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.

Identification of a key role of widespread epigenetic drift in Barrett's esophagus and esophageal adenocarcinoma.

BACKGROUND: Recent studies have identified age-related changes in DNA methylation patterns in normal and cancer tissues in a process that is called epigenetic drift. However, the evolving patterns, functional consequences, and dynamics of epigenetic drift during carcinogenesis remain largely unexplored. Here we analyze the evolution of epigenetic drift patterns during progression from normal squamous esophagus tissue to Barrett's esophagus (BE) to esophageal adenocarcinoma (EAC) using 173 tissue samples from 100 (nonfamilial) BE patients, along with publically available datasets including The Cancer Genome Atlas (TCGA). RESULTS: Our analysis reveals extensive methylomic drift between normal squamous esophagus and BE tissues in nonprogressed BE patients, with differential drift affecting 4024 (24%) of 16,984 normally hypomethylated cytosine-guanine dinucleotides (CpGs) occurring in CpG islands. The majority (63%) of islands that include drift CpGs are associated with gene promoter regions. Island CpGs that drift have stronger pairwise correlations than static islands, reflecting collective drift consistent with processive DNA methylation maintenance. Individual BE tissues are extremely heterogeneous in their distribution of methylomic drift and encompass unimodal low-drift to bimodal high-drift patterns, reflective of differences in BE tissue age. Further analysis of longitudinally collected biopsy samples from 20 BE patients confirm the time-dependent evolution of these drift patterns. Drift patterns in EAC are similar to those in BE, but frequently exhibit enhanced bimodality and advanced mode drift. To better understand the observed drift patterns, we developed a multicellular stochastic model at the CpG island level. Importantly, we find that nonlinear feedback in the model between mean island methylation and CpG methylation rates is able to explain the widely heterogeneous collective drift patterns. Using matched gene expression and DNA methylation data in EAC from TCGA and other publically available data, we also find that advanced methylomic drift is correlated with significant transcriptional repression of ~ 200 genes in important regulatory and developmental pathways, including several checkpoint and tumor suppressor-like genes. CONCLUSIONS: Taken together, our findings suggest that epigenetic drift evolution acts to significantly reduce the expression of developmental genes that may alter tissue characteristics and improve functional adaptation during BE to EAC progression.

Cost Effectiveness of Screening Patients With Gastroesophageal Reflux Disease for Barrett's Esophagus With a Minimally Invasive Cell Sampling Device.

BACKGROUND & AIMS: It is important to identify patients with Barrett's esophagus (BE), the precursor to esophageal adenocarcinoma (EAC). Patients with BE usually are identified by endoscopy, which is expensive. The Cytosponge, which collects tissue from the esophagus noninvasively, could be a cost-effective tool for screening individuals with gastroesophageal reflux disease (GERD) who are at increased risk for BE. We developed a model to analyze the cost effectiveness of using the Cytosponge in first-line screening of patients with GERD for BE with endoscopic confirmation, compared with endoscopy screening only. METHODS: We incorporated data from a large clinical trial of Cytosponge performance into 2 validated microsimulation models of EAC progression (the esophageal adenocarcinoma model from Massachusetts General Hospital and the microsimulation screening analysis model from Erasmus University Medical Center). The models were calibrated for US Surveillance, Epidemiology and End Results data on EAC incidence and mortality. In each model, we simulated the effect of a 1-time screen for BE in male patients with GERD, 60 years of age, using endoscopy alone or Cytosponge collection of tissue, and analysis for the level of trefoil factor 3 with endoscopic confirmation of positive results. For each strategy we recorded the number of cases of EAC that developed, the number of EAC cases detected with screening by Cytosponge only or by subsequent targeted surveillance, and the number of endoscopies needed. In addition, we recorded the cumulative costs (including indirect costs) incurred and quality-adjusted years of life lived within each strategy, discounted at a rate of 3% per year, and computed incremental cost-effectiveness ratios (ICERs) among the 3 strategies. RESULTS: According to the models, screening patients with GERD by Cytosponge with follow-up confirmation of positive results by endoscopy would reduce the cost of screening by 27% to 29% compared with screening by endoscopy, but led to 1.8 to 5.5 (per 1000 patients) fewer quality-adjusted life years. The ICERs for Cytosponge screening compared with no screening ranged from $26,358 to $33,307. For screening patients by endoscopy compared with Cytosponge the ICERs ranged from $107,583 to $330,361. These results were sensitive to Cytosponge cost within a plausible range of values. CONCLUSIONS: In a comparative modeling analysis of screening strategies for BE in patients with GERD, we found Cytosponge screening with endoscopic confirmation to be a cost-effective strategy. The greatest benefit was achieved by endoscopic screening, but with an unfavorable cost margin.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success.

