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

Published OnlineFirst October 20, 2016; DOI: 10.1158/0008-5472.CAN-16-1054

Cancer Integrated Systems and Technologies: Mathematical Oncology Research

Quantifying the Dynamics of Field Cancerization in Tobacco-Related Head and Neck Cancer: A Multiscale Modeling Approach Marc D. Ryser1, Walter T. Lee2,3, Neal E. Ready4, Kevin Z. Leder5, and Jasmine Foo6

Abstract

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

Introduction Major Findings Head and neck squamous cell carcinoma (HNSCC) arises in the Patient age at diagnosis was found to be a critical predictor epithelial lining of the oral cavity, pharynx, and larynx. The annual of the size and multiplicity of precancerous lesions. This incidence rate of HNSCC is estimated to be around 600,000 new finding challenges the current one-size-fits-all approach to cases worldwide (1), and in the United States alone, the death toll surgical excision margins. is approximately 11,500 cases per year (2). While a subgroup of HNSCC, including the oropharynx, is caused by infection with high-risk types of the human papillomavirus (HPV; ref. 3), the majority of HNSCC are HPV-negative and primarily associated with tobacco use and alcohol consumption (1). Despite a growing number of therapeutic strategies, survival in HPV-negative HNSCC has not improved significantly over the past decades, with a low median survival of approximately 20 months (4). 1Duke University, Department of Mathematics, Durham, North Carolina. 2Division Poor prognosis in tobacco-related head and neck cancers is of Head and Neck Surgery & Communication Sciences, Duke University School of commonly attributed to the development of local recurrences and Medicine, Durham, North Carolina. 3Section of Otolaryngology-Head and Neck 4 metastases after removal of the primary tumor (1). Field cancer- Surgery, Durham VA Medical Center, Durham, North Carolina. Division of fi Medical Oncology, Duke University School of Medicine, Durham, North Carolina. ization, or the presence of premalignant elds surrounding the 5Department of Industrial & Systems Engineering, University of Minnesota, primary tumor, has been shown to drive the high rate of local Minneapolis, Minnesota. 6School of Mathematics, University of Minnesota, Min- recurrence (5–11). In fact, molecular studies have shown that the neapolis, Minnesota. majority of HPV-negative HNSCC develop within local fields of Note: Supplementary data for this article are available at Cancer Research premalignant cells that are clonally related to the resected primary Online (http://cancerres.aacrjournals.org/). cancer (7, 9). These fields can be much larger than the actual fi Corresponding Authors: Jasmine Foo, Department of Mathematics, University carcinoma and are generally dif cult to detect without genomic of Minnesota, 240 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455. analyses due to their visually normal appearance (12). If such an Phone: 612-625-0131; Fax: 612-626-2017; E-mail: [email protected]; and Marc D. invisible premalignant field extends beyond the surgical margins, Ryser, Department of Mathematics, Duke University, 120 Science Drive, 117 the portion of the field left behind after resection of the primary Physics Building, Durham, NC 27708. Phone: 919-669-2847; Fax: 919-660- tumor increases the risk of subsequent recurrence and contributes 2821; E-mail: [email protected] to poor prognosis (11). The occurrence of precancerous fields was doi: 10.1158/0008-5472.CAN-16-1054 first reported by Slaughter and colleagues (5) and has since been 2016 American Association for Cancer Research. documented in most epithelial cancers (10, 13–15).

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Quick Guide to Equations and Assumptions

Model Assumptions We developed and calibrated a spatial stochastic model of tobacco-related head and neck squamous cell carcinoma at the tissue level. The major model assumptions are:

* (Epi)genetic events lead to mutated cells with increased ﬁtness advantage, and mutant clones can spread through the basal layer of the affected epithelium prior to onset of invasive cancer. * Because of the time scales of carcinogenesis, only long-lived progenitor cells in the basal layer of the epithelium are relevant; this monolayer of progenitor cells is modeled as a two-dimensional lattice, where each node is occupied by a cell. * Wild-type and mutant progenitor cells undergo evolutionary competition in the basal layer; only nearest-neighbor interactions are considered. * Tissue architecture and homeostasis are maintained (constant population size) until the invasive cancer stage.

Key Model Parameters

Total population size (N); cellular transition rates from normal to precancer (u1) and from precancer to carcinoma in situ (u2), respectively; relative proliferative advantage of precancer (s1) and carcinoma in situ cells (s2); mean sojourn time from preclinical lesion to clinical diagnosis with cancer (1=c).

