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Genetic GIScience: Toward a Place-Based Synthesis ofthe Genome, Exposome, and BehavomeGeoffrey M. Jacqueza, Clive E. Sabelb & Chen Shica Department of Geography, University at Buffalo—State University of New York, andBioMedwareb School of Geographical Sciences, University of Bristolc Department of Geography, University at Buffalo—State University of New YorkPublished online: 27 Apr 2015.

To cite this article: Geoffrey M. Jacquez, Clive E. Sabel & Chen Shi (2015): Genetic GIScience: Toward a Place-Based Synthesis of the Genome, Exposome, and Behavome, Annals of the Association of American Geographers, DOI:10.1080/00045608.2015.1018777

To link to this article: http://dx.doi.org/10.1080/00045608.2015.1018777

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Genetic GIScience: Toward a Place-Based Synthesisof the Genome, Exposome, and Behavome

Geoffrey M. Jacquez,* Clive E. Sabel,y and Chen Shiz

*Department of Geography, University at Buffalo—State University of New York, and BioMedwareySchool of Geographical Sciences, University of Bristol

zDepartment of Geography, University at Buffalo—State University of New York

The exposome, defined as the totality of an individual’s exposures over the life course, is a seminal con-cept in the environmental health sciences. Although inherently geographic, the exposome as yet is unfa-miliar to many geographers. This article proposes a place-based synthesis, genetic geographic informationscience (genetic GIScience), that is founded on the exposome, genomeC, and behavome. It provides animproved understanding of human health in relation to biology (the genomeC), environmental exposures(the exposome), and their social, societal, and behavioral determinants (the behavome). Genetic GIS-cience poses three key needs: first, a mathematical foundation for emergent theory; second, process-basedmodels that bridge biological and geographic scales; third, biologically plausible estimates of space–timedisease lags. Compartmental models are a possible solution; this article develops two models using pan-creatic cancer as an exemplar. The first models carcinogenesis based on the cascade of mutations and cel-lular changes that lead to metastatic cancer. The second models cancer stages by diagnostic criteria.These provide empirical estimates of the distribution of latencies in cellular states and disease stages, andmaps of the burden of yet to be diagnosed disease. This approach links our emerging knowledge of geno-mics to cancer progression at the cellular level, to individuals and their cancer stage at diagnosis, and togeographic distributions of cancer in extant populations. These methodological developments and exem-plar provide the basis for a new synthesis in health geography: genetic GIScience. Key Words: cancer epi-demiology, dynamical systems, genetic GIScience, health geography, space–time.

环境暴露（exposome），定义为个人一生中的总体暴露量，是环境健康科学中一个具有影响力的概念。儘

管环境暴露在本质上是地理的，但却尚未被诸多地理学者所熟知。本文提出一个根据地方的综合性基因

地理信息科学（genetic GIScience），该科学以环境暴露、基因组C与环境暴露的决定因素（behavome）为基础。此一概念，提供了人类健康之于生物（基因组C）、环境暴露（exposome），及其社会互动、社

会组织结构和行为的决定因素（behavome）的改良式理解。基因地理信息科学，提出三大主要需求：首

先，是新兴理论的数学基础；再者，是连结生物与地理尺度、以过程为基础的模型；第三，是对空间—时间的传染病迟滞进行生物学的可靠估计。划分的模型，是一个可能的解决方法；本文运用胰脏癌作为

范例，建立两种模型。第一个模型，根据导致转移型癌症的一系列变异与细胞改变，将致癌作用进行模

式化。第二个模型，则根据诊断标准，模式化癌症阶段。这些模型，提供了细胞状态与疾病阶段中，潜

伏因素的分佈之经验性估计，以及尚未被诊断出的疾病之压力描绘。本研究方法，将我们正在形成的基

因知识，连结至细胞层级的癌症进程、个人及其确诊时的癌症阶段，以及癌症在现今人口中的地理分

佈。这些方法论的发展与范例，为健康地理学提供了一个崭新的综合体之基础：基因地理信息科学。 关键词：癌症流行病学，动态系统，基因地理信息科学，健康地理学，空间—时间。

El exposoma, definido como la totalidad de las exposiciones a las que se somete un individuo en el curso dela vida, es un concepto seminal en las ciencias de la salud ambiental. Aunque es inherentemente geo-gr�afico, hasta ahora el exposoma no es familiar para la mayor�ıa de los ge�ografos. Este art�ıculo propone unas�ıntesis basada en lugar, la ciencia de la informaci�on geogr�afica gen�etica (SIGciencia gen�etica), la cual est�afundamentada en el exposoma, el genomaC y el “conductoma” (behavome). Tal s�ıntesis facilita un mejorentendimiento de la salud humana en relaci�on con la biolog�ıa (el genomaC), las exposiciones ambientales(el exposoma) y sus determinantes sociales, sociol�ogicos y conductuales (el conductoma). La SIGcienciagen�etica plantea tres necesidades claves: primera, una fundamentaci�on matem�atica para la teor�ıa emer-gente; segunda, modelos basados en proceso que conecten las escalas biol�ogica y geogr�afica; tercera, estima-tivos biol�ogicamente plausibles de los rezagos espacio-temporales de la enfermedad. Los modeloscompartimentados pueden ser una posible soluci�on; este art�ıculo desarrolla dos modelos, utilizando comoreferente el c�ancer pancre�atico. El primero modela la carcinog�enesis con base en la cascada de mutacionesy cambios celulares que desembocan en c�ancer metast�asico. El segundo modela las etapas del c�ancer con

Annals of the Association of American Geographers, 0(0) 2015, pp. 1–19� 2015 by Association of American GeographersInitial submission, August 2013; revised submissions, February and May 2014; final acceptance, May 2014

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criterios de diagn�ostico. Estos modelos proveen estimativos emp�ıricos de la distribuci�on de latencias enestados celulares y etapas de la enfermedad, y mapas de la carga de una enfermedad que todav�ıa est�a porser diagnosticada. Tal enfoque enlaza nuestro emergente conocimiento de la ciencia del genoma con laprogresi�on del c�ancer a nivel celular, con los individuos y su etapa del c�ancer en diagn�ostico, y con las dis-tribuciones geogr�aficas del c�ancer en poblaciones existentes. Estos desarrollos metodol�ogicos y el ejemploson la base para una nueva s�ıntesis en geograf�ıa de la salud: la SIGciencia gen�etica. Palabras clave: epi-demiolog�ıa del c�ancer, sistemas din�amicos, SIGciencia gen�etica, geograf�ıa de la salud, espacio-tiempo.

Environment, social, and individual factors all playa role in an individual’s health and well-being.Linking social and health data to a particular

location is important because where we live can anddoes influence our health (Tunstall, Shaw, and Dorling2004). Health outcomes are related to an individual’sphysical and social environment, including factors suchas water, soil, and air content; exposure to hazardousmaterials; tobacco smoke; occupation; marital status;social support; and characteristics of the home, in addi-tion to the composition of the local built environment(Marmot 2000; Pickle, Waller, and Lawson 2005).

Geographical epidemiology rests largely on theassumption that the spatial incidence of diseases holdsa key to their cause. High population mobility, longlatent periods, and environmental change complicatematters, however, distorting what might otherwise bea direct relationship between cause and effect (G. M.Jacquez 2004; Kwan 2009). This gives rise to what hasbeen called the space–time lag (Dearwent, Jacobs, andHalbert 2001; Griffith and Paelinck 2009). From ageographical point of view, this means that the placeor environment where the case is discovered and diag-nosed is not necessarily the same place or environmentwhere the exposure occurred (Picheral 1982; Sabelet al. 2000; Sabel et al. 2003).

