition implicitly assumes that an ongoing carcinogenic process is unaffected by the studied radiation exposure. However, there is strong evidence that radiation can also accelerate an existing clonal development towards cancer. In this work, we define different association measures that an observed cancer was newly induced, accelerated, or retarded. The measures were quantified exemplarily by Monte Carlo simulations that track the development of individual cells. Three biologically based two-stage clonal expansion (TSCE) models were applied. In the first model, radiation initiates cancer development, while in the other two, radiation has a promoting effect, i.e. radiation accelerates the clonal expansion of pre-cancerous cells. The parameters of the TSCE models were derived from breast cancer data from the atomic bomb survivors of Hiroshima and Nagasaki. For exposure at age 30, all three models resulted in similar estimates of AS at age 60. For the initiation model, estimates of association were nearly identical to AS. However, for the promotion models, the cancerous clonal development was frequently accelerated towards younger ages, resulting in associations substantially higher than AS. This work shows that the association between a given cancer and exposure in an affected person depends on the underlying biological mechanism and can be substantially larger than the AS derived from classic radioepidemiology.

Epithelial and stromal co-evolution and complicity in pancreatic cancer

Pancreatic ductal adenocarcinomas are distinguished by their robust desmoplasia, or fibroinflammatory response. Dominated by non-malignant cells, the mutated epithelium must therefore combat, cooperate with or co-opt the surrounding cells and signalling processes in its microenvironment. It is proposed that an invasive pancreatic ductal adenocarcinoma represents the coordinated evolution of malignant and non-malignant cells and mechanisms that subvert and repurpose normal tissue composition, architecture and physiology to foster tumorigenesis. The complex kinetics and stepwise development of pancreatic cancer suggests that it is governed by a discrete set of organizing rules and principles, and repeated attempts to target specific components within the microenvironment reveal self-regulating mechanisms of resistance. The histopathological and genetic progression models of the transforming ductal epithelium must therefore be considered together with a programme of stromal progression to create a comprehensive picture of pancreatic cancer evolution. Understanding the underlying organizational logic of the tumour to anticipate and pre-empt the almost inevitable compensatory mechanisms will be essential to eradicate the disease.

Telomeres, the loop tying cancer to organismal life-histories

Recent developments in telomere and cancer evolutionary ecology demonstrate a very complex relationship between the need of tissue repair and controlling the emergence of abnormally proliferating cells. The trade-off is balanced by natural and sexual selection and mediated via both intrinsic and environmental factors. Here, we explore the effects of telomere-cancer dynamics on life history traits and strategies as well as on the cumulative effects of genetic and environmental factors. We show that telomere-cancer dynamics constitute an incredibly complex and multifaceted process. From research to date, it appears that the relationship between telomere length and cancer risk is likely nonlinear with good evidence that both (too) long and (too) short telomeres can be associated with increased cancer risk. The ability and propensity of organisms to respond to the interplay of telomere dynamics and oncogenic processes, depends on the combination of its tissue environments, life history strategies, environmental challenges (i.e., extreme climatic conditions), pressure by predators and pollution, as well as its evolutionary history. Consequently, precise interpretation of telomere-cancer dynamics requires integrative and multidisciplinary approaches. Finally, incorporating information on telomere dynamics and the expression of tumour suppressor genes and oncogenes could potentially provide the synergistic overview that could lay the foundations to study telomere-cancer dynamics at ecosystem levels.

Invited Commentary: Mechanistic and Biologically Based Models in Epidemiology-A Powerful Underutilized Tool

Mechanistic and biologically based mathematical models of chronic and behavioral disease processes aim to capture the main mechanistic or biological features of the disease development and to connect these with epidemiologic outcomes. These approaches have a long history in epidemiologic research and are complementary to traditional epidemiologic or statistical approaches to investigate the role of risk factor exposures on disease risk. Simonetto et al. (Am J Epidemiol. 2022;191(10):1766-1775) present a mechanistic, process-oriented model to investigate the role of smoking, hypertension, and dyslipidemia in the development of atherosclerotic lesions and their progression to myocardial infarction. Their approach builds on and brings to cardiovascular disease the ideas and perspectives of earlier mechanistic and biologically based models for the epidemiology of cancer and other chronic diseases, providing important insights into the mechanisms and epidemiology of smoking related myocardial infarction. We argue that although mechanistic modeling approaches have demonstrated their value and place in epidemiology, they are highly underutilized. We call for efforts to grow mechanistic and biologically based modeling research, expertise, and awareness in epidemiology, including the development of training and collaboration opportunities to attract more students and researchers from science, technology, engineering, and medical field into the epidemiology field.