Key Equations

We were interested in quantifying the geometry of the ﬁeld of precancerous cells surrounding the tumor at time of diagnosis (s3). The key equations are: (i) The survival function (probability that cancer has not been diagnosed by time (t) of the model, Z t l StðÞ¼ect þ cect exp g 1=3;t3 lt þ ct dt; 1=3 0 3

2 where g is the incomplete gamma function, l Nu1s1 and u2s2pc2ðs1Þ=3: (ii) Conditioned on diagnosis occurring at time t, the probability density function of the radius of the precancer field that surrounds the primary tumor, Z t 3 = ; 3 clz 2 zðÞr c2ðÞt s gðÞ1 3 s PðR ðÞ¼t rj s ¼ tÞ¼ 1 = ðÞr c ðÞt s exp þ l s cðÞt s ds l 3 str c2 2 1=3 S'ðÞt 0 3 3 3 for all r 2½0; c2t, and zero otherwise, where c2 is the radial expansion speed of the precancer field and z 3=c2: (iii) Conditioned on diagnosis occurring at time t, the probability of harboring two or more clonally unrelated precancer fields is Z ðÞcþl t t lce s3 ðÞ2lþc s PðMtðÞ> 1j s3 ¼ tÞ¼1 1 e e ds: S'ðÞt 0

Model Calibration The microscopic tissue-level models were calibrated on the basis of population-level incidence data. Using a computational Bayesian framework, we determined the posterior distributions for the identiﬁable parameters l, ; and c: On the basis of the posterior distributions, we derived model-based predictions of ﬁeld quantities at time of diagnosis.

To date, it remains difficult to account for the phenomenon of tissue in absence of any information on the extent of the suspected field cancerization in clinical practice. The main reason for this field. To overcome this barrier, we synthesized data and knowl- translational barrier is a poor understanding of the dynamics and edge sources from the tissue, clinical and population scales to geometry of these invisible fields. Indeed, it is impossible to develop a quantitative model of HNSCC carcinogenesis that account for the risk factor of an unresected field of precancerous accounts for spatial features of the precancer field. On the basis

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of this model, we then sought to identify aspects of standard starts expanding, further hits to the EGFR or TGFb pathways can clinical practice that could be improved by means of patient- lead to moderate dysplasia, CIS, and eventually invasive HNSCC. specific modeling tools. Microscopic model of carcinogenesis To capture the spatial dynamics of the above mechanisms of Materials and Methods carcinogenesis, we developed a stochastic Moran model on a Biological mechanism of carcinogenesis regular two-dimensional lattice (27, 28). Initially, all cells on the To model the carcinogenesis of tobacco-related HNSCC, we lattice are normal progenitor cells (type 0) and proliferate at rate fi rst developed a spatial stochastic model of homeostasis in f0. Cell division is stochastic, and when a progenitor cells divides, stratified squamous epithelia of the head and neck. The homeo- one daughter cell replaces the mother cell, and the other daughter static epithelia of this region undergo periodic bottom–up renew- cell replaces one of the nearest neighbor cells on the lattice, chosen al (16), whereby long-lived progenitor cells in the basal layer of uniformly at random. Each normal cell can, at rate u1,a, acquire a the epithelium give rise to transit amplifying cells (TAC) of limited mutation to become a mildly dysplastic cell (type 0). At the tissue proliferative potential (17, 18). As they divide, the TAC move level, this leads to a patch of dysplasia as illustrated in the first fi fi toward the super cial layers of the strati ed epithelium, where panel of Fig. 1C. The proliferation rate of type 0 cells is still f0, but they eventually exit the cell cycle and get sloughed off at the tissue acquisition of a second hit, at cellular rate u1,b, can transform type surface. Because differentiating TAC are lost from the tissue within 0 cells into precancerous cells (type 1). Type 1 cells in turn have a a few weeks (16), they are unlikely to contribute to the emergence proliferative advantage f1 ¼ f0 (1 þ s1) over type 0 and type 0 cells of a neoplastic clone of cells, and it suffices to focus on the and can clonally expand as precancerous fields of moderate population of progenitor cells in the bottom layer of the dysplasia by replacing neighboring cells of lower proliferative epithelium. potential, see second panel in Fig. 1C. Mathematically, we can The transformation from normal to cancerous cells is largely simplify the model by deriving the effective mutation rate u1 from attributed to the successive accumulation of (epi)genetic aberra- type 0 to type 1 cells: the probability 01 that a type 0 cell gives rise tions, see Fig. 1A. Once a normal progenitor cells has acquired a to growing field of type 1 cells before its progeny dies out is given growth advantage, the resulting clone of mutant cells starts by (27) spreading across the affected epithelium by replacing adjacent 1=2 1=2 1=2 p u ; s log 1=u ; s ðAÞ cells of lower proliferative potential (19). There are a multitude of 01 1 b 1 1 b 1