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.

A Molecular Clock Infers Heterogeneous Tissue Age Among Patients with Barrett's Esophagus.

Biomarkers that drift differentially with age between normal and premalignant tissues, such as Barrett's esophagus (BE), have the potential to improve the assessment of a patient's cancer risk by providing quantitative information about how long a patient has lived with the precursor (i.e., dwell time). In the case of BE, which is a metaplastic precursor to esophageal adenocarcinoma (EAC), such biomarkers would be particularly useful because EAC risk may change with BE dwell time and it is generally not known how long a patient has lived with BE when a patient is first diagnosed with this condition. In this study we first describe a statistical analysis of DNA methylation data (both cross-sectional and longitudinal) derived from tissue samples from 50 BE patients to identify and validate a set of 67 CpG dinucleotides in 51 CpG islands that undergo age-related methylomic drift. Next, we describe how this information can be used to estimate a patient's BE dwell time. We introduce a Bayesian model that incorporates longitudinal methylomic drift rates, patient age, and methylation data from individually paired BE and normal squamous tissue samples to estimate patient-specific BE onset times. Our application of the model to 30 sporadic BE patients' methylomic profiles first exposes a wide heterogeneity in patient-specific BE onset times. Furthermore, independent application of this method to a cohort of 22 familial BE (FBE) patients reveals significantly earlier mean BE onset times. Our analysis supports the conjecture that differential methylomic drift occurs in BE (relative to normal squamous tissue) and hence allows quantitative estimation of the time that a BE patient has lived with BE.

The Role of Gastroesophageal Reflux and Other Factors during Progression to Esophageal Adenocarcinoma.

BACKGROUND: U.S. esophageal adenocarcinoma (EAC) incidence increased over 5-fold between 1975 and 2009. Symptomatic gastroesophageal reflux disease (sGERD) elevates the risk for EAC. However, a simple calculation suggests that changes in sGERD prevalence can explain at most approximately 16% of this trend. Importantly, a mechanistic understanding of the influence of sGERD and other factors (OF) on EAC is lacking. METHODS: A multiscale model was developed to estimate temporal trends for sGERD and OF, and their mechanistic role during carcinogenesis. Model calibration was to Surveillance, Epidemiology, and End Results (SEER) incidence and age-dependent sGERD data using maximum likelihood and Markov chain Monte Carlo (MCMC) methods. RESULTS: Among men, 77.8% [95% credibility interval (CI), 64.9%-85.6%] of the incidence trend is attributable to OF, 13.4% (95% CI, 11.4%-17.3%) to sGERD, and 8.8% (95% CI, 4.2%-13.7%) to sGERD-OF interactions. Among women, 32.6% (95% CI, 27.0%-39.9%) of the trend is attributable to OF, 13.6% (95% CI, 12.5%-15.9%) to sGERD, and 47.4% (95% CI, 30.7%-64.6%) to interactions. The predicted trends were compared with historical trends for obesity, smoking, and proton pump inhibitor use. Interestingly, predicted OF cohort trends correlated most highly with median body mass index (BMI) at age 50 (r = 0.988 for men; r = 0.998 for women). CONCLUSIONS: sGERD and OF mechanistically increase premalignant cell promotion, which increases EAC risk exponentially with exposure duration. IMPACT: Surveillance should target individuals with long-duration sGERD and OF exposures.

A Multiscale Model Evaluates Screening for Neoplasia in Barrett's Esophagus.