Many studies examining associations between geo-graphical patterns of health and disease and causal fac-tors assume that current residence in an area can beequated with exposure to conditions that currently(and historically) pertain there (Bentham 1988). Thisis important, as the place of residence at the time ofdiagnosis or death is often adopted by epidemiologistsand geographers as the location for further analysis ofthe disease in question. Yet people move, and henceprevious exposure to pathogens will not be included inthe study. The problems will be greater for diseasesthat have a long lag or latency period, allowing plentyof time for mobility of the population. By adoptingonly the current residential address, not only will anindividual’s migration history be neglected but addi-tionally the daily “activity spaces” and associateduncertainties will be ignored (G. M. Jacquez 2004;

Kwan 2012). For chronic diseases such as cancer, weoften use the place of residence at diagnosis or death torecord the health event. But where people reside attime of diagnosis could be far removed from wherethey lived when causative exposures occurred. This dis-connect is widely recognized (Wheeler, Ward, andWaller 2012), yet techniques for estimating appropriatesampling distributions for latencies for the geographicmodeling of human diseases that are biologically rea-sonable, based on observable disease states, and thatincorporate knowledge of disease progression are sel-dom available. This article attempts to address thisneed using the construct of genetic GIScience.

Space–Time Geovisualization andModeling

There is a long and rich history of geographers inves-tigating space–time interaction from H€agerstraandthrough Forer to the present (H€agerstraand 1970; Forer1978; Richardson et al. 2013). Interest has focused onthe space–time cube. Space–time paths or geospatiallifelines have largely been used to visualize (oftenneglecting modeling) individual mobilities throughspace, such as Forer’s work in Auckland visualizingstudent lifestyles (Huisman and Forer 1998). Kwan(2000) has used the cube—she uses the term space–timeaquarium—to study accessibility differences among gen-der and different ethnic groups in Portland. Miller(1999) applied its principles in trying to establishaccessibility measures in an urban environment. Forphysical environmental exposures, Hedley et al. (1999)created an application in a geographical informationsystem (GIS) environment for radiological hazardexposure, and Gulliver and Briggs (2005) modeledspace–time interactions to traffic derived air pollution.Others have assessed similarity in geospatial lifelinesand clustered them to quantify disease patterns formobile populations (Sinha and Mark 2005; G. M.Jacquez et al. 2013). Modeling latency between expo-sure and disease outcomes largely remains neglected,however.

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Recent improved data gathering techniques, includ-ing the wider availability of Global Positioning System(GPS), cell phone, and social media data haverenewed interest in time geography and the space–time cube. Dykes and Mountain (2003) discussed datacollection techniques by mobile phone, GPS, andlocation-based services and suggested a visual analyti-cal method to deal with the data gathered. Lam(2012) and Bian et al. (2012) both discussed ongoingchallenges to health risk assessment despite the wideravailability of individual-level data.

The Exposome, GenomeC, and Behavome

A new synthesis in health geography we are callinggenetic GIScience seeks to document, quantify, andmodel the relationships among place, the genome, theexposome (Wild 2005, 2012), and the behavome thatare the determinants of illness and wellness (Figure 1).This builds on and extends prior constructs in human

biology and ecology, such as the nature–nurture debateand Meade’s triangle of human ecology, which viewedhealth outcomes as the result of place- and time-spe-cific interactions among populations, their environ-ments, and their behaviors (Meade 1977).

This paradigm requires an explicit understanding ofhow these determinants are related to space–time pat-terns of health outcomes in human populations.Because the genome, exposome, and behavome aredefined at the level of the individual, techniques forestimating disease latency—the time between theonset of disease and its diagnosis—are essential. A sec-ond key need is the ability to integrate and model theinfluence of the genome, exposome, and behavomeacross biological scales and to then geographicallymap the results at local and regional scales. Finally,sound theory often requires a solid mathematical foun-dation, and one must be established for genetic GIS-cience. This article seeks to begin to mathematicallyformalize these requirements, and poses an exampleusing one of the least understood cancers, pancreaticcancer.

Exposome

The term exposome was introduced by Wild (2005)to “encompass life-course environmental exposures(including lifestyle factors), from the prenatal periodonwards . . . the exposome is a highly variable entitythat evolves throughout the lifetime of the individual”(1848). The exposome concept recognizes three broadcategories of nongenetic exposures: internal (e.g.,metabolism), specific external (e.g., air pollution), andgeneral external (e.g., socioeconomic factors; Wild2012). Although a person’s genome is fixed at concep-tion, internal and external sources of exposure causethe human’s internal chemical environment to varythroughout life (Rappaport 2011; Miller and Jones2014). Essentially, an individual will have a particularprofile of exposure at any given point in time thatmakes the characterization of the exposome so chal-lenging (Wild 2012). It is a concept to measure effectsof a lifelong exposure to environmental influences onhuman health and therefore requires longitudinal sam-pling especially during fetal development, early child-hood, puberty, and the reproductive years (Rappaport2011). These measures include external monitoringand modeling of media such as air and water but alsobiomonitoring (i.e., measurements) of biologicalmarkers of exposure through methods such as blood or

Figure 1. Schematic representation of genetic geographic infor-mation science (genetic GIScience). The three primary determi-nants of health, both in terms of illness and well-being, are (1) anindividual’s biology, which can quantified as his or her genomeC,made up of the genome (genetic composition), regulome (whichcontrols gene expression), proteome (complement of amino acidsand proteins), and metabalome (the basis of metabolism andhomeostasis); (2) the environments he or she experiences, whichcould be quantified as the exposome, defined as the totality ofexposures over the life course (Wild 2005); (3) the totality of anindividual’s health behaviors over the life course, which could bequantified as the behavome and mediate the exposome and inter-actions between the exposome and the genomeC. These determi-nants of human health act through place, defined as thegeographic, environmental, social, and societal milieus experi-enced over a person’s life course. This synthesis is referred to asgenetic GIScience.

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urine sampling (Lioy and Rappaport 2011). Rappaport(2011) prioritized a top-down approach, applying bio-monitoring to identify all important exposures, over abottom-up approach that is based on air, water, or soilsamples to identify all exogenous exposures.

Van Tongeren and Cherrie (2012), on the otherhand, supported the aim of developing an integratedconcept of exposomics, taking all sources of availableexposure information into account. Internal and exter-nal exposure data, personal behavior, and environ-mental measurements could thus be used to determinethe exposome. This requires the collaboration ofresearchers from a variety of disciplines to promote theconcept and unravel complex relationships amongsocial interactions, biological effects, and the risk ofdiseases (Wild 2012), an endeavor suited to but largelyunexploited by geographers.

The exposome has a public health-oriented objec-tive and the aim of its application is to aggregate upfrom a group of individuals to a population, providingthe basis for public health decisions (Wild 2012).