Familial Pancreatic Cancer

Individuals at increased risk of developing pancreatic cancer, including those with a significant family history of the disease and those with pancreatic cancer susceptibility gene variants, can benefit from pancreas surveillance. Most pancreatic cancers diagnosed during surveillance are early-stage and such patients can achieve long-term survival. Determining who should undergo pancreas surveillance is still a work-in-progress, but the main tools clinicians use to estimate an individual's risk of pancreatic cancer are patient's age, the extent of their family history of pancreatic cancer, and whether or not they have a pancreatic cancer susceptibility gene mutation.

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.

Cancer development is a multistep process often starting with a single cell turning into a tumor cell whose progeny growths via clonal expansion into a macroscopic tumor with billions of cells. While experimental insight exists on the cellular scale and cancer registries provide statistics on detectable tumors, the complex dynamics leading from the microscopic cellular scale to a macroscopic tumor is still not fully resolved. Models of cancer biology are commonly used to explain incidence rates but usually require the fit of several biological parameters due to the complexity of the incorporated processes. We employ a cell-based model based on the competition in colonic crypts, to reproduce epidemiological age-specific incidence rates of colon cancer. Due to the focus on the early stage of tumor development, only the time scale in the model has to be calibrated. The agreement between theoretical prediction and epidemiological observation suggests that the fate of tumor development is dominated by the early phase of tumor development long before a tumor becomes detectable.

Mathematical modeling for mutator phenotype and clonal selection advantage in the risk analysis of lung cancer

Cancer is one of the leading diseases for human mortality. Although substantial research works have been conducted to investigate the initiation and progression of cancer disease, it is still an active debate regarding the function of mutations conferring a clone advantage and the importance of mutator phenotypes caused by the mutation of stability genes. To address this issue further, we develop a mathematical model based on the incidence data of non-small cell lung cancer and small cell lung cancer from the Surveillance Epidemiology and End Results registry in the USA. The key biological parameters have been analyzed to investigate the potential effective measures for inhibiting the risk of lung cancer. Although the first event is the gene mutation that leads to clonal expansion of cells for lung cancer, the simulation results show that the clonal advantage of cancer cells alone is insufficient to cause tumorigenesis. Our analysis suggests that mutations in genes that keep genetic stability are critical in the development of lung cancer. This implies that mutator phenotype is an important indicator for the diagnosis of lung cancer, which can enable early detection and treatment to reduce the risk of lung cancer effectively. Furthermore, the parameter analysis indicates that it would be highly effective to control the risk of lung cancer by inhibiting the transformation rate from the normal cells to mutated cells and the clonal expansion of cells with fewer gene mutations.

Aspirin's effect on kinetic parameters of cells contributes to its role in reducing incidence of advanced colorectal adenomas, shown by a multiscale computational study

Aspirin intake has been shown to lead to significant protection against colorectal cancer, for example with an up to twofold reduction in colorectal adenoma incidence rates at higher doses. The mechanisms contributing to protection are not yet fully understood. While aspirin is an anti-inflammatory drug and can thus influence the tumor microenvironment, in vitro and in vivo experiments have recently shown that aspirin can also have a direct effect on cellular kinetics and fitness. It reduces the rate of tumor cell division and increases the rate of cell death. The question arises whether such changes in cellular fitness are sufficient to significantly contribute to the epidemiologically observed protection. To investigate this, we constructed a class of mathematical models of in vivo evolution of advanced adenomas, parameterized it with available estimates, and calculated population level incidence. Fitting the predictions to age incidence data revealed that only a model that included colonic crypt competition can account for the observed age-incidence curve. This model was then used to predict modified incidence patterns if cellular kinetics were altered as a result of aspirin treatment. We found that changes in cellular fitness that were within the experimentally observed ranges could reduce advanced adenoma incidence by a sufficient amount to account for age incidence data in aspirin-treated patient cohorts. While the mechanisms that contribute to the protective effect of aspirin are likely complex and multi-factorial, our study demonstrates that direct aspirin-induced changes of tumor cell fitness can significantly contribute to epidemiologically observed reduced incidence patterns.

Molecular Biologic and Epidemiologic Insights for Preventability of Colorectal Cancer

The etiology of colorectal cancer (CRC) has been informed from both a molecular biology perspective, which concerns the study of the nature, timing, and consequences of mutations in driver genes, and epidemiology, which focuses on identifying risk factors for cancer. For the most part, these fields have developed independently, and it is thus important to consider them in a more integrated manner. The molecular mutational perspective has stressed the importance of mutations due to replication of adult stem cells, and the molecular fingerprint of most CRCs does not suggest the importance of direct carcinogens. Epidemiology has identified numerous modifiable risk factors that account for most CRCs, most of which are not direct mutagens. The distribution of CRCs across the large bowel is not uniform, which is possibly caused by regional differences in the microbiota. Some risk factors are likely to act through or interact with the microbiota. The mutational perspective informs when risk factors may begin to operate in life and when they may cease to operate. Evidence from the mutational model and epidemiology supports that CRC risk factors begin early in life and may contribute to the risk of early-onset CRC. Later in carcinogenesis, there may be a "point of no return" when sufficient mutations have accumulated, and some risk factors do not affect cancer risk. This period may be at least 5-15 years for some risk factors. A more precise knowledge of timing of risk factor to cancer is required to inform preventive efforts.