Barrett's esophagus (BE) patients are routinely screened for high grade dysplasia (HGD) and esophageal adenocarcinoma (EAC) through endoscopic screening, during which multiple esophageal tissue samples are removed for histological analysis. We propose a computational method called the multistage clonal expansion for EAC (MSCE-EAC) screening model that is used for screening BE patients in silico to evaluate the effects of biopsy sampling, diagnostic sensitivity, and treatment on disease burden. Our framework seamlessly integrates relevant cell-level processes during EAC development with a spatial screening process to provide a clinically relevant model for detecting dysplastic and malignant clones within the crypt-structured BE tissue. With this computational approach, we retain spatio-temporal information about small, unobserved tissue lesions in BE that may remain undetected during biopsy-based screening but could be detected with high-resolution imaging. This allows evaluation of the efficacy and sensitivity of current screening protocols to detect neoplasia (dysplasia and early preclinical EAC) in the esophageal lining. We demonstrate the clinical utility of this model by predicting three important clinical outcomes: (1) the probability that small cancers are missed during biopsy-based screening, (2) the potential gains in neoplasia detection probabilities if screening occurred via high-resolution tomographic imaging, and (3) the efficacy of ablative treatments that result in the curative depletion of metaplastic and neoplastic cell populations in BE in terms of the long-term impact on reducing EAC incidence.

Incremental benefits of screening colonoscopy over sigmoidoscopy in average-risk populations: a model-driven analysis.

PURPOSE: Screening colonoscopy and flexible sigmoidoscopy (FSG) reduce the risk of colorectal cancer (CRC), but the magnitude and duration of protection, particularly against right-sided cancer, remain uncertain. We computed the incremental benefit of colonoscopy over FSG using a validated mathematical model, which reflects colorectal neoplasia growth characteristics while allowing uncertainty in endoscopic detection and removal of adenomas. METHODS: We calibrated models of CRC incidence within a multistage clonal expansion framework to data from: (1) San Francisco-Oakland SEER registry (reference population) and (2) FSG long-term follow-up data from 50,757 individuals after a negative FSG in the Kaiser Permanente system. We compared the residual CRC risks after FSG with full-length colonoscopy. RESULTS: Our model mirrors trial data with 10-year CRC risk reductions after FSG screening at age 50 years of approximately one-third; the optimal age for a 'once-only' FSG exam was between ages 50 and 60 years; and the greater benefit was for men compared with women. There were considerable incremental gains in reduction in CRC risk by colonoscopy compared with FSG with the greatest benefit for screening colonoscopy at age 50 years. These results held up against lowering the right-sided adenoma detection sensitivity by 30%, as well as reducing the curative efficacy of polypectomy throughout the colon. CONCLUSIONS: Mathematical modeling of CRC screening, which takes account of important aspects of tumor biology, demonstrates superior risk reductions by colonoscopy over FSG. Our predictions provide further rationale for recommending screening colonoscopy in average-risk populations before the age of 60.

Exploring the recent trend in esophageal adenocarcinoma incidence and mortality using comparative simulation modeling.

BACKGROUND: The incidence of esophageal adenocarcinoma (EAC) has increased five-fold in the United States since 1975. The aim of our study was to estimate future U.S. EAC incidence and mortality and to shed light on the potential drivers in the disease process that are conduits for the dramatic increase in EAC incidence. METHODS: A consortium of three research groups calibrated independent mathematical models to clinical and epidemiologic data including EAC incidence from the Surveillance, Epidemiology, and End Results (SEER 9) registry from 1975 to 2010. We then used a comparative modeling approach to project EAC incidence and mortality to year 2030. RESULTS: Importantly, all three models identified birth cohort trends affecting cancer progression as a major driver of the observed increases in EAC incidence and mortality. All models predict that incidence and mortality rates will continue to increase until 2030 but with a plateauing trend for recent male cohorts. The predicted ranges of incidence and mortality rates (cases per 100,000 person years) in 2030 are 8.4 to 10.1 and 5.4 to 7.4, respectively, for males, and 1.3 to 1.8 and 0.9 to 1.2 for females. Estimates of cumulative cause-specific EAC deaths between both sexes for years 2011 to 2030 range between 142,300 and 186,298, almost double the number of deaths in the past 20 years. CONCLUSIONS: Through comparative modeling, the projected increases in EAC cases and deaths represent a critical public health concern that warrants attention from cancer control planners to prepare potential interventions. IMPACT: Quantifying this burden of disease will aid health policy makers to plan appropriate cancer control measures. Cancer Epidemiol Biomarkers Prev; 23(6); 997-1006. ©2014 AACR.