GenomeCThe genomeC is made up of the individual’s

genome (genetic composition), regulome (which con-trols gene expression), proteome (their complement ofamino acids and proteins), and metabalome (the basisof metabolism and homeostasis). Together, these con-stitute a good portion of an individual’s biologicalmakeup. The last few years have seen major advancesin our ability to quantify the genomeC. Technologyimprovements have dramatically reduced genomesequencing costs. In 2000 the Human Genome Projectsequenced the first whole human genome, at a cost ofover US$2 billion (Davies 2010). In 2012, the 1000Genomes Project released their Phase 1 sequencingdata (Pybus et al. 2014), documenting genetic varia-tion in more than 1,000 individuals from twenty-fivepopulations from around the globe (The 1000Genomes Project Consortium 2012). Genomesequencing costs continue to drop, and the US$1,000whole sequence genome is now available (Hayden2014). In medical practice and research, wholegenome sequencing poses ethical challenges regardinginformation disclosure to the individual, especiallygiven incomplete knowledge of the genetic basis ofdisease (Yu et al. 2013). Nonetheless, whole genomesequencing as a commodity will soon cost US$100.Dramatic cost reductions are occurring in the exome,

epigenome, and other genomeC constituents (Mefford2012; Meissner 2012; Weinhold 2012; Zentner andHenikoff 2012). It is clear that measurements of thegenomeC will soon be widely and inexpensively avail-able and will be incorporated into individual elec-tronic health records, notwithstanding the informaticsand ethical challenges posed by their integration(Hazin et al. 2013; Kho et al. 2013; Tarczy-Hornochet al. 2013; Flintoft 2014).

As our understanding of the genetic bases of diseasehas grown, the need for a systems biology approach thatintegrates across genetic, cellular, organ, individual,and population-level scales is increasingly recognized(Ore�si�c 2014). How can we incorporate knowledge,for example, of the cascade of genetic mutations lead-ing to pancreatic cancer into our understanding ofcancer latency, and how might this impact estimatesof the burden of cancer at the population level? Howdo changes manifested in pancreatic cells as a result ofmutations translate into cancer progression, and canwe construct models that capture biological nuanceyet are suited to GIScience? For geographers, how cansystems biology approaches be integrated into space–time geographic disease models? This article addressesthese needs by linking a model of carcinogenesis at thecellular level with a model of cancer stages at the indi-vidual and population level.

Behavome

The behavome is made up of an individual’s health-related behaviors over the life course and is the mostinchoate of the genetic GIScience triad of thegenomeC, exposome, and behavome. Recognitionmethods for assessing individual behaviors have beenan important research topic for decades. With theadvent of sensors in residences, health care facilities,and even wearable sensors on patients, the issue ofmultisensor data fusion for activity recognition hasemerged. These technologies are already beingdeployed and assessed in nursing home and assistedliving facilities but as yet have little penetration in thegeographic literature. Recent research has demon-strated that these methods can identify risky behaviorswith good accuracy and low deployment costs(Palumbo et al. 2013). The Internet of things, includ-ing smart homes, smart cars, and smart workplaces, isin the early phase of what many predict to be explosivegrowth (Ashton 2009). In 2008 the number of deviceson the Internet exceeded the number of people, and in2020 it will exceed 50 billion devices (Swan 2012).

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Information on when, where, and how we use applian-ces, electronic devices, machinery, and environmentalcontrols in home and workplace settings and whilecommuting has yet to be used to quantify the behav-ome. The value of near real-time data on ambienttemperatures and how often and when we use therefrigerator might have enormous value for quantify-ing, for example, personal energy budgets, a key prob-lem in cancer etiology (Ballard-Barbash et al. 2013;Hursting 2014). A variety of different approaches forassessing health behaviors have been suggested usingtechnologies such as inertial sensors, GPS, smarthomes, radio frequency identification, and others.Most promising is the sensor fusion approach thatcombines data from several sensors simultaneously(Lowe and �OLaighin 2014). To our knowledge, tech-nologies such as Google Glass have yet to be used forcapturing video images to chronicle dietary intake andother health-related activities. Other potential appli-cations include quantification of personalized environ-mental metrics such as individual walkability (e.g.,Mayne et al. 2013). Once health-related behaviors areknown, the possibility of using gamification (Whitson2013) and other approaches to encourage salubriousbehaviors becomes possible (Schoech et al. 2013).

Contribution of This Article

This article proposes a synthesis of the genomeC,exposome, and behavome that is place based and offersa promising new landscape for research in health geog-raphy—genetic GIScience. The potential researchcontributions this synthesis offers geographers aremanifold, including health geography, quantitativemethods, behavioral geography, visualization, space–time modeling, and social geography. The exposomeand behavome are new concepts with many unsolvedgaps of their own, several of which are addressed inthis article. First, we demonstrate how disease laten-cies could be estimated using compartmental modelsand data available from systems biology. Diseaselatency estimation is a key problem for space–timelags in health geography. Second, space–time modelsthat account for individual disease processes yet pro-vide geographic estimates of disease burden are almostentirely lacking in health geography, a significant gapaddressed by this article. Finally, as a motivatingexample, we develop and apply a comprehensivemodeling approach that estimates cancer latency, cou-ples carcinogenesis and stage models, and represents

and links processes at the genomic level (e.g., muta-tion events, cascades of genetic changes that lead tocancer), cellular level (e.g., cell replication and death,DNA repair), organ level (e.g., carcinogenesis in situand metastases to distant organs), individual level(e.g., cancer staging in the individual, progression ofindividuals through cancer stages), to the populationlevel (e.g., predicted geographic distributions of undi-agnosed cancers). This by no means addresses all ofthe challenges and gaps posed by genetic GIScience,but it hopefully illustrates the promise of this researchdirection and perhaps points the way forward.

It is important to note that the breadth of the con-cept and challenge represented in Figure 1 is substan-tial. This aim of this contribution is to communicateits scope, identify key research problems, and proposea way forward. The example of pancreatic cancer pre-sented here deals primarily with the genomeC. At thetime of this writing, measurement of the exposome isat a nascent stage, and the term behavome is new.When data from the exposome and behavome becomeavailable, they can be incorporated into the modelingframework through place- and person-specific effectson model flow parameters; for example, DNA muta-tion and repair rates. Opportunities for such adapta-tion and extension of the modeling framework areidentified in the discussion.

We begin with an introduction to the approach forthe modeling and analysis of dynamic geographic sys-tems using process-based temporal lags. This is followedby a brief background on latency estimation approachesthat motivate the use of residence times in compart-mental systems. A primer on compartmental analysis ispresented, followed by a simple three-stage model ofdisease and results for distributions of residence times.Next, the specific example of pancreatic cancer is con-sidered, and a five-state model of carcinogenesis isdeveloped along with its biological foundation. A sec-ond model of progression through cancer stages basedon diagnostic criteria used by the American CancerAssociation follows. These models are linked usingknowledge of the mapping of stage of diagnosis withprogression of tumor growth and metastatic capacity.This is applied to data from the Michigan cancer regis-try on stage at diagnosis for all incident pancreatic can-cers in white males from 1985 to 2005 in the Detroitmetropolitan area. Potential applications of thisapproach and next steps are then discussed.

The generalized approach (Figure 2, left) applies toany geographic system amenable to a compartmentalrepresentation. Here the emphasis is on the

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development of a minimally sufficient but mechanisti-cally reasonable systems model. An example applica-tion to a dynamic geographic systems model of cancerusing residence times to estimate latency is shown inFigure 2 (right).

Ideally, genetic GIScience will be based on model-based theory with several characteristics. First, modelsmust be biologically reasonable and capture relevantaspects of disease etiology and natural history. Second,they must provide estimates of the distributions of dis-ease latency. Third, they must be estimable fromempirical data, so we can derive latency distributionsfrom observable measures and based on the currentstate of knowledge of the disease. Fourth, they mustprovide for geographically referenced data on individ-uals. The derivation of biologically based estimates ofdisease latency is a difficult problem, and we next con-sider alternative approaches to latency estimation.