Revelations About Aging and Disease from Unconventional Vertebrate Model Organisms

Aging is a major risk factor for multiple diseases. Understanding the underlying mechanisms of aging would help to delay and prevent age-associated diseases. Short-lived model organisms have been extensively used to study the mechanisms of aging. However, these short-lived species may be missing the longevity mechanisms that are needed to extend the lifespan of an already long-lived species such as humans. Unconventional long-lived animal species are an excellent resource to uncover novel mechanisms of longevity and disease resistance. Here, we review mechanisms that evolved in nonmodel vertebrate species to counteract age-associated diseases. Some antiaging mechanisms are conserved across species; however, various nonmodel species also evolved unique mechanisms to delay aging and prevent disease. This variety of antiaging mechanisms has evolved due to the remarkably diverse habitats and behaviors of these species. We propose that exploring a wider range of unconventional vertebrates will provide important resources to study antiaging mechanisms that are potentially applicable to humans.

Synthetic biomarkers: a twenty-first century path to early cancer detection

Detection of cancer at an early stage when it is still localized improves patient response to medical interventions for most cancer types. The success of screening tools such as cervical cytology to reduce mortality has spurred significant interest in new methods for early detection (for example, using non-invasive blood-based or biofluid-based biomarkers). Yet biomarkers shed from early lesions are limited by fundamental biological and mass transport barriers - such as short circulation times and blood dilution - that limit early detection. To address this issue, synthetic biomarkers are being developed. These represent an emerging class of diagnostics that deploy bioengineered sensors inside the body to query early-stage tumours and amplify disease signals to levels that could potentially exceed those of shed biomarkers. These strategies leverage design principles and advances from chemistry, synthetic biology and cell engineering. In this Review, we discuss the rationale for development of biofluid-based synthetic biomarkers. We examine how these strategies harness dysregulated features of tumours to amplify detection signals, use tumour-selective activation to increase specificity and leverage natural processing of bodily fluids (for example, blood, urine and proximal fluids) for easy detection. Finally, we highlight the challenges that exist for preclinical development and clinical translation of synthetic biomarker diagnostics.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background

It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events.

Methods

Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence.

Results

We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age.

Conclusions

This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

Risk of lung cancer due to external environmental factor and epidemiological data analysis

Lung cancer is a cancer with the fastest growth in the incidence and mortality all over the world, which is an extremely serious threat to human's life and health. Evidences reveal that external environmental factors are the key drivers of lung cancer, such as smoking, radiation exposure and so on. Therefore, it is urgent to explain the mechanism of lung cancer risk due to external environmental factors experimentally and theoretically. However, it is still an open issue regarding how external environment factors affect lung cancer risk. In this paper, we summarize the main mathematical models involved the gene mutations for cancers, and review the application of the models to analyze the mechanism of lung cancer and the risk of lung cancer due to external environmental exposure. In addition, we apply the model described and the epidemiological data to analyze the influence of external environmental factors on lung cancer risk. The result indicates that radiation can cause significantly an increase in the mutation rate of cells, in particular the mutation in stability gene that leads to genomic instability. These studies not only can offer insights into the relationship between external environmental factors and human lung cancer risk, but also can provide theoretical guidance for the prevention and control of lung cancer.

Recent Trends in the Incidence and Survival of Stage 1A Pancreatic Cancer: A Surveillance, Epidemiology, and End Results Analysis

BACKGROUND

Rapid access to pancreatic imaging and regular pancreatic surveillance may help identify stage I pancreatic cancer. We investigated recent trends in the stage of newly diagnosed pancreatic ductal adenocarcinoma (PDACs), age at diagnosis, and survival.

METHODS

Trends in age-adjusted incidence of stage IA PDAC between 2004 and 2016 were determined from the National Cancer Institute's Surveillance, Epidemiology and End Results database. All tests were two-sided.

RESULTS

The incidence of stage IA PDAC cases diagnosed increased statistically significantly from 2004 to 2016 (annual percent change = 14.5, 95% confidence interval [CI] = 11.4 to 17.7; P < .001). During the study period, average age at diagnosis for stage IA and IB casesAQ3 declined by 3.5 years (95% CI = 1.2 to 5.9; P = .004) and 5.5 years (95% CI = 3.4 to 7.6; P < .001), whereas average age increased for higher-stage cases (by 0.6 to 1.4 years). Among stage IA cases, the proportion of blacks was smaller (10.2% vs 12.5%), and the proportion of other non-Caucasians was higher compared with higher-stage cases (11.9% vs 8.4%; P < .001). Stage IA cases were more likely to carry insurance (vs Medicaid or none) than higher-stage cases (cases aged younger than 65 years; odds ratio = 2.45, 95% CI = 1.96 to 3.06; P < .001). The 5-year overall survival for stage IA PDAC improved from 44.7% (95% CI = 31.4 to 63.7) in 2004 to 83.7% (95% CI = 78.6% to 89.2%) in 2012; 10-year survival improved from 36.7% (95% CI = 24.1 to 55.8) in 2004 to 49.0% (95% CI = 37.2% to 64.6%) in 2007.

