A computational modelling approach for deriving biomarkers ...cancerpreventionresearch.aacrjournals.org/content/canprevres/early/... · A Computational Modelling Approach for Deriving
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
A Computational Modelling Approach for Deriving Biomarkers to Predict Cancer Risk inPremalignant Disease
Andrew Dhawan1, Trevor A. Graham2,*, Alexander G. Fletcher3,4,*
1 School of Medicine, Queen’s University, Kingston, Ontario, Canada2 Barts Cancer Institute, Queen Mary University of London, London, UK3 Mathematical Institute, University of Oxford, Oxford, UK4 School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
Running title: Biomarker evaluation for premalignant disease in silico
Financial support: A. Dhawan acknowledges support from a J.D. Hatcher Award, School ofMedicine, Queen’s University, Canada. T.A. Graham acknowledges support from CancerResearch UK. A.G. Fletcher acknowledges support by the UK Engineering and PhysicalSciences Research Council through grant EP/I017909/1 (www.2020science.net).
* Corresponding authors:Alexander G. FletcherSchool of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road,Sheffield, S3 7RH, UKTel: +44 (0)114 222 3846Email: [email protected]
Trevor A. GrahamBarts Cancer Institute, Barts and the London School of Medicine and Dentistry, Queen MaryUniversity of London, London EC1M 6BQ, UKTel: +44 (0)20 7882 6231Email: [email protected]
Conflict of interest statement: The authors declare no conflict of interest.
Word count: 6000Abstract word count: 219Number of tables: 2Number of figures: 7Number of supplementary data: 24 (17 supplementary tables, 5 supplementary figures, 1document of supplementary figure legends, 1 document of supplementary text)
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
scribing these kinds of important biological complexities within a model is a necessary next
step for the development of in silico biomarker development platform that is of general use.
Increasing the realism of the model would improve confidence that the predicted prognostic
value of any biomarker was not an artefact of the over-simplified model, although we have
shown that our results are somewhat robust to alterations of a number of the key parameters in
our model. Incorporating additional biological realism would also facilitate the in silico testing of
the prognostic value of a full range of specific biological features; for example, the expression
of a protein that fulfils a particular biological function, such as modulating cell adhesion.
Our study demonstrates how a computational model offers a platform for the initial de-
velopment of novel prognostic biomarkers: computational models can be viewed as a high-
throughput and cost-effective screening tool with which to identify the most promising biomark-
ers for subsequent empirical testing. This work provides the rationale for constructing an in
silico biomarker development platform that would lessen the current restrictions imposed by
the sole reliance on empirical testing.
Acknowledgments
The authors wish to thank the anonymous reviewers for their insightful comments and sug-
gested improvements to the manuscript.
References
1. Reid BJ, Kostadinov R, Maley CC. New strategies in Barrett’s esophagus: integratingclonal evolutionary theory with clinical management. Clin Cancer Res. 2011;17:3512–9.
2. Jones JL. Progression of ductal carcinoma in situ: the pathological perspective. BreastCancer Res. 2006;8:204.
3. Crawford ED. Understanding the epidemiology, natural history, and key pathways in-volved in prostate cancer. Urology. 2009;73:S4–10.
4. Miyamoto H, Miller JS, Fajardo DA, Lee TK, Netto GJ, Epstein JI. Non-invasive papillaryurothelial neoplasms: The 2004 WHO/ISUP classification system. Pathol Int. 2010;60:1–8.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
5. Hvid-Jensen F, Pedersen L, Drewes AM, Sørensen HT, Funch-Jensen P. Incidenceof adenocarcinoma among patients with Barrett’s esophagus. New Engl J Med.2011;365:1375–83.
6. Coldiron BM, Mellette JR, Hruza GJ, Helm TN, Garcia CA. Addressing overdiagnosisand overtreatment in cancer. Lancet Oncol. 2014;15:e307.
7. Paik S, Tang G, Shak S, Kim C, Baker J, Kim W, et al. Gene expression and benefit ofchemotherapy in women with node-negative, estrogen receptor-positive breast cancer. JClin Oncol. 2006;24:3726–34.
8. Paez JG, Janne PA, Lee JC, Tracy S, Greulich H, Gabriel S, et al. EGFR mutations in lungcancer: correlation with clinical response to gefitinib therapy. Science. 2004;304:1497–500.
9. Maley CC, Galipeau PC, Li X, Sanchez CA, Paulson TG, Reid BJ. Selectively advan-tageous mutations and hitchhikers in neoplasms p16 lesions are selected in Barrett’sEsophagus. Cancer Res. 2004;64:3414–27.