Disease Latency Estimation

Several techniques exist for modeling diseaselatency, including representations of cohort exposures,

developmental stages of vulnerability, models ofempirical induction periods, and compartmental mod-els. We summarize these before focusing on residencetimes in compartmental systems.

Cohort exposures arise when a common exposureoccurs for a group of individuals, resulting in an overallincrease in disease risk. Here the temporal lag betweenthe causal event and health outcomes is directlyobservable. For example, Chernobyl released radioac-tive iodide over Belarus and led to an increase in pedi-atric thyroid cancers. The latent period for tumordevelopment was four to six years (Nikiforov andGnepp 1994).

Developmental stages of vulnerability arise when thetiming and characteristics of biological stages of devel-opment are associated with increased risk of an adversehealth event in later years. For example, genetic riskaccounts for approximately 10 to 15 percent of breastcancer cases, and the windows of vulnerability occurbefore a woman’s first birth and during the develop-ment of breast tissues (Colditz and Frazier 1995). Herean average latency and its distribution could be esti-mated as the time from the developmental stage to dis-ease diagnosis.

Figure 2. Steps in dynamic geographic systems analysis (left) and specific application to cancer using knowledge of residential history tobudget excess risk (right).

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The empirical induction period models latency as thesum of induction and latent periods defined as theperiods between causal action and disease initiation(induction) and between disease initiation and detec-tion (latent). The sum of the induction and latentperiods is the empirical induction period. The induc-tion period is not estimable except in relation to spe-cific etiologic factors, as different exposures havedifferent levels of effect on disease expression(Rothman 1981).

Residence times in compartmental models of diseasecan be obtained directly from the model itself. For agiven compartmental model and parameter values, themean residence time and distribution of residencetimes in each compartment are known. This resultholds for both deterministic and stochastic compart-mental models but has yet to be used in geographicmodels of human disease. When the compartmentscorrespond to stages of disease, the compartmental res-idence times are estimates of disease latency. Com-partmental models thus are best constructed socompartments correspond to known disease states(e.g., are biologically reasonable), and the coefficientsgoverning transitions between compartments are for-mulated in terms of known biological and infectionprocesses (e.g., the mechanics are process-based). Resi-dence times from compartmental models thus conveythe characteristics required at the beginning of thissection: (1) They can be formulated in a biologicallyreasonable fashion; (2) they provide estimates of thedistribution of latencies; and (3) whether a givenmodel, and hence its residence times, is estimable isknown once the model and observable measures areidentified. The remainder of this article employs com-partmental models. A primer on compartmental mod-els is provided as supplemental material on thepublisher’s Web site.

Residence Times

Residence times are the time required for a particleto enter and then exit a compartment. Compartmentresidence times could be used in model validation bycomparing residence times from the model to theobserved residence times. For linear compartmentalmodels the residence times are inverse exponentialfunctions, and closed-form solutions for calculatingthe probability density functions are known (J. A. Jac-quez 1996). In deterministic nonlinear compartmentalsystems, the distributions of residence times are

functions of the state variables and hence of thecompartments’ sizes. The probability density functionsof linear stochastic models are the same as for theirdeterministic analog. The probability density func-tions of residence times for nonlinear stochastic sys-tems differ from those of their nonlinear deterministiccounterpart, however (J. A. Jacquez 2002). This articlepresents residence times linear deterministic stage-based models of cancer, which also apply to their lin-ear stochastic counterparts.

Simplicity versus Complexity, and Implications forResidence Times

There is a tension between simplicity, which makesmodels easier to understand and mathematically trac-table, and complexity, which seeks to incorporate thenuances and details of a complex reality. Simplicitymight correspond to a representation with fewer com-partments, an implicit combining of compartmentsthat has implications for the modeling of residencetimes. When the residence times for a compartment ina model are too short, the creation of subcompart-ments to represent that compartment can be used toobtain longer average residence times (J. A. Jacquezand Simon 2002). Correspondence of residence timesto those observed in the system under scrutiny thuscan be used as a diagnostic for model oversimplifica-tion and misspecification.

Modeling Carcinogenesis: Cancer in theIndividual

For the geographic modeling of disease we are inter-ested in identifying places and subpopulations charac-terized by an excess of cancer for individuals in thosestates of carcinogenesis when exposures to mutagensmight have been causal. That is, we are looking forthe geographic signature of the actions of past envi-ronmental exposures that gave rise to cancers. To dothis we require biologically reasonable models of carci-nogenesis (e.g., the biological events that have canceras their sequelae) and cancer stages (how cancers prog-ress once they have started). We begin withcarcinogenesis.

The initial biological event leading to cancer isdamage to DNA. Such damage occurs on one DNAstrand, and repair mechanisms can reverse that dam-age. Whether the damage is maintained among daugh-ter cells depends on the timing of replication and

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repair. If replication occurs before repair, the damagedDNA strand is passed on to the daughter cells (a fixedmutation). Notice that only some of these mutationsare deleterious and lead to cancers.

Carcinogenesis models usually treat irreversiblesteps in the chain of mutations leading to cancer ascomprised of substates with reversible damage attribut-able to DNA repair mechanisms (Kopp-Schneider,Portier, and Rippman 1991; J. A. Jacquez 1999). Thelast few years have seen dramatic advances in ourunderstanding of tumor genetics, and it now is possibleto sequence the genomes sampled from cancer tumorsto elucidate the sequence of mutations that lead tocancer. The specific mutations vary from one tumor to

another and from one patient to another, but the stepsof mutation, repair, and fixation of deleterious muta-tions via replication events are largely the same. Thesubstates of a model of carcinogenesis thus should beconstructed to correspond to the observed tumor mor-phological characteristics, with flows correspondingto state transitions from mutation, repair, andreplication.

Consider pancreatic cancer (Figure 3) and its corre-sponding compartmental model (Figure 4). A cascadeof specific mutation events lead to pancreatic cancer(Alian et al. 2014), although these differ from onepatient to another (Maitra and Hruban 2008). Thesemutations include KRAS2, p16/CDKN2A, TP53,

Figure 4. Model of pancreatic cancer carcinogenesis.

Figure 3. Schematic of the evolution of pancreatic cancer. Normal pancreatic duct epithelial cells undergo mutation events to become aninitiated tumor cell. Additional mutations and clonal expansions lead eventually to a founder cell of the index pancreatic cancer clone.These produce subclones with metastatic capacity, eventually leading to dissemination to distant organs such as the liver. Times shown arethe empirical residence times in each system state. Source: Adapted from Yachida et al. (2010). Reprinted by permission from MacmillanPublishers Ltd.: Nature. (Color figure available online.)

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SMAD4/DPC4, and other genes and result in genomicand transcriptomic alterations that lead to invasion,metastases, cell cycle deregulation, and enhanced can-cer cell survival (Maitra and Hruban 2008). Precursorlesions include the mucinous cycstic neoplasm (MCN),the intraductal papillary mucinous neoplasm (IPMN),and the pancreatic intraepithelial neoplasia (PanIN).Here we consider the PanIN pathway, which is thoughtresponsible for the majority of pancreatic cancers.