Time-series analyses of air pollution and mortality in the United States: a subsampling approach.

BACKGROUND: Hierarchical Bayesian methods have been used in previous papers to estimate national mean effects of air pollutants on daily deaths in time-series analyses. OBJECTIVES: We obtained maximum likelihood estimates of the common national effects of the criteria pollutants on mortality based on time-series data from ≤ 108 metropolitan areas in the United States. METHODS: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24-hr mean pollutant concentration on the previous day, while controlling for weather and temporal trends. We considered five pollutants [PM10, ozone (O3), carbon monoxide (CO), nitrogen dioxide (NO2), and sulfur dioxide (SO2)] in single- and multipollutant analyses. Flexible ambient concentration-response models for the pollutant effects were considered as well. We performed limited sensitivity analyses with different degrees of freedom for time trends. RESULTS: In single-pollutant models, we observed significant associations of daily deaths with all pollutants. The O3 coefficient was highly sensitive to the degree of smoothing of time trends. Among the gases, SO2 and NO2 were most strongly associated with mortality. The flexible ambient concentration-response curve for O3 showed evidence of nonlinearity and a threshold at about 30 ppb. CONCLUSIONS: Differences between the results of our analyses and those reported from using the Bayesian approach suggest that estimates of the quantitative impact of pollutants depend on the choice of statistical approach, although results are not directly comparable because they are based on different data. In addition, the estimate of the O3-mortality coefficient depends on the amount of smoothing of time trends.

Impact of tumor progression on cancer incidence curves.

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

Biomarker-based early cancer detection: is it achievable?

A new mathematical model evaluates the power of blood-based biomarkers for early cancer detection.

Number and size distribution of colorectal adenomas under the multistage clonal expansion model of cancer.

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

Multiscale estimation of cell kinetics.

We introduce a methodology based on the Luria-Delbruck fluctuation model for estimating the cell kinetics of clonally expanding populations. In particular, this approach allows estimation of the net cell proliferation rate, the extinction coefficient and the initial (viable) population size. We present a systematic approach based on spatial partitioning, which captures the local fluctuations of the number and sizes of individual clones. However, partitioning introduces measurement error by inflating the number of clones, which is dependent on time and the degree of cell migration. We perform various in silico experiments to explore the properties of the estimators and we show that there exists a direct relationship between precision and observation time. We also explore the trade-off between the measurement error and the estimation accuracy. By exploring different scales of cellular fluctuations, from the entire population down to those of individual clones, we show that this methodology is useful for inferring important parameters in neoplastic progression.

Colorectal cancer incidence trends in the United States and United kingdom: evidence of right- to left-sided biological gradients with implications for screening.

Several lines of evidence support the premise that screening colonoscopy reduces colorectal cancer (CRC) incidence, but there may be differential benefits for right- and left-sided tumors. To better understand the biological basis of this differential effect, we derived biomathematical models of CRC incidence trends in U.S. and U.K. populations, representing relatively high- and low-prevalence screening, respectively. Using the Surveillance Epidemiology and End Results (SEER) and the Office for National Statistics (ONS) registries (both 1973-2006), we derived stochastic multistage clonal expansion (MSCE) models for right-sided (proximal colon) and left-sided (distal colon and rectal) tumors. The MSCE concept is based on the initiation-promotion-progression paradigm of carcinogenesis and provides a quantitative description of natural tumor development from the initiation of an adenoma (via biallelic tumor suppressor gene inactivation) to the clinical detection of CRC. From 1,228,036 (SEER: 340,582; ONS: 887,454) cases, parameter estimates for models adjusted for calendar-year and birth-cohort effects showed that adenoma initiation rates were higher for right-sided tumors, whereas, paradoxically, adenoma growth rates were higher for left-sided tumors. The net effect was a higher cancer risk in the right colon only after age 70 years. Consistent with this finding, simulations of adenoma development predicted that the relative prevalence for right- versus left-sided tumors increases with increasing age, a differential effect most striking in women. Using a realistic biomathematical description of CRC development for two nationally representative registries, we show age- and sex-dependent biological gradients for right- and left-sided colorectal tumors. These findings argue for an age-, sex-, and site-directed approach to CRC screening.