genetic alterations commonly found in HPV-negative HNSCC s1 where s1 ¼ . At rate u2, type 1 cells in turn can mutate into (1), but both the total number and temporal ordering of events 1 þ s1 necessary for cancer initiation are patient- and tumor-specific malignant (type 2) cells that initiate growth of cancer, see third fi (20). In view of this genotypic heterogeneity, we focused on the panel in Fig. 1C. Cancer cells have a tness advantage of s2 over phenotypic progression instead. Indeed, the majority of tobacco- type 1 cells and hence divide at rate f2 ¼ f1 (1 þ s2). Finally, the related HNSCC progress through a series of precancerous stages time between onset of CIS and diagnosis was modeled as an called epithelial dysplasia, see Fig. 1B (21, 22). These stages are exponentially distributed random variable with rate c, see Fig. 1B. fi fi histopathologically classified into three categories: mild, moder- The reason for this simpli ed transition model from rst cancer ate, and severe dysplasia [carcinoma in situ (CIS); ref. 23]. On the cell to diagnosis is two-fold. First, upon penetration of the fi basis of this observation, we modeled neoplastic progression at basement membrane and in ltration of the stroma, the epithelial the cellular level in four stages (Fig. 1A), developing from normal architecture is irreversibly disrupted and the microscopic dynam- cells (type 0) into mildly dysplastic cells (type 0), into moder- ics with lateral displacement no longer apply; second, depending ately dysplastic cells (type 1), and eventually into severely dys- on the location of the lesion and the patient's behavior, time to plastic cells (type 2). clinical diagnosis can be highly variable. Although the number and ordering of mutations responsible for HNSCC carcinogenesis are not unique, a better understanding Mesoscopic model approximation of the genetic underpinnings and fitness landscapes of the phe- We previously derived the following mesoscopic approxima- notypic transitions enhances the mechanistic foundation of the tion to the spatial model that enables analytical calculations of fi model, see Fig. 1A. It is generally accepted that loss of function of waiting times and eld geometries (28, 29). In the mesoscopic the tumor suppressor gene TP53, either through mutation or loss model, the arrival of expanding type 1 clones is a stochastic of heterozygosity, is an early event during tumorigenesis of Poisson process with rate Nu1s1. The factor s1 accounts for the fl HNSCC. Indeed, histopathologic studies have found that expand- fact that the progeny of a new type 1 cell will either uctuate to 1 fi ing cancer fields are preceded by small TP53-mutated patches extinction with probability s1 or expand inde nitely with (<200 cells in diameter; ref. 8). Two studies (21, 22) found no probability s1. Next, we characterized the growth of an expanding significant differences in proliferation index for low-grade dys- type 1 clone on the basis of a shape theorem (30). According to the plasia compared with normal tissue, even though mutant TP53 theorem, expanding type 1 clones asymptotically grow as a convex was significantly elevated in low-grade dysplasia (22). This sug- symmetric shape with constant radial growth rate c2. Simulations gests that a likely first step of tumorigenesis is the formation of an of the process show that this shape can be approximated as a disk evolutionarily neutral patch (mild dysplasia) of TP53þ/ cells. or circle, see (29). The rate c2 in turn dependsp onffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the selective Once a cell within this patch acquires a further genetic aberration, advantage s1. For small s1 it scales as c2ðs1Þ 4ps1=logð1=s1Þ either through methylation or deletion of CDKN2A (24) or where fðsÞgðsÞ means that fðsÞ=gðsÞ!1 as s ! 0 (28); for through gain or amplification of CCND1 (25), the resulting clone larger values of s1, we used numerical simulations to estimate the has a selective advantage over its neighboring cells and causes the value of c2, see Fig. 3 in ref. 29. In particular, for s1 > 0:5, we found emergence of an expanding precancer field (26). Once the field an approximately linear dependence c2ðs1Þ0:6s1þ0:22 (29).