CONCLUSIONS

In recent years, the proportion of patients diagnosed with stage IA PDAC has increased, their average age at diagnosis has decreased, and their overall survival has improved. These trends may be the result of improved early diagnosis and early detection.

Modeling historic incidence trends implies early field cancerization in esophageal squamous cell carcinoma

Patterns of cancer incidence, viewed over extended time periods, reveal important aspects of multistage carcinogenesis. Here we show how a multistage clonal expansion (MSCE) model for cancer can be harnessed to identify biological processes that shape the surprisingly dynamic and disparate incidence patterns of esophageal squamous cell carcinoma (ESCC) in the US population. While the dramatic rise in esophageal adenocarcinoma (EAC) in the US has been largely attributed to reflux related increases in the prevalence of Barrett’s esophagus (BE), the premalignant field in which most EAC are thought to arise, only scant evidence exists for field cancerization contributing to ESCC. Our analyses of incidence patterns suggest that ESCC is associated with a premalignant field that may develop very early in life. Although the risk of ESCC, which is substantially higher in Blacks than Whites, is generally assumed to be associated with late-childhood and adult exposures to carcinogens, such as from tobacco smoking, alcohol consumption and various industrial exposures, the temporal trends we identify for ESCC suggest an onset distribution of field-defects before age 10, most strongly among Blacks. These trends differ significantly in shape and strength from field-defect trends that we estimate for US Whites. Moreover, the rates of ESCC-predisposing field-defects predicted by the model for cohorts of black children are decreasing for more recent birth cohorts (for Blacks born after 1940). These results point to a potential etiologic role of factors acting early in life, perhaps related to nutritional deficiencies, in the development of ESCC and its predisposing field-defect. Such factors may explain some of the striking racial differences seen in ESCC incidence patterns over time in the US.

We used a cell-level carcinogenesis model to analyze incidence patterns of esophageal squamous cell carcinoma (ESCC) in the US. We found an important role of an esophageal field-defect that is predicted to occur predominantly in childhood and predisposes to ESCC in adult life. Age-specific ESCC incidence patterns are also known to differ considerably between Blacks and Whites, and between males and females in the US, but the model consistently predicts early-childhood field-defects in all four groups. The estimated historical field-defect trends appear consistent with possible early childhood nutritional deficiencies.

Periodic Fluctuations in the Incidence of Gastrointestinal Cancer

Purpose

Native stem cells can be periodically replaced during short and long epigenetic intervals. Cancer-prone new stem cells might bring about periodic (non-stochastic) carcinogenic events rather than stochastic events. We investigated the epigenetic non-stochastic carcinogenesis by analyzing regular fluctuations in lifelong cancer incidence.

Materials and Methods

Korean National Cancer Screening Program data were collected between 2009 and 2016. Non-linear and log-linear regression models were applied to comparatively evaluate non-stochastic and stochastic increases in cancer incidence. Prediction performances of regression models were measured by calculating the coefficient of determination, R².

Results

The incidence of gastric and colorectal cancers fluctuated regularly during both short (8 years) and long (20 years) intervals in the non-linear regression model and increased stochastically in the log-linear regression model. In comparison between the 20-year interval fluctuation model and the stochastic model, R² values were higher in the 20-year interval fluctuation model of men with gastric cancer (0.975 vs. 0.956), and in the stochastic model of men with colorectal cancer (0.862 vs. 0.877) and women with gastric cancer (0.837 vs. 0.890) and colorectal cancer (0.773 vs. 0.809). Men with gastric cancer showed a high R² value (0.973) in the 8-year interval fluctuation model as well.

Conclusion

Lifelong incidence of gastrointestinal cancer tended to fluctuate during short and long intervals, especially in men with gastric cancer, suggesting the influence of an epigenetic schedule.