Carcinogenesis is initiated by a mutation in a nor-mal cell that leads to accelerated cell proliferation.Waves of clonal expansion along with additionalmutations progress to PanIN during time T1 (Fig-ure 3). This corresponds to the substates q1 (normalcell) and q2 (PanIN) in the model in Figure 4. Onefounder cell from a PanIN lesion will start the parentalclone that will initiate an infiltrating carcinoma; thisis indicated by the irreversible flow (k32) from q2 to q3in Figure 4. Here substate q3 is the parental clone, andsubstate q4 indicates subclones with metastatic capac-ity. The flow k32 to substate q3 thus represents that rep-lication that gives rise to the index pancreatic cancerlesion (the cells in q3), along with the mutation eventsthat confer metastatic capacity (resulting in the cellsin q4). The empirical residence time in substates q3and q4 is T2. The irreversible flow k54 indicates a pro-liferation and spreading of cells with metastatic capac-ity, with metastases (state q5) to other organs such asthe liver occurring in time T3. The observed averagetimes in each model state are T1 D 11.7 years, T2 D6.8 years, and T3 D 2.7 years (Campbell et al. 2010).These are the empirical residence times in those statesdescribing pancreatic carcinogenesis and were esti-mated from tumor histology and tumor genetics. Thismodel is consistent with recent findings regardingmechanisms of pancreatic tumorigenesis. For example,inflammation and injury are implicated as a precursorevent in some pancreatic cancers, leading to acinar-to-ductal metaplasia (ADM). ADM is reversible, butan oncogenic mutation in KRAS prevents this, andthe injured cells enter the pathway to PanIN. Addi-tional mutation events then can result in pancreatic

ductal adenocarcinoma (Seton-Rogers 2012), repre-sented by the “pancreatic cancer” metacompartmentin Figure 4. Details on model specification, systemequations, parameter estimates, and equilibrium con-ditions are provided in the supplemental materials onthe publisher’s Web site.

Residence Times

For an outflow connected system without inflow andcomprised of n compartments (Figure 5), the compart-ment sizes and density function of residence times,given an input of 1 unit at t D 0 into compartment 1,are (J. A. Jacquez 2002)

qn D kn¡ 1tn¡ 1

.n¡ 1/!e¡ kt (1)

u.r; t/D kntn¡ 1

.n¡ 1/!e¡ kt: (2)

Here r specifies the proportions of particles in the ncompartments such that the first compartment has size1, and the others have size 0. This means that the ini-tial conditions specify that all particles at time 0 are incompartment 1. These equations could be applied tosolve for the density function of residence times in thecompartmental model of pancreatic cancer (Figure 4)in the subsystems PanIN, pancreatic cancer, and meta-static pancreatic cancer, given certain simplifyingassumptions.

See the supplemental material provided on the pub-lisher’s Web site for the estimation of residence timesin the compartmental model of pancreatic cancer.

Modeling Cancer Stages: Cancer in Populations

We now present a model of pancreatic cancer stages(Figure 6). Here, the unit of observation is the cancerpatient, and we observe counts of patients in early-and late-stage pancreatic cancer, before and after diag-nosis (Figures 7A and 7B). Counts of people in early

Figure 5. Outflow connected n compartment system useful for solving for the probability density function and cumulative distributionfunction of residence times.

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and late stages prior to diagnosis are representedby q6 and q7. Compartment q8 is made up ofpatients who have been diagnosed, in either early-or late-stage cancer. The flow of the number ofhealthy individuals entering early-stage cancer isF60. The rate of progression from early- to late-stage cancer is k76. Diagnosis events from earlyand late stages are given by the rates k86 and k87.Death from the compartments is represented bym6, m7, and m8.

The system equations for this stage-based model ofpancreatic cancer are

dq6dt

D F60¡ q6.k76C k86Cm6/

dq7dt

D q6k76 ¡ q7.k87Cm7/

dq8dt

D q6k86C q7k87¡ q8m8: (3)

Equilibrium occurs under the following conditions:

0D dq6dt

D dq7dt

D dq8dt

q6D F60.k76C k86Cm6/

q7 D q6k76.k87Cm7/

q8D q6k86C q7k87m8

: (4)

Figure 7. Choropleth maps of pancreatic cancer cases in southeastMichigan, 1985–2005: (A) incident cases; (B) stage-known cases;(C) silent (yet to be diagnosed) cases. (Color figure available online.)

Figure 6. Stage-based model of pancreatic cancer. Here the com-partment sizes are number of patients with early (q6) and late-stagecancers (q7) prior to diagnosis, and the number diagnosed (q8).

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The number of incident early- and late-stage cancers(compartment q8) is directly observable in most of thestates in the United States from cancer registry data.The flows q6k86 and q7k87 are observable as the numberin a defined time period of early- and late-stage diag-noses. The mortality rate q8m8 is directly observable asthe number of diagnosed pancreatic cancer patientswho die in a defined time period. The quantities q6m6

and q7m7 are the number of deaths of people withearly- and late-stage undiagnosed pancreatic cancer.The estimation of parameter values and the number ofyet-to-be-diagnosed cancer cases will be demonstratedlater in the example of pancreatic cancer in southeastMichigan.

Carcinogenesis and Stage-Based Model of PancreaticCancer

The carcinogenesis model deals with pancreaticcancer cells in histological and genetic states as com-partment members, whereas the stage-based modeluses individuals and the stage of their pancreatic can-cer to define compartment membership. The model ofcarcinogenesis informs the stage model through anequivalence of residence times and model states(Tables 1 and 2).

Application: Pancreatic Cancer inSoutheast Michigan

To demonstrate the approach, we apply the stage-based model to incident pancreatic cancer cases insoutheastern Michigan. We employ the four stepsillustrated in Figure 2, customized to this specificapplication.

1. Develop the minimally sufficient biologicallyreasonable systems model.

2. Solve for residence times, compartment sizes,and flows.

3. Map the data to identify local populations withexcess risk.

4. Interpret the results.

Background and Data

An analysis of pancreatic cancer mortality in whitemales in Michigan counties in two time periods from1950 to 1970 and 1970 to 1995 found statistically sig-nificant clusters that persisted in Wayne County in

Table 1. Equivalence of model states and residence times between carcinogenesis- and stage-based models, usingdiagnostic pancreatic cancer staging according to the American Cancer Society American Joint Committee on Cancer

(Edge et al. 2010)

Stage modelcompartment

Carcinogenesismodel compartment Description

American Joint Committee onCancer staging Residence time

q6 q3, q4 In situ, local, not diagnosed In situ: AJCC Tis, N0, M0Local: AJCC IA, IB, N0, M0

T2: 6:8§ 3:4 years

q7 q5 Regional, distant, not diagnosed Regional: AJCC IIA, IIBDistant: AJCC IV

T3: 2:7§ 1:2 years

q8 — Diagnosed pancreatic cancer May be in situ, local, regional, ordistant; in most cases

pancreatic cancer is diagnosedat an advanced stage

T4: 0:5§ 0:25 years (2011 five-year survival rate < 6% andaverage life expectancy afterdiagnosis is 3–9 months)

Note:AJCC D American Joint Committee on Cancer; Tis D carcinoma in situ; N0D no regional lymph node metastasis; M0 D no distant metastasis.