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Figure 1. Stochastic model of carcinogenesis in HPV-negative HNSCC. A, At the cellular level, accumulation of genetic alterations leads to increasingly malignant phenotypes. The cellular mutation rates between normal (type 0), dysplastic (type 0, type 1), and cancerous (type 2) cells are indicated above the solid arrows. The

type-specific proliferation rates fi depend on the relative selective advantages si as specified. Genetic events associated with the phenotypic transitions are listed below the solid transition arrows (see eq. A); the number and temporal ordering of these events is not unique. B, At the tissue level, carcinogenesis manifests itself through the emergence of a patch of mild dysplasia, which can give rise to a field of moderate dysplasia (the precancer field). The first viable cancer cell arises within the growing precancer field, leading to carcinoma in situ and eventually invasive HNSCC. The time between cancer initiation and diagnosis is modeled as an exponential random variable with rate c. C, At the organ level, a possible scenario of carcinogenesis is illustrated in three consecutive snapshots. Left, a small patch of mild dysplasia (neutral evolution) appears in the normal tissue. Middle, the patch gives rise to a positively selected precancer field that expands into the normal epithelium; clonally unrelated patches of mild dysplasia may arise at any time. Right, the precancer field that gives rise to the primary tumor is called the local field, whereas the clonally independent precancer field that starts growing is referred to as a distant field.

Finally, we note that multiple precancer fields of type 1 cells can Registries, 2000–2012) in a Bayesian framework. As we focused coexist as illustrated in Fig. 1C. on HPV-negative cancers, we restricted our search to males and females diagnosed with malignant tumors in the following cat- Incidence data egories of "Site Recode ICD-O-3/WHO 2008": lip, tongue, floor of To parameterize the tissue-level model and ensure its compat- mouth, gum and other mouth, hypopharynx, and larynx (31). We ibility with population-level data, we calibrated the mesoscopic further excluded cases with primary site labeled as "C01.9-Base of approximation of the microscopic model on the basis of age- tongue" because cancers at this site are commonly HPV-positive specific incidence rates from the Surveillance, Epidemiology, and (32). We derived the number of susceptible individuals and the End Results (SEER) program of the National Cancer Institute (18 number of cancer cases diagnosed in each of the following age