Different Mechanisms of Cigarette Smoking-Induced Lung Cancer

The risk of cigarette smoking plays a pivotal role in increasing the incidence rates of lung cancer. This paper sheds new light on modeling the impact of cigarette smoking on lung cancer evolution, especially genetic instability and the number of gene mutations in the genome of stem cells. To handle this issue, we have set up stochastic multi-stage models to fit the data set of the probabilities of current and former smokers from the Nurses' Health Study cohort of females (NHS) and the Health Professionals Follow up Study cohort of men (HPFS). Throughout this paper, we consider both mutation rates and clonal expansion rates as parameters in each compartment. For current and former smokers, three-driver mutations are most likely to take place in the progression of lung cancer under smoking risk. For current smokers, our findings reveal that two to sixteen gene mutations are required to obtain a cancerous cell among men and women in US. Moreover, two to six (eleven) cancer-mutations are available in the pathway to lung cancer among former smokers who have quit smoking for more (less) than ten years for both male and female patients. This highlights that cigarette smoking stimulates the number of driver mutations during lung tumorigenesis in both sexes. It is very crucial to examine the role of cigarette smoking in determining whether genomic instability is an early stage or late stage in the process of lung carcinogenesis.

Mathematical model of colorectal cancer initiation

Quantifying evolutionary dynamics of cancer initiation and progression can provide insights into more effective strategies of early detection and treatment. Here we develop a mathematical model of colorectal cancer initiation through inactivation of two tumor suppressor genes and activation of one oncogene, accounting for the well-known path to colorectal cancer through loss of tumor suppressors APC and TP53 and gain of the KRAS oncogene. In the model, we allow mutations to occur in any order, leading to a complex network of premalignant mutational genotypes on the way to colorectal cancer. We parameterize the model using experimentally measured parameter values, many of them only recently available, and compare its predictions to epidemiological data on colorectal cancer incidence. We find that the reported lifetime risk of colorectal cancer can be recovered using a mathematical model of colorectal cancer initiation together with experimentally measured mutation rates in colorectal tissues and proliferation rates of premalignant lesions. We demonstrate that the order of driver events in colorectal cancer is determined primarily by the fitness effects that they provide, rather than their mutation rates. Our results imply that there may not be significant immune suppression of untreated benign and malignant colorectal lesions.

Risk of lung adenocarcinoma from smoking and radiation arises in distinct molecular pathways

KRAS mutations of lung adenocarcinoma (LADC) are associated with smoking but little is known on other exposure-oncogene associations. Hypothesizing that different inciting agents may cause different driver mutations, we aimed to identify distinct molecular pathways to LADC, applying two entirely different approaches. First, we examined clinicopathologic features and genomic signatures of environmental exposures in the large LADC Campbell data set. Second, we designed a molecular mechanistic risk model of LADC (M3LADC) that links environmental exposure to incidence risk by mathematically emulating the disease process. This model was applied to incidence data of Japanese atom-bomb survivors which contains information on radiation and smoking exposure. Grouping the clinical data by driver mutations revealed two main distinct molecular pathways to LADC: one unique to transmembrane receptor-mutant patients that displayed robust signatures of radiation exposure and one shared between submembrane transducer-mutant patients and patients with no evident driver mutation that carried the signature of smoking. Consistently, best fit of the incidence data was achieved with a M3LADC with two pathways: in one LADC risk increased with radiation exposure and in the other with cigarette consumption. We conclude there are two main molecular pathways to LADC associated with different environmental exposures. Future molecular measurements in lung cancer tissue of atom-bomb survivors may allow to further test quantitatively the M3LADC-predicted link of radiation to transmembrane receptor mutations. Moreover, the developed molecular mechanistic model showed that for low doses, as relevant e.g. for medical imaging, smokers have the same radiation risk compared with never smokers.

Mathematical modeling of female breast cancer in Japan

Cancer incidence rates are significantly different all over the world. Breast cancer is affected by many factors, the most important being genetics and lifestyle. The aim of this paper is to study the mutation mechanisms of breast cancer for Japanese women by fitting the incidence data of three high-quality population areas in Japan from 1985 to 2010. To achieve this goal, we have set up multi-stage models within the mathematical model of Moolgavkar, Venzon, and Knudson. Such models take both mutation rates and clonal expansion rates as parameters in each compartment into consideration. Based on our simulation outcomes, two to twelve driver mutations are sufficient in the pathway to female breast cancer in Japan. On the other hand, a previous study demonstrated that breast cancer in American women requires two to fourteen gene mutations to get a cancerous cell. Moreover, the 3-stage mathematical model is the optimal model as it fits clinical data very nicely for all affected cases of females in Japan and the US. The genetic instability has a prominent effect on the tumorigenesis of Japanese females caused by the first four driver mutations. The calculated results for Japanese women are compared with previous works for American women.

Context-dependent selection as the keystone in the somatic evolution of cancer

Somatic evolution of cancer involves a series of mutations, and attendant changes, in one or more clones of cells. A “bad luck” type model assumes chance accumulation of mutations. The clonal expansion model assumes, on the other hand, that any mutation leading to partial loss of regulation of cell proliferation will give a selective advantage to the mutant. However, a number of experiments show that an intermediate pre-cancer mutant has only a conditional selective advantage. Given that tissue microenvironmental conditions differ across individuals, this selective advantage to a mutant could be widely distributed over the population. We evaluate three models, namely “bad luck”, context-independent, and context-dependent selection, in a comparative framework, on their ability to predict patterns in total incidence, age-specific incidence, stem cell number-incidence relationship and other known phenomena associated with cancers. Results show that among the factors considered in the model, context dependence is necessary and sufficient to explain observed epidemiological patterns, and that cancer evolution is largely selection-limited, rather than mutation-limited. A wide range of physiological, genetic and behavioural factors influence the tissue micro-environment, and could therefore be the source of this context dependence in somatic evolution of cancer. The identification and targeting of these micro-environmental factors that influence the dynamics of selection offer new possibilities for cancer prevention.