Table 2. Correspondence of modeled cancer stages toanatomic stages from the American Joint Committee

on Cancer

Model stage AJCC stage Prognostic groups Diagnosed

Stage 0 Tis N0 M0 NEarly (q6) Stage IA T1 N0 M0 N

Stage IB T2 N0 M0 NStage IIA T3 N0 M0 N

Late (q7) Stage IIB T1–3 N1 M0 NStage III T4 Any N M0 NStage IV Any T Any N M1 N

Diagnosed (q8) Any stage Any T Any N Any M Y

Note: AJCC D American Joint Committee on Cancer. Primary tumor (T)coding: Tis D carcinoma in situ; T1 D tumor limited to pancreas, 2 cm orless in greatest dimension; T2 D tumor limited to pancreas, more than2 cm in greatest dimension; T3 D tumor extends beyond the pancreas butwithout involvement of the celiac axis or the superior mesenteric artery;T4D tumor involves the celiac axis or the superior mesenteric artery (unre-sectable primary tumor). Regional lymph nodes (N) coding: N0 D noregional lymph node metastasis; N1 D regional lymph node metastasis. Dis-tant metastasis (M) coding: M0 D no distant metastasis; M1 D distantmetastasis.

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both time periods and that expanded to includeadjacent Macomb County in 1970 to 1995 (G. M.Jacquez 2009). This finding was confirmed usingmore recent incidence and mortality data from theSurveillance Epidemiology and End Results program(SEER; Ries et al. 2007). Seventeen registry areas areincluded in the SEER program: Atlanta, rural Geor-gia, California (Bay Area, San Francisco–Oakland,San Jose–Monterey, Los Angeles, and Greater Cali-fornia), Connecticut, Hawaii, Iowa, Kentucky, Louisi-ana, New Jersey, New Mexico, Seattle-Puget Sound,Utah, and Detroit. In 2000 to 2004, Detroit had thehighest age-adjusted incidence rate of pancreatic can-cer for white males at 15.0 cases per 100,000 out ofall of the seventeen registry areas and the secondhighest mortality rate at 12.9 deaths per 100,000. Incontrast, the SEER-wide averages for white males inthis period were 12.8 incident cases and 12.0 deathsper 100,000. Notice that the incidence is nearly equalto the deaths for the SEER-wide averages (12.8 vs.12.0), but the incident cases in Detroit exceed themortality rate by a larger difference (15.0 vs. 12.9).This is consistent with the observation that pancre-atic cancer incidence in Detroit is increasing andthat the Detroit system might not be in equilibrium.In terms of our compartmental model, it appears theflows in (F06) exceed the flows out due to mortality(q8m8). Notably, the Detroit registry pancreatic cancermortality for white males in 2000 to 2004 increased onaverage 0.9 percent per year (calculated by SEER*Statfrom the National Vital Statistics System public usedata file). The population covered by the Detroit regis-try in this period was 1,365,315 white males. The find-ing of excess pancreatic cancer mortality withincreasing incidence was thus independently con-firmed by data from SEER and found to persist from1950 through 2004 (G. M. Jacquez 2009).

As a follow-up to this study, we obtained annualincidence data from the Michigan Cancer Surveil-lance Program (MCSP) for the period from 1985 to2005. The Michigan Cancer Registry is a gold-stan-dard registry with its completeness and accuracy certi-fied on an annual basis, and MCSP compiles cancerrecords for the state. Funded in part by the NationalProgram of Cancer Registries of the Centers for Dis-ease Control, the MCSP is nationally certified by theNorth American Association of Central Cancer Regis-tries. External audits have found a completeness per-centage of 95 percent or higher on the population-based data collected by the MCSP.

Data Cleaning and Processing

The geocoding budget and numbers of observationsare as follows. A total of 11,068 pancreatic cancercases were diagnosed between 1 January 1985 and 31December 2005. Of these, 192 addresses of place of res-idence at diagnosis failed to geocode, leaving 10,876cases with known places of residence at diagnosis.Stage at diagnosis (in situ, local, regional, distant, andunknown) was recorded as unknown for 2,250 of these,leaving 8,826 cases with known place of residence andknown stage at diagnosis. The head of pancreas andpancreas not otherwise specified were the most fre-quent primary sites, with 4,496 and 1,621 cases, respec-tively. Males accounted for 4,202 cases and females4,424. By race, 6,356 cases were whites, 2,192 blacks,and the balance American Indian (8 cases), Asian (61cases), and other or unknown groups (9 cases).

Analysis Steps

Step 1: Describe the Model

We employ the model of pancreatic cancer stagesin Figures 7A and 7B and system equations inEquation 3.

Step 2: Estimate Flows, Compartment Sizes, andResidence Times

The quantities directly observable are the incidentflows into compartment 8 from early- and late-stagebut not diagnosed cancers. We use the data for all inci-dent pancreatic cases, whether they were geocoded ornot and whether the stage at diagnosis was known orunknown. Let oe be the total number of cases from1985 through 2005 observed in the early stage, oL bethe number in late stages, and ou be the number in anunknown stage. Y is the number of years over whichthe observations accrued (twenty-one years). We canthen estimate the flows into compartment q8 for early-and late-stage cancers as

dq6k86 D .oe C .oe=.oeC oL//ou/

YD 1246:8

21D 59:37

(5)dq7k87 D .oLC .oL=.oeC oL//ou/

Y

D 1246:8

21D 467:67:

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The units on these are number of cases in the givenstage diagnosed per year. According to the AmericanCancer Society, for all stages of pancreatic cancercombined, the one-year relative survival rate is 20 per-cent, and the five-year rate is 4 percent. For m8 D 0:8deaths per diagnosed case year, and assuming the equi-librium condition in Equation 5, we estimate the sizeof compartment q8 as

bq8 D q6k86C q7k87m8

D 658:81: (6)

This is the average number of diagnosed and surviving(not yet deceased) pancreatic cancer cases. For thelate-stage but not diagnosed cases in compartment q7we note that at equilibrium

q7.k87Cm7/D q6k76: (7)

The rate m7 is deaths of late-stage but not diagnosedcases that are not diagnosed after the death event andthus do not flow into compartment q8 (they wouldhave to be diagnosed to enter this compartment). Weimpose m7 D 0, under the assumption that all of thelate-stage pancreatic cancer cases are diagnosed (thisassumption can be relaxed but seems reasonablebecause late-stage pancreatic cancers are by definitionadvanced and metastatic). Hence, deaths for late-stagebut not yet diagnosed cases are diagnosed after theydecease. This then yields

q7k87D q6k76D 467:67: (8)

Again, the units here are number of cases per year.Because q7k87D q6k76 and q6k86D 59:37;

bq7 D 59:37k76

.k86C k87/: (9)

The age-adjusted annual mortality rate from all causesin Michigan in 2010 was 764.2 deaths per 100,000(Mini~no and Murphy 2012) and has decreased from1,027.1 deaths per 100,000 in 1985 (Michigan Depart-ment of Community Health 2012). We therefore esti-mated the background mortality rate from 1985 to2005 as the sum of the age-adjusted death rates for allraces and sexes divided by the number of years beingconsidered, yielding a twenty-one-year average of924.05 deaths per 100,000. We set person-specific

annual death rate m6 D 0:00924 and using the equilib-rium condition for compartment q6 obtain

q6 D F60.k76C k86 Cm6/

F60D q6.k76 C k86Cm6/

cF60 D 467:67C 59:37C q6m6

cF60 D 467:67C 59:37C 59:37

k86m6 D 527:04C 0:5486

k86

bq6 D F60¡ 527:04

0:009241: (10)

Earlier we demonstrated an equivalence between resi-dence times in early and late cancer stages (q6 and q7)and residence times in the carcinogenetic model ofPanIN and its sequelae. Then the residence time in q6is T2, and in q7 it is T3. It still remains to solve for theresidence time in q8, T4. Consider a pulse of newlydiagnosed cases entering q8 either from q6 (diagnosedin early stage) or q7 (diagnosed in late stage). Recallthat the median survival after diagnosis is six monthsand that the one-year survival rate is about 20 percent.Expressing time in days, we wish to fit the Erlang dis-tribution such that CDF(182.5 days) D 0.5 and CDF(365 days) D 0.8. We solved this using the formula-tion for a one-compartment system with m8 as theexit. At a daily mortality rate of m8D 0:0038, we findCDF(182.5 days) D 0.5002 and CDF(365 days) D0.7502.