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where u s pc2ðÞs l Nu s ; 2 2 2 1 ; ðCÞ 1 1 3 R x a1 t gða; xÞ¼ 0 t e dt is the lower incomplete G -function, and c is the transition rate from onset of CIS to diagnosis. The parameter groups (eq. C) have the following interpretation: l is the initiation rate of expanding type 1 clones, see also previous paragraph; can 3 2 1=3 be rewritten as ðgt2 Þ=3, where t2 ¼ðc2u2s2Þ is approximately the time it takes for an expanding type 1 clone to give rise to an expanding type 2 clone (28). On the basis of SðtÞ; we then computed the hazard function hðtÞ¼S0ðtÞ=SðtÞ, which provides a direct link to the SEER-derived age-specific incidence rates. The derivation of the likelihood function used for inference is outlined in Supplementary Information S1. We then used a computational Markov Chain Monte Carlo (MCMC) Metropolis Hastings algorithm to derive posterior distributions for the parameters l, ,andc.Weusedimproper priors over ½0; ¥ for all 3 parameters and ran a Markov chain of length 500,000. Computations were performed in MATLAB (Version 8.5.0, The MathWorks Inc. 2015). To determine plau- sible initial conditions and step lengths for the MCMC algorithm, we independently estimated the 3-parameter groups based on literature estimates of the underlying biologic parameters, see Supplementary Information S2. After discarding the Figure 2. first 50,000 burn-in steps, we sampled every 100th step to MCMC summary. MCMC Metropolis Hastings algorithm was used to infer the characterize the posterior distributions. Convergence to steady- posterior distribution of the model parameters l, ,andc. A total of 500,000 state was visually ascertained. Credible intervals (CI; 95%) fi iterations were computed; the rst 50,000 burn-in iterations were discarded for the posterior distributions were computed by discarding and then 1 in 100 samples was used to estimate the posterior distribution. A, Model fit to SEER data; age-specific incidence is restricted to smokers (see main the 2.5% largest and smallest values for each parameter. The text for details). The data point at 85 years reflects the incidence estimate for marginals of the posterior distributions for l, ; and c are patients aged 85 years and older. B, Marginal distributions of l, ,andc. summarized in Fig. 2B. Median estimates and 95% CIs of the posterior distributions, together with the literature-based order of magnitude estimates are summarized in Table 1. Goodness groups: 15–19 years, 20–24 years,...,80–84 years, and 85þ years. of fit was deemed satisfactory on the basis of visual inspection, We note that the age-specific incidence curve for HPV-negative see Fig. 2A. HNSCC has a peaked profile, see Fig. 2A. However, the model To compare model predictions with clinical recurrence pat- developed here predicts monotonically increasing incidence rates terns, SEER (13 Registries, 1991–2011) was queried for a and thus cannot recapitulate peaked incidence patterns. Because retrospective analysis of the recurrence risk in patients diag- changing baseline risks are more likely to cause the peaked nosed and treated for HNSCC lesions of size 3cm.Data profile than changes in biological parameters (see Supplemen- extraction was performed using an MP-SIR session with the tary Information S1), we truncated the incidence data used for software SEERStat (http://seer.cancer.gov/seerstat). Again, we parameter inference at the age of 74 years instead of introduc- focused on the predominantly HPV-negative sites as specified ing additional age-dependent model parameters. The vast under "Model calibration." Only patients aged 18 to 85 years at majority of HPV-negative HNSCC are attributed to tobacco diagnosis with a known tumor size of 30 mm were included. consumption (33, 34); thus, we reduced the pool of susceptible Patients with unknown surgery status, unknown radiation individuals to the approximately 20% of current smokers status, and those identified at autopsy or on death certificate within the considered age groups (35). Furthermore, we only were excluded. The following categorical variables were assumed the exposure to start at the age of 15 years (36, 37). extracted from the dataset: age at diagnosis (younger: 18–49 years, older: 50–85 years) and treatment (surgery only, radia- Parameter inference tion only, surgery and radiation). For each patient, the time To compare the model predictions with SEER data, we first from diagnosis to recurrence (defined as second malignant derived the age-specific incidence function under the evolutionary event in any of the included head and neck sites), death, or model at the tissue-level. To this end, we defined the random censoring (defined as the minimum of end-of-study, loss to variable s3 as the time from mean age at smoking initiation to follow-up, and 10 years) was calculated. For each of the three diagnosis with invasive cancer and calculated the survival function treatment groups with known treatment status, a univariate Cox proportional hazards regression for recurrence was per- StðÞPðÞ¼s t 3 Z formed on the basis of the categorical age at diagnosis variable, t l fi < ect þ cect exp g 1=3;t3 lt þ ct dt; ðBÞ strati ed into younger ( 50 years) and older (50 years) 1=3 0 3 patients. Kaplan–Meier curves were used to visualize the

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Table 1. Parameter estimates: MCMC and literature-based Parameter Units Prior Median (95% CI) Literature estimates l [y1] ½0; ¥ 4.3 103 (4.0 103–4.8 103) 103 q [y3] ½0; ¥ 5.9 106 (4.4 106–7.9 106) 104 c [y1] ½0; ¥ 9.8 102 (6.7 102–13.5 102) 101 NOTE: For each parameter, the median and 95% CIs for the MCMC Metropolis-Hastings–derived posterior distributions and the literature-based estimates are shown.

results. Hazard ratios with 95% CIs were computed, and all P compute the probability density function of the local field values were calculated as two-sided with significance declared radius as follows: Z for P values below 0.05. Computations were performed in R t clz 2 PðR ðtÞ¼ rj s ¼ tÞ¼ 1 = ðr c ðt sÞÞ (http://www.R-project.org). l 3 S'ðtÞ str c2 2 0 zðr c ðt sÞÞ3 gð1=3;s3Þ exp 2 þ l s cðt sÞ ds; ðDÞ Results 3 31=3 Local field size at diagnosis 3 To characterize the field geometry at time of diagnosis where z 3=c2. We refer to Supplementary Information S3 with invasive cancer, we first derived the size distribution of for details of the calculation. The corresponding density the local field. More precisely, denoting the radius of the functions (eq. D) for ages at diagnosis of 40, 60, and 80 fi local eld at time t by RlðtÞ, we conditioned on fs3 ¼ tg to years are shown in Fig. 3A. Unfortunately, these results have

Figure 3. Field characteristics as a function of age at diagnosis. A, Probability density function of the field radius at diagnosis is shown for patient ages 40, 60, and 80 years, respectively. Calculations were performed using the median posterior values of l, ; and c as shown in Table 1, and c2 ¼ 0:4 (see also Supplementary Information S2). B, On the basis of the posterior distributions, the statistics of the relative mean field radius (RMFR) for different ages at diagnosis were computed. Median and 95% CIs are shown. C, Probability distribution of the number of distant fields is shown for patient ages 40, 60, and 80 years, respectively. Parameter values as in A. D, Probability of multiple unrelated fields at time of diagnosis was computed on the basis of the posterior distributions. Median and 95% CIs are shown.