Predicting colorectal cancer risk from adenoma detection via a two-type branching process model

Despite advances in the modeling and understanding of colorectal cancer development, the dynamics of the progression from benign adenomatous polyp to colorectal carcinoma are still not fully resolved. To take advantage of adenoma size and prevalence data in the National Endoscopic Database of the Clinical Outcomes Research Initiative (CORI) as well as colorectal cancer incidence and size data from the Surveillance Epidemiology and End Results (SEER) database, we construct a two-type branching process model with compartments representing adenoma and carcinoma cells. To perform parameter inference we present a new large-size approximation to the size distribution of the cancer compartment and validate our approach on simulated data. By fitting the model to the CORI and SEER data, we learn biologically relevant parameters, including the transition rate from adenoma to cancer. The inferred parameters allow us to predict the individualized risk of the presence of cancer cells for each screened patient. We provide a web application which allows the user to calculate these individual probabilities at https://ccrc-eth.shinyapps.io/CCRC/. For example, we find a 1 in 100 chance of cancer given the presence of an adenoma between 10 and 20mm size in an average risk patient at age 50. We show that our two-type branching process model recapitulates the early growth dynamics of colon adenomas and cancers and can recover epidemiological trends such as adenoma prevalence and cancer incidence while remaining mathematically and computationally tractable.

Colorectal cancer is a major public health burden. The development of colorectal cancer starts with the mutational initiation of non-cancerous growths in the form of benign adenomatous polyps. These adenomas grow over time with the potential to develop into carcinomas. Many mathematical and simulation-based models have been used to gain insight into this process. We aimed to understand rates of adenoma growth and transition into carcinomas, to enable better planning of colorectal cancer screening strategies. To this end, we expand the two-type branching process model, and fit it on data describing the frequency of sizes of adenomas and carcinomas. The results provide new, data-based, estimates of the rates of development for colorectal cancer.

Identification of Differentially Expressed Genes to Establish New Biomarker for Cancer Prediction

The goal of the human genome project is to integrate genetic information into different clinical therapies. To achieve this goal, different computational algorithms are devised for identifying the biomarker genes, cause of complex diseases. However, most of the methods developed so far using DNA microarray data lack in interpreting biological findings and are less accurate in disease prediction. In the paper, we propose two parameters risk_factor and confusion_factor to identify the biologically significant genes for cancer development. First, we evaluate risk_factor of each gene and the genes with nonzero risk_factor result misclassification of data, therefore removed. Next, we calculate confusion_factor of the remaining genes which determines confusion of a gene in prediction due to closeness of the samples in the cancer and normal classes. We apply nondominated sorting genetic algorithm (NSGA-II) to select the maximally uncorrelated differentially expressed genes in the cancer class with minimum confusion_factor. The proposed Gene Selection Explore (GSE) algorithm is compared to well established feature selection algorithms using 10 microarray data with respect to sensitivity, specificity, and accuracy. The identified genes appear in KEGG pathway and have several biological importance.

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.

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

Implications of Epigenetic Drift in Colorectal Neoplasia

Many normal tissues undergo age-related drift in DNA methylation, providing a quantitative measure of tissue age. Here, we identify and validate 781 CpG islands (CGI) that undergo significant methylomic drift in 232 normal colorectal tissues and show that these CGI continue to drift in neoplasia while retaining significant correlations across samples. However, compared with normal colon, this drift advanced (∼3-4-fold) faster in neoplasia, consistent with increased cell proliferation during neoplastic progression. The observed drift patterns were broadly consistent with modeled adenoma-to-carcinoma sojourn time distributions from colorectal cancer incidence data. These results support the hypothesis that, beginning with the founder premalignant cell, cancer precursors frequently sojourn for decades before turning into cancer, implying that the founder cell typically arises early in life. At least 77% to 89% of the observed drift variance in distal and rectal tumors was explained by stochastic variability associated with neoplastic progression, whereas only 55% of the variance was explained for proximal tumors. However, gene-CGI pairs in the proximal colon that underwent drift were significantly and primarily negatively correlated with cancer gene expression, suggesting that methylomic drift participates in the clonal evolution of colorectal cancer. Methylomic drift advanced in colorectal neoplasia, consistent with extended sojourn time distributions, which accounts for a significant fraction of epigenetic heterogeneity in colorectal cancer. Importantly, these estimated long-duration premalignant sojourn times suggest that early dietary and lifestyle interventions may be more effective than later changes in reducing colorectal cancer incidence. SIGNIFICANCE: These findings present age-related methylomic drift in colorectal neoplasia as evidence that premalignant cells can persist for decades before becoming cancerous.See related commentary by Sapienza, p. 437.