Put another way, this states that for a pulse of casesdiagnosed on the same day, about 50 percent will bealive after 182.5 days, and about 25 percent will bealive after one year. This indicates that our fairly sim-ple model of compartment q8 is reasonably complete,at least in terms of its ability to represent observed six-month and one-year survival statistics.

Now that we have estimated m8 we use therelationship

q8Ddq6k86 C dq6k86

m8

(11)

to solve for the size of compartment 8, yielding379.98, q̂8 D 379:98: This is the estimated averagenumber of diagnosed but not deceased pancreaticcancer cases in the study area.

Earlier we solved for q6 and q7 using observed quan-tities such as incident early- and late-stage pancreaticcancer case diagnoses. It is interesting to note for q6

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that an alternative solution is to use the observed resi-dence time in early stage, T2, to then solve for q6. Thisprovides a validation of the estimate.

Define k0 to be the sum of the outflow coefficientsfrom compartment q6, k

0 D k76C k86Cm6: Notice thatwe can now estimate k0 using the methods developedearlier for the residence time of the Erlang distribu-tion. Specifically, solve for k0 for a one-compartmentsystem such that the mean residence time is T2. Thisyields an estimate k0D 0:00028, which is the per casedaily rate of exit from early-stage but not yet diagnosedpancreatic cancer, attributable to background mortal-ity, progression to advanced cancer, and diagnosis.Multiplying by q6 and using hat notation to indicatevalues we can estimate from the observed data yields

q6D dq6k76 C dq6k86 C dq6m6 : (12)

We now divide through by q6, rearrange, and have anestimator for q6 as

bq6 Ddq6k76 C dq6k86bk0 ¡cm6

: (13)

Using the values obtained earlier yields (written usingannual time orientation)

bq6 D 467:67C 59:39

0:1022¡ 0:00924D 5669:75: (14)

This is the estimated number of early-stage cancersthat are in the population but not yet diagnosed. Wenow use a similar approach to solve for the estimatednumber of undiagnosed advanced cancers, q7. Recallthat at equilibrium the inflows into this compartmentmust equal the outflows, hence q7k87D q6k76. This isestimated as the observed number of diagnosedadvanced-stage cancers, and for our system

dq7k87 D dq6k76 D 467:67, and bq6 D dq6k76bk87

. Again, we

estimate ck87 using the Erlang distribution of residence

times. Specifically, solve for ck87 for a one-compart-ment system such that the mean residence time is T3.

This gives ck87 D 0:000703, which is the estimateddaily diagnosis rate per person with advanced-stagepancreatic cancer. Using annual values we now

estimate

bq7 Ddq6k76ck87

D 467:67

0:257D 1; 822:6: (15)

This is the number of individuals with undiagnosedadvanced-stage pancreatic cancer.

Step 3: Map Undiagnosed Early- and Late-StagePancreatic Cancers; Assess Clustering of Advanced-StageCancers in Those Age Fifty-Five and Younger

We now estimate the numbers of undiagnosed can-cers in total and for both early and late stages. Wedefine the estimated relative risks for total undiag-nosed (TRR), early-stage undiagnosed (ERR), andlate-stage undiagnosed (LRR) as the proportion ofcases in each of these groups (total undiagnosed, earlystage undiagnosed, late stage undiagnosed) relative tothe total number of diagnosed cases,

dTRRD bq6 C bq7bq8

D 5; 669:75C 1; 822:6

379:6D 19:72 (16)

dERRD bq6bq8

D 5; 669:75

379:6D 14:92

dLRRD bq7bq8

D 1; 822:6

379:6D 4:80:

We find that the total number of silent (yet to be diag-nosed) cases is more than nineteen times the numberdiagnosed. Hence, for each case that is diagnosed weestimate that there are nineteen pancreatic cancercases in the at-risk population that have yet to be diag-nosed. Of these, almost fifteen are in the early stages ofpancreatic cancer, and nearly five are advanced. Thismeans that application of a screen for early-stage pan-creatic cancer could dramatically reduce pancreaticcancer mortality, as such a large proportion of undiag-nosed cases are in the early stages.

The choropleth maps of pancreatic cancer cases areshown in Figures 7A and 7B. The map and the fre-quency distribution of the estimated count of silent(yet to be diagnosed) cases are in shown in Figure 7Cand Figure 8.

Step 4: Interpret Results

This analysis of pancreatic cancer in Michigan dem-onstrated several important findings. First, the burden

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of undiagnosed pancreatic cancers in this population islarge, approximately nineteen times the number ofdiagnosed pancreatic cancer cases. This indicates thata screening test for detecting early-stage pancreaticcancer, coupled with appropriate surgical and chemo-therapeutic intervention, has the potential to dramati-cally reduce pancreatic cancer mortality in thispopulation. Second, we estimate that there are1; 822:6 undiagnosed advanced-stage pancreatic can-cer cases in this population. Some of these will bediagnosed prior to death, and others will be diagnosedpostmortem. The demands on treatment resources inthe last months of advanced pancreatic cancer are sub-stantial and this estimate can be used to predict thedemand for health care resources and to predict careexpenses. Third, there is some evidence that pancre-atic cancer risk in this population is increasing. TheSEER results place pancreatic cancer incidence andmortality among the highest in all SEER registries,and the change in the annual incidence rate is about0.9 percent per year. We found a small but statisticallysignificant relative risk of being fifty-five or youngerand late stage at diagnosis when we consider 1985 to2005 combined. This suggests the possible action of arisk factor for pancreatic cancer that is affecting youn-ger members of this population. Demographic factorssuch as differential migration cannot be excludedwithout further analysis, however, and in any eventthe relative risk is not large. Finally, the map of silent(yet to be diagnosed) pancreatic cancer cases directlysupports targeting of diagnostic services, planning forupcoming in-home health care needs, and the

geographic allocation of future screening programs tolocal populations with high demand.

Discussion

This research addresses several important topics inthe modeling of space–time systems, cancer biology,and cancer surveillance. It has developed, to ourknowledge, the first comprehensive modelingapproach that estimates cancer latency, couples carci-nogenesis and stage models, and represents and linksprocesses at the genomic level (e.g., mutation events,cascades of genetic changes that lead to cancer), cellu-lar level (e.g., cell replication and death, DNA repair),organ level (e.g., carcinogenesis in situ and metastasesto distant organs), individual level (e.g., cancer stagingin the individual, progression of individuals throughcancer stages), and population level (e.g., geographicdistributions of local populations in cancer stages, esti-mates of the predicted geographic distributions ofundiagnosed cancers). Specific benefits of theapproach include the following.

1. The genetic GIScience construct makes placeexplicit in the emerging exposome–genomeC–behavome synthesis and demonstrates the vitalcontribution to be made by geography.

2. It is process based, capturing the known biologi-cal characteristics and mechanics of the cancerprocess at multiple scales (e.g., genomic topopulation).

3. It provides estimates of cancer latency, based onthe known genetic and histologic characteristicsof the cancer.

4. The latency estimates are integrated into spatio-temporal models of cancer incidence, mortality,and future cancer burden.