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an explicit dependence on the radial growth rate of the pre- least 2 clonally unrelated fields in the head and neck region at cancer field, c2ðs1Þ, which cannot be directly estimated due to time of diagnosis, identifiability constraints (we used literature-based estimates PðMtðÞ>1j s3 ¼ tÞ instead). To overcome this issue, we focused on the relative Z ðÞcþl t t lce 3 ðEÞ size of a precancerous field compared with the field size at ¼ 1 1 e s eðÞ2lþc sds: the age of 50 years. More precisely, we introduced the S'ðÞt 0 relative mean field radius (RMFR), defined as the mean field Accounting for the posterior distributions of the parameter radius at a given age divided by the mean field radius at age groups, the probability of harboring at least one distant field is 50 years. Indeed, the RMFR is completely specified by the shown as a function of age at diagnosis in Fig. 3D. The model inferred parameters l, and c and does not explicitly predicts that the probability (95% CI) of harboring at least one depend on c2 (see Supplementary Information S3). On the distant field increases by one order of magnitude from 2.1% basis of the posterior distributions from the Bayesian infer- (2.0%–2.4%) at 20 years of age to 20.0% (18.6%–22.7%) at ence, we computed the RMFR as a function of patient age at 80 years of age. diagnosis in Fig. 3B. The model predicted an approximately linear increase in RMFR between the ages of 20 and 90 years, Age-specific recurrence patterns andthemedian(95%CI)RFMRatage90wasfoundtobe To test the validity of our model, we made model-based 1.90 (1.88–1.93). predictions and tested them against outcome data from SEER. The first prediction was based on the fact that current clinical Multiple fields at diagnosis practice recommends an age-independent excision margin width In addition to the local fieldsizeatdiagnosis,weestimated of 1 cm (38, 39). Considering the predicted increase of local field the probability of harboring distant fields in addition to the size with age at diagnosis (Fig. 3A), an age-independent margin local field. The exact distribution of the total number MðtÞ of width implies that, for the same tumor size, the area of precan- clonally independent fields, including the local and all distant cerous tissue left behind after resection of a primary tumor is fields, is found in SupplementaryInformationS3.InFig.3C, bigger in older patients (with larger precancer fields) than in the probability distribution for the number of multiple fields is younger patients (with smaller precancer fields), see Fig. 4. This shown for different ages at diagnosis (40, 60, and 80 years), increase in recurrence risk in older patients is further increased by based on the median posterior values of l, ; and c.Usingthis the elevated probability of harboring distant fields (Fig. 3B) that distribution, we then computed the probability of harboring at may not be affected by local excision of the primary tumor. To test

Figure 4. Surgical margins and residual field. A, Illustration of age-related differences in local field size and number of unrelated fields. Before surgery, only one local field may be present in a younger patient (left), whereas a larger local field and additional distant fields may be present in an older patient (right). B, During surgery, the local field is removed in the younger patient (left) but only partially resected in the older patient (right), where the residual field portions elevate the risk of recurrence.

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Figure 5. Recurrence-free survival after treatment of primary tumor. Recurrence-free survival among younger (<50 years) and older (50 years) patients, stratiﬁed by treatment regime. A, surgery only; B, surgery and radiation; C, radiation only. Analyses restricted to primary tumors of size 3 cm. Signiﬁcant difference in recurrence risk for surgery only, P < 0.0001.