Metabolome analysis for pancreatic cancer risk in nested case-control study: Japan Public Health Center-based prospective Study

Discovery of a high-risk group for pancreatic cancer is important for prevention of pancreatic cancer. The present study was conducted as a nested case-control study including 170 pancreatic cancer cases and 340 matched controls of our population-based cohort study involving 30 239 subjects who answered a baseline questionnaire and supplied blood samples. Twelve targeted metabolites were quantitatively analyzed by gas chromatography/tandem mass spectrometry. Odds ratios (OR) and their corresponding 95% confidence intervals (CI) were calculated using conditional logistic regression models. Statistically significant P-value was defined as P < .05. Increasing 1,5-anhydro-d-glucitol (1,5-AG) levels were associated with a decreasing trend in pancreatic cancer risk (OR of quartile 4 [Q4], 0.50; 95% CI, 0.27-0.93; P = .02). Increasing methionine levels were also associated with an increasing trend of pancreatic cancer risk (OR of Q4, 1.79; 95% CI, 0.94-3.40: P = .03). Additional adjustment for potential confounders attenuated the observed associations of 1,5-AG and methionine (P for trend = .06 and .07, respectively). Comparing subjects diagnosed in the first 0-6 years, higher levels of 1,5-AG, asparagine, tyrosine and uric acid showed a decreasing trend for pancreatic cancer risk (P for trend = .04, .04, .04 and .02, respectively), even after adjustment for potential confounders. We found that the 12 target metabolites were not associated with pancreatic cancer risk. However, metabolic changes in the subjects diagnosed in the first 0-6 years showed a similar tendency to our previous reports. These results might suggest that these metabolites are useful for early detection but not for prediction of pancreatic cancer.

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.

A mechanistic model for atherosclerosis and its application to the cohort of Mayak workers

We propose a stochastic model for use in epidemiological analysis, describing the age-dependent development of atherosclerosis with adequate simplification. The model features the uptake of monocytes into the arterial wall, their proliferation and transition into foam cells. The number of foam cells is assumed to determine the health risk for clinically relevant events such as stroke. In a simulation study, the model was checked against the age-dependent prevalence of atherosclerotic lesions. Next, the model was applied to incidence of atherosclerotic stroke in the cohort of male workers from the Mayak nuclear facility in the Southern Urals. It describes the data as well as standard epidemiological models. Based on goodness-of-fit criteria the risk factors smoking, hypertension and radiation exposure were tested for their effect on disease development. Hypertension was identified to affect disease progression mainly in the late stage of atherosclerosis. Fitting mechanistic models to incidence data allows to integrate biological evidence on disease progression into epidemiological studies. The mechanistic approach adds to an understanding of pathogenic processes, whereas standard epidemiological methods mainly explore the statistical association between risk factors and disease outcome. Due to a more comprehensive scientific foundation, risk estimates from mechanistic models can be deemed more reliable. To the best of our knowledge, such models are applied to epidemiological data on cardiovascular diseases for the first time.

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.

Parameter estimation from data is an important part of mathematical modeling, and structural identifiability is the study of what parametric information exists, for a given model, in ideal data. Unfortunately, for a variety of reasons, there is often less information available in our real data sets. The study of these problems is called practical identifiability. In this study, we consider a family of models of cancer biology that are commonly used to explain cancer incidence in terms of underlying biological parameters. Using profile likelihoods, a widely applicable numerical tool, we demonstrate that even though the more complex models we consider have theoretically more identifiable parameters, the data contains only three pieces of practically identifiable information for each model: the product of the initiating mutation rates, the net cell proliferation rate, and the scaled malignant conversion rate. This result can be interpreted biologically: we can determine only the product of cell mutation rates not the intermediate rates themselves. Our result limits the interpretability of previous work, but we propose a novel parameterization to resolve the identifiability issue. Ultimately, our analysis demonstrates the importance of verifying the practical identifiability of parameters before assigning too much weight to the interpretation of their estimated values.

Natural Selection in Cancer Biology: From Molecular Snowflakes to Trait Hallmarks

Evolution by natural selection is the conceptual foundation for nearly every branch of biology and increasingly also for biomedicine and medical research. In cancer biology, evolution explains how populations of cells in tumors change over time. It is a fundamental question whether this evolutionary process is driven primarily by natural selection and adaptation or by other evolutionary processes such as founder effects and drift. In cancer biology, as in organismal evolutionary biology, there is controversy about this question and also about the use of adaptation through natural selection as a guiding framework for research. In this review, we discuss the differences and similarities between evolution among somatic cells versus evolution among organisms. We review what is known about the parameters and rate of evolution in neoplasms, as well as evidence for adaptation. We conclude that adaptation is a useful framework that accurately explains the defining characteristics of cancer. Further, convergent evolution through natural selection provides the only satisfying explanation both for how a group of diverse pathologies have enough in common to usefully share the descriptive label of "cancer" and for why this convergent condition becomes life-threatening.