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

The observation that the age-specific incidence curve of many carcinomas is approximately linear on a double logarithmic plot has led to much speculation regarding the number and nature of the critical events involved in carcinogenesis. By a consideration of colorectal and pancreatic cancers in the Surveillance Epidemiology and End Results (SEER) registry we show that the log-log model provides a poor description of the data, and that a much better description is provided by a multistage model that predicts two basic phases in the age-specific incidence curves, a first exponential phase until the age of approximately 60 followed by a linear phase after that age. These two phases in the incidence curve reflect two phases in the process of carcinogenesis. Paradoxically, the early-exponential phase reflects events between the formation (initiation) of premalignant clones in a tissue and the clinical detection of a malignant tumor, whereas the linear phase reflects events leading to initiated cells that give rise to premalignant lesions because of abrogated growth/differentiation control. This model is consistent with Knudson's idea that renewal tissue, such as the colon, is converted into growing tissue before malignant transformation. The linear phase of the age-specific incidence curve represents this conversion, which is the result of recessive inactivation of a gatekeeper gene, such as the APC gene in the colon and the CDKN2A gene in the pancreas.

Preneoplastic lesion growth driven by the death of adjacent normal stem cells.

Clonal expansion of premalignant lesions is an important step in the progression to cancer. This process is commonly considered to be a consequence of sustaining a proliferative mutation. Here, we investigate whether the growth trajectory of clones can be better described by a model in which clone growth does not depend on a proliferative advantage. We developed a simple computer model of clonal expansion in an epithelium in which mutant clones can only colonize space left unoccupied by the death of adjacent normal stem cells. In this model, competition for space occurs along the frontier between mutant and normal territories, and both the shapes and the growth rates of lesions are governed by the differences between mutant and normal cells' replication or apoptosis rates. The behavior of this model of clonal expansion along a mutant clone's frontier, when apoptosis of both normal and mutant cells is included, matches the growth of UVB-induced p53-mutant clones in mouse dorsal epidermis better than a standard exponential growth model that does not include tissue architecture. The model predicts precancer cell mutation and death rates that agree with biological observations. These results support the hypothesis that clonal expansion of premalignant lesions can be driven by agents, such as ionizing or nonionizing radiation, that cause cell killing but do not directly stimulate cell replication.

Does folic acid supplementation prevent or promote colorectal cancer? Results from model-based predictions.

Folate is essential for nucleotide synthesis, DNA replication, and methyl group supply. Low-folate status has been associated with increased risks of several cancer types, suggesting a chemopreventive role of folate. However, recent findings on giving folic acid to patients with a history of colorectal polyps raise concerns about the efficacy and safety of folate supplementation and the long-term health effects of folate fortification. Results suggest that undetected precursor lesions may progress under folic acid supplementation, consistent with the role of folate role in nucleotide synthesis and cell proliferation. To better understand the possible trade-offs between the protective effects due to decreased mutation rates and possibly concomitant detrimental effects due to increased cell proliferation of folic acid, we used a biologically based mathematical model of colorectal carcinogenesis. We predict changes in cancer risk based on timing of treatment start and the potential effect of folic acid on cell proliferation and mutation rates. Changes in colorectal cancer risk in response to folic acid supplementation are likely a complex function of treatment start, duration, and effect on cell proliferation and mutations rates. Predicted colorectal cancer incidence rates under supplementation are mostly higher than rates without folic acid supplementation unless supplementation is initiated early in life (before age 20 years). To the extent to which this model predicts reality, it indicates that the effect on cancer risk when starting folic acid supplementation late in life is small, yet mostly detrimental. Experimental studies are needed to provide direct evidence for this dual role of folate in colorectal cancer and to validate and improve the model predictions.