the resulting hypothesis of an age-dependent recurrence risk, we surrounding tissue portions. Thus, there is a need for noninvasive performed a retrospective time-to-event analysis for patients with methods to predict the extent of the field and to make patient- small 3 cm) tumors who received surgery but no radiation (n ¼ tailored decisions with respect to optimal treatment modality, size 9,665). In alignment with our model-based prediction, we found of excision margins, and frequency of postoperative surveillance. a 58% increase in recurrence risk in older patients (50 years, n ¼ In this work, we developed and calibrated a mechanistic model of 7,774) than in younger patients (<50 years, n ¼ 1,891; HR, 1.58; spatial tumorigenesis in tobacco-related HNSCC. Following the 95% CI, 1.27–2.10; P < 0.0001). The corresponding Kaplan– lines of previous multiscale modeling work (40–43), we linked Meier curve for recurrence-free survival is shown in Fig. 5A. biologic mechanism at the tissue scale to data at the population Because adjuvant radiation therapy after surgery targets the scale and used a Bayesian framework to ensure compatibility of margins of the resected tissue portion, the combination of surgery the model dynamics across scales. Using the model, we made and radiation is more likely to eradicate the entire local field and predictions about the geometry of precancerous fields at the time hence diminish the recurrence risk from a residual field portion. of diagnosis with invasive cancer and tested them against out- Therefore, we hypothesized a reduction in the age-related differ- come data. ence in recurrence risk among patients who received radiation in The models predicted a strong dependence of the local field size addition to surgery. This prediction was corroborated by the on age at diagnosis. More precisely, we found the expected field analysis of outcome data. Repeating the above time-to-event size of the local precancerous field surrounding the primary tumor analysis for patients who received both surgery and radiation, to double between the ages of 50 and 90 years. The model further we found a smaller, nonsignificant difference (HR, 1.29; 95% CI, predicted a substantial increase in the probability of harboring 0.91–1.84) between older (50 years, n ¼ 4,537) and younger independent synchronous fields at the time of diagnosis, increas- patients (<50 years, n ¼ 993), see Fig. 5B. ing to 20% at age 80. Together, these findings indicate that the Finally, we note that for the patient group with radiation but current one-size-fits-all approach to the width of surgical excision without surgery (Fig. 5C), no significant difference in recurrence margins may need to be critically re-evaluated. risk between the two age groups was observed. Interestingly, in On the basis of the model predictions, we hypothesized that comparison to younger patients (<50 years, n ¼ 266), older larger local fields and a higher risk of harboring multiple fields in patients (50 years, n ¼ 2,622) did have a slightly smaller older patients would translate into a higher recurrence risk in recurrence risk (HR, 0.78; CI, 0.40–1.52). However, we were not older than in younger patients when treated by surgery only. We able to draw any definite conclusions because of a small sample tested this hypothesis by analyzing recurrence patterns in younger size and patient attrition in the younger age group. (<50 years) and older (50 years) patients who received surgery without radiation. As predicted, we found a higher risk of local recurrence in older patients than in younger patients. In contrast, Discussion we did not find a statistically significant age effect in patients who Leftover fields of precancerous tissue that are not removed received adjuvant radiation therapy. This is consistent with the during resection of HPV-negative, tobacco-related HNSCC lead observation that radiation is less focalized than surgical excision to an increased risk of local recurrence. Because of their visually and hence is more likely to remove the surrounding field portions, normal appearance, epithelial precancer fields are generally not even in older patients with larger fields. In addition, radiation may detectable at the time of surgery without harmful biopsies of the have an age-specific effect on local recurrence that is independent