5. The impacts of cancer screening and diagnosiscould be represented in the model by diagnosisevents through which individuals progress fromundiagnosed (silent) to diagnosed stages. Thisprovides a ready mechanism for modelingimprovements in pancreatic cancer screening.

6. It predicts the burden of silent cancer (yet to bediagnosed) and geographically allocates thesesilent cancers by cancer stages into local geo-graphic populations. This provides the quantita-tive support necessary for forecasting the futurecancer burden.

Figure 8. Frequency histogram of silent (yet to be diagnosed) pan-creatic cancer cases in the greater Detroit metropolitan area.(Color figure available online.)

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7. The model is readily updatable. As knowledge ofcancer genomics becomes more detailed, it couldbe incorporated into the carcinogenesis modelby updating the cascade of events that underpinthe flows and stages.

8. It provides a quantitative basis for evaluatingalternative treatments and for predicting treat-ment efficacy, provided by the equations andconditions for cancer progression, metastasis,and remission.

Several caveats apply. Assumptions implicit in com-partmental models include the homogeneity assump-tion, which states that the particles being modeledbehave in an identical fashion. This means that thepancreatic cancer cells in each compartment of the car-cinogenesis model, and the cases in each compartmentof the stage model, are assumed to behave in fashionsidentical to other particles in the compartment underconsideration. This assumption is typical of all model-ing approaches (because all models involve simplifica-tion and abstraction) and can be relaxed when neededby adding additional compartments to capture impor-tant aspects of heterogeneity. A second assumption ofthe compartmental approach is that of instantaneousand complete mixing. This assures that the kinetics(e.g., necessary for calculation of transit and residencetimes) of each particle can be calculated without con-sideration of when they entered the compartment orthe order in which they entered. A final assumption isthat the particles in the compartments (e.g., cells orcases) are subdividable, such that a flow of 0.3 cells ispossible. This clearly is incorrect for cells and peoplebut in practice is not a bad assumption when the num-ber of particles in any given compartment is large.

The parameter estimates for cell replication, celldeath, DNA mutation rates, repair rates, metastasesinitiation, cancer promotion, and so on were extractedfrom the literature by the first author, who is not atrained oncologist or cell biologist. Although webelieve that the broad strokes are largely correct, theparameter estimates in this article are initial onesonly, and the specific results might need to be revised.The overall mathematical and systems biologyapproach at this juncture appears sound, and it is theirexposition that is the main contribution of this article(and not the initial parameter estimates).

There are several future directions for this research.First, knowledge of the exposome and its impacts oncarcinogenesis could be incorporated by linking flowsand coefficients related to specific exposures relevant

to carcinogenetic events such as mutation, cell prolif-eration, replication, and other biological mechanismsthrough which environmental exposures affect cancerinitiation and progression. For example, nonmutationalmechanisms (i.e., epigenetic events that turn genes onor off through methylation) can be incorporated intothe model through those model coefficients that affecttumor initiation and progression. This requires knowl-edge or hypotheses regarding how the epigenetic eventunder consideration affects carcinogenesis.

Second, the diversity of different pathways to can-cer could be represented by fitting models for eachpathway. For pancreatic cancers, precursor lesionsinclude the MCN, the IPMN, and the PanIN. In thisarticle we modeled the PanIN pathway, as it is the oneresponsible for the majority of pancreatic cancers.Pathway-specific models could be developed for can-cers that are initiated by MCN and IPMN lesions.

Third, the carcinogenesis model provides specificconditions for cancer progression, metastasis, andremission. These could be used to predict treatmentefficacy and to evaluate alternative treatments byincorporating information on how specific treatmentsaffect those model coefficients describing cancer cellproliferation, death, and progression to distant sites.Information on how combinations of agents that differ-entially affect cancer cell proliferation, death, and met-astatic capacity could be used in the model to evaluatenovel multichemothearaputic agent treatment regimes.

Fourth, latency itself could be influenced by place-based exposure profiles. Cancer might appear earlier athigher exposures, and causative exposures might varyfrom one place to another. In the carcinogenesismodel for the individual, this would be treated by mak-ing the mutation coefficients (presented in this articleas parameters) functions based on location history.Similarly, the underlying population of undiagnosedindividuals likely would have diverse exposure histo-ries, and such heterogeneity would result in a distribu-tion of expected times to diagnosis. The keymethodology underpinning these (and other) elabora-tions is the ability to realistically model disease laten-cies, a major contribution of this article.

Finally, the technique is readily extensible to differ-ent cancers, and also to other chronic diseases.

A note on latency modeling in geographic anddynamical systems is warranted. A frequently usedapproach available in most dynamical system modelingsoftware is the incorporation of specific time lags, inwhich the model incorporates explicit delays, in theflow from one compartment to another. Hence, one

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could simply represent cancer latency by explicitlydelaying (e.g., holding back) the entry of particles inthe model to a destination compartment once theyhave exited the source compartment. This has two dis-advantages. First, a priori knowledge of the time lag isrequired and, second, the use of explicit time lagsimplies the model is incomplete. When the compart-mental system is properly specified, a distribution of res-idence times is observed that is Erlang distributed andthat is representative of the empirical latency times.

A primary objective of this article has been to intro-duce the construct of genetic GIScience (Figure 1)and to illustrate how it could be used to inform ourunderstanding of geographic variation in humanhealth by incorporating knowledge of the genomeC,exposome, and behavome. Geographers are largelybeing bypassed in the fast-moving exposome initiative.This article tries to correct this, but more needs to bedone. Can geographers, for example, incorporate thesocial dimension more explicitly into the exposome?

The example of pancreatic cancer was used todevelop process-based approaches for estimating dis-ease latency, a key problem that must be solved foreffective disease mapping and surveillance. This reliedheavily on the genomeC dimension of genetic GIS-cience, and much work is needed to develop andexploit the exposome and behavome dimensions. Themodels developed can incorporate the exposomethrough their impact on mutation, although work isneeded to make this more explicit and place based.The use of wearable sensors at the human boundarylayer should prove useful in this regard. The behav-ome, defined as behaviors over an individual’s lifecourse that affect health, are not explicitly modeled inthis article, and the quantification, representation, andmodeling of the behavome is expected to be a richfuture research area at the interface of human, physi-cal, medical, and behavioral geography.

Acknowledgments

We thank Jaymie Meliker and Chantel Sloan andcolleagues at the first Geolife Roundtable meeting(March 2013 in Gavle, Sweden) for thoughtful discus-sion and encouragement. We thank our colleagues inAustralia’s Cooperative Research Centers for SpatialInformation (CRCSI) Health Program—Narelle Mul-lan, Tarun Weeamanthri, and Peter Woodgate. Thefirst and second authors are Co-Science Directors ofCRCSI Health Australia. We thank members of the

Eagle Pass Yellowstone Expedition—Richard Marston,Andrew Marcus, and David Mattern for insightful crit-icism and comments. This avenue of research (integra-tion of geography and population genetics) wassuggested to the first author by John A. Jacquez in the1990s.

Supplemental Material

Supplemental data for this article can be accessedon the publisher’s Web site at http://dx.doi.org/10.1080/00045608.2015.1018777

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Correspondence: Department of Geography, University at Buffalo–State University of New York, Buffalo, NY 14261, e-mail: gjac-quez@buffalo.edu (Jacquez); chenshi@buffalo.edu (Shi); School of Geographical Sciences, University of Bristol, Clifton, Bristol BS8 1SS,UK, e-mail: c.sabel@bristol.ac.uk (Sabel).

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