Glutathione maintenance mitigates age-related susceptibility to redox cycling agents

Isolated hepatocytes from young (4-6mo) and old (24-26mo) F344 rats were exposed to increasing concentrations of menadione, a vitamin K derivative and redox cycling agent, to determine whether the age-related decline in Nrf2-mediated detoxification defenses resulted in heightened susceptibility to xenobiotic insult. An LC50 for each age group was established, which showed that aging resulted in a nearly 2-fold increase in susceptibility to menadione (LC50 for young: 405μM; LC50 for old: 275μM). Examination of the known Nrf2-regulated pathways associated with menadione detoxification revealed, surprisingly, that NAD(P)H: quinone oxido-reductase 1 (NQO1) protein levels and activity were induced 9-fold and 4-fold with age, respectively (p=0.0019 and p=0.018; N=3), but glutathione peroxidase 4 (GPX4) declined by 70% (p=0.0043; N=3). These results indicate toxicity may stem from vulnerability to lipid peroxidation instead of inadequate reduction of menadione semi-quinone. Lipid peroxidation was 2-fold higher, and GSH declined by a 3-fold greater margin in old versus young rat cells given 300µM menadione (p<0.05 and p≤0.01 respectively; N=3). We therefore provided 400µMN-acetyl-cysteine (NAC) to hepatocytes from old rats before menadione exposure to alleviate limits in cysteine substrate availability for GSH synthesis during challenge. NAC pretreatment resulted in a >2-fold reduction in cell death, suggesting that the age-related increase in menadione susceptibility likely stems from attenuated GSH-dependent defenses. This data identifies cellular targets for intervention in order to limit age-related toxicological insults to menadione and potentially other redox cycling compounds.

Characteristic patterns of cancer incidence: Epidemiological data, biological theories, and multistage models

We investigate and classify several patterns in cancer incidence and relative risk data which persist across different countries and multiple published studies. We then explore biological hypotheses as well as many mathematical models in the literature that attempt to explain these patterns. A general modeling framework is presented which is general enough to model most of observed behaviors. It is our belief that this model has sufficient flexibility to be adapted to new information as it is discovered. As one application of this framework, we give a model for the effect of aging on the process of carcinogenesis.

Quantifying the Dynamics of Field Cancerization in Tobacco-Related Head and Neck Cancer: A Multiscale Modeling Approach

High rates of local recurrence in tobacco-related head and neck squamous cell carcinoma (HNSCC) are commonly attributed to unresected fields of precancerous tissue. Because they are not easily detectable at the time of surgery without additional biopsies, there is a need for noninvasive methods to predict the extent and dynamics of these fields. Here, we developed a spatial stochastic model of tobacco-related HNSCC at the tissue level and calibrated the model using a Bayesian framework and population-level incidence data from the Surveillance, Epidemiology, and End Results (SEER) registry. Probabilistic model analyses were performed to predict the field geometry at time of diagnosis, and model predictions of age-specific recurrence risks were tested against outcome data from SEER. The calibrated models predicted a strong dependence of the local field size on age at diagnosis, with a doubling of the expected field diameter between ages at diagnosis of 50 and 90 years, respectively. Similarly, the probability of harboring multiple, clonally unrelated fields at the time of diagnosis was found to increase substantially with patient age. On the basis of these findings, we hypothesized a higher recurrence risk in older than in younger patients when treated by surgery alone; we successfully tested this hypothesis using age-stratified outcome data. Further clinical studies are needed to validate the model predictions in a patient-specific setting. This work highlights the importance of spatial structure in models of epithelial carcinogenesis and suggests that patient age at diagnosis may be a critical predictor of the size and multiplicity of precancerous lesions. Cancer Res; 76(24); 7078-88. ©2016 AACR.

Cell Fusion in the War on Cancer: A Perspective on the Inception of Malignancy

Cell fusion occurs in development and in physiology and rarely in those settings is it associated with malignancy. However, deliberate fusion of cells and possibly untoward fusion of cells not suitably poised can eventuate in aneuploidy, DNA damage and malignant transformation. How often cell fusion may initiate malignancy is unknown. However, cell fusion could explain the high frequency of cancers in tissues with low underlying rates of cell proliferation and mutation. On the other hand, cell fusion might also engage innate and adaptive immune surveillance, thus helping to eliminate or retard malignancies. Here we consider whether and how cell fusion might weigh on the overall burden of cancer in modern societies.