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of the field size. For example, studies on the effects of radiotherapy the classical multistage model (49) to the incidence data, see in patients with ductal carcinoma in situ reported a higher like- Supplementary Information S4. While the inferred number of 3 lihood of recurrence in patients who received adjuvant radiation stages corresponds well to the current understanding of HNSCC therapy compared with those who did not (44, 45). It is important etiology, the model fit was found to be poor. More recently, to note that the observed recurrence patterns may be due to a A study (47) showed that nonspatial 2-stage clonal expansion combination of several biologic and clinical factors, not just the models yield good fits to the data when accounting for period and age-related size of the precancer field. cohort effects in biologic parameters. Nevertheless, our findings Our study has several limitations. First, inherent limitations suggest that for solid cancers subject to field cancerization, spatial of the SEER database such as ascertainment biases and incom- effects may play an important role in shaping population-level plete recurrence records may impact the validity of our results incidence patterns. (46). Second, HPV status is not recorded in SEER, and despite While our predictions for age-dependent recurrence risks and careful selection of sites that are predominantly HPV-negative, field sizes were successfully corroborated by SEER-based outcome a portion of recorded cases may have been misclassified. Third, data, pathologic studies are needed to provide a definite confir- although the incidence data used for model calibration were mation of our models. Our predictions of an increase in field size restricted to a relatively short period (2000–2012), it is likely in older patients will hopefully spur a critical re-evaluation of the subject to secular trends that are at least partially due to one-size-fits-all approach to surgical excision margin width, as changing smoking patterns in the population (4, 47). In addi- well as the effectiveness of surgery without radiation therapy in tion, it has been shown that smoking cessation leads to a slow older patients with extended exposure and potentially very large decrease in head and neck cancer risk (48), which may result in fields. In addition, appropriate follow-up intervals for the mon- differential field sizes between former and current tobacco itoring of local recurrences may be optimized according to users. In future work, the use of more granular smoking patient-specific predicted field geometries, and a quantitative prevalence and cancer incidence data, adjusted for secular understanding of the field dynamics combined with a set of trends, is expected to address these issues and improve the reliable biomarkers for premalignant fields may enable physicians model predictions. Fourth, a limitation shared with most to perform targeted risk-assessments in high-risk groups, such as multistage modeling analyses is the assumption of identical heavy smokers. Finally, the proposed modeling framework can be parameters for all individuals. This issue is partially mitigated applied to other 2-dimensional epithelial sites affected by field by the Bayesian approach, which provides posterior distribu- cancerization, such as bladder, esophagus and skin, and it may tion of parameters rather than point estimates. However, incor- provide valuable insights into observed differences in field extent porating patient-level heterogeneity into the modeling frame- and outcome between HPV-positive and HPV-negative head and work constitutes a critical next step toward the long-term goal neck cancers. of developing personalized approaches to head and neck cancer care. Finally, we did not explicitly account for the role of the Disclosure of Potential Conflicts of Interest immune system as a first line of defense against neoplastic No potential conflicts of interest were disclosed. progression. Although immune effects could be incorporated into the model, current knowledge about the exact mechanisms Disclaimer of immune response to neoplastic transformation seems insuf- The views expressed in this article are those of the author and do not ficient to develop meaningful models. necessarily represent the views of the Department of Veterans Affairs or the United States government. Historically, different types of multistage models have been used to infer the nature of cancer-causing mechanisms on the Authors' Contributions basis of incidence and mortality data. The first such models (49) Conception and design: M.D. Ryser, W.T. Lee, K.Z. Leder, J. Foo were based on the assumption that cancer arises as the product of Development of methodology: M.D. Ryser, W.T. Lee, K.Z. Leder, J. Foo an organ-specific number of rare mutations. These models Acquisition of data (provided animals, acquired and managed patients, assumed a well-mixed population of cells and neglected cellular provided facilities, etc.): W.T. Lee dynamics and spatial tissue structure. Later, these models were Analysis and interpretation of data (e.g., statistical analysis, biostatistics, extended to account for clonal expansions of precancerous cells computational analysis): M.D. Ryser, N.E. Ready, J. Foo (40, 41, 50) and used to analyze the number and size of prema- Writing, review, and/or revision of the manuscript: M.D. Ryser, W.T. Lee, N.E. Ready, K.Z. Leder, J. Foo lignant clones in nonspatial populations, both for exponential Study supervision: W.T. Lee, J. Foo mean growth (51) and for more general growth dynamics (52, 53). In parallel to multistage models, population dynamic mod- Acknowledgments els such as the Wright–Fisher and Moran processes have also been The authors thank Prof. F. Michor (Dana-Farber Cancer Institute) and Prof. R. used to model cancer initiation under well-mixed assumptions Durrett (Duke University) for valuable feedback on model design and analysis. (54, 55). In these models, the expansion of premalignant clones is constrained by competition with healthy cells or premalignant Grant Support cells at other stages. Our current work constitutes an extension of The study was supported by the following grants: NIH R01-GM096190 and both multistage and population dynamic models. In particular, SNSF P300P-154583 (M.D. Ryser); NSF CMMI-1362236 (K.Z. Leder); and NSF DMS-1224362 and NSF DMS-1349724 (J. Foo). we accounted for the spatial structure of the epithelial lining of The costs of publication of this article were defrayed in part by the payment of head and neck sites, and we developed a mechanistic model on page charges. This article must therefore be hereby marked advertisement in the basis of the current understanding of tissue homeostasis and accordance with 18 U.S.C. Section 1734 solely to indicate this fact. molecular biology of HPV-negative HNSCC. Using the spatially explicit model, we achieved a very good fit to the SEER-based Received April 28, 2016; revised August 26, 2016; accepted September 19, incidence data, Fig. 2A. For the sake of comparison, we also fitted 2016; published OnlineFirst October 20, 2016.

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Dynamics of Field Cancerization

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7088 Cancer Res; 76(24) December 15, 2016 Cancer Research

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

Marc D. Ryser, Walter T. Lee, Neal E. Ready, et al.

Cancer Res 2016;76:7078-7088. Published OnlineFirst October 20, 2016.

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