10. Ludwig JA, Weinstein JN. Biomarkers in cancer staging, prognosis and treatment selec-tion. Nat Rev Cancer. 2005;5:845–56.
11. Lari SA, Kuerer HM. Biological markers in DCIS and risk of breast recurrence: a system-atic review. J Cancer. 2011;2:232–61.
13. Marusyk A, Almendro V, Polyak K. Intra-tumour heterogeneity: a looking glass for can-cer? Nat Rev Cancer. 2012;12:323–34.
14. Ein-Dor L, Zuk O, Domany E. Thousands of samples are needed to generate a robustgene list for predicting outcome in cancer. Proc Natl Acad Sci USA. 2006;103:5923–8.
15. Maley CC, Galipeau PC, Finley JC, Wongsurawat VJ, Li X, Sanchez CA, et al. Ge-netic clonal diversity predicts progression to esophageal adenocarcinoma. Nat Genet.2006;38:468–73.
16. Park SY, Gonen M, Kim HJ, Michor F, Polyak K. Cellular and genetic diversity in theprogression of in situ human breast carcinomas to an invasive phenotype. J Clin Invest.2010;120:636.
17. Bochtler T, Stolzel F, Heilig CE, Kunz C, Mohr B, Jauch A, et al. Clonal heterogeneity asdetected by metaphase karyotyping is an indicator of poor prognosis in acute myeloidleukemia. J Clin Oncol. 2013;p. JCO–2013.
18. Yap TA, Gerlinger M, Futreal PA, Pusztai L, Swanton C. Intratumor heterogeneity: seeingthe wood for the trees. Sci Transl Med. 2012;4:127ps10.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
19. Almendro V, Cheng YK, Randles A, Itzkovitz S, Marusyk A, Ametller E, et al. Inferenceof tumor evolution during chemotherapy by computational modeling and in situ analysisof genetic and phenotypic cellular diversity. Cell Rep. 2014;6:514–27.
20. Michor F, Iwasa Y, Nowak MA. Dynamics of cancer progression. Nat Rev Cancer.2004;4:197–205.
21. Durrett R, Moseley S. Evolution of resistance and progression to disease during clonalexpansion of cancer. Theor Pop Biol. 2010;77:42–8.
22. Beerenwinkel N, Antal T, Dingli D, Traulsen A, Kinzler KW, Velculescu VE, et al. Geneticprogression and the waiting time to cancer. PLoS Comput Biol. 2007;3:e225.
23. Bozic I, Antal Tr, Ohtsuki H, Carter H, Kim D, Chen S, et al. Accumulation ofdriver and passenger mutations during tumor progression. Proc Natl Acad Sci USA.2010;107:18545–50.
24. Martens EA, Kostadinov R, Maley CC, Hallatschek O. Spatial structure increases thewaiting time for cancer. New J Phys. 2011;13:115014.
25. Anderson ARA, Weaver AM, Cummings PT, Quaranta V. Tumor morphology andphenotypic evolution driven by selective pressure from the microenvironment. Cell.2006;127:905–15.
26. Anderson ARA, Hassanein M, Branch KM, Lu J, Lobdell NA, Maier J, et al. Microenviron-mental independence associated with tumor progression. Cancer Res. 2009;69:8797–8806.
27. Korolev KS, Xavier JB, Gore J. Turning ecology and evolution against cancer. Nat RevCancer. 2014;14:371–80.
28. Williams T, Bjerknes R. Stochastic model for abnormal clone spread through epithelialbasal layer. Nature. 1972;236:19–21.
29. Foo J, Leder K, Ryser MD. Multifocality and recurrence risk: a quantitative model of fieldcancerization. J Theor Biol. 2014;355:170–84.
30. Gillespie DT. A general method for numerically simulating the stochastic time evolutionof coupled chemical reactions. J Comput Phys. 1976;22:403–34.
31. Kuukasjarvi T, Kononen J, Helin H, Holli K, Isola J. Loss of estrogen receptor in recur-rent breast cancer is associated with poor response to endocrine therapy. J Clin Oncol.1996;14:2584–9.
32. Kroger N, Milde-Langosch K, Riethdorf S, Schmoor C, Schumacher M, Zander AR, et al.Prognostic and predictive effects of immunohistochemical factors in high-risk primarybreast cancer patients. Clin Cancer Res. 2006;12:159–68.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
33. Arteaga CL, Sliwkowski MX, Osborne CK, Perez EA, Puglisi F, Gianni L. Treatment ofHER2-positive breast cancer: current status and future perspectives. Nat Rev Clin Oncol.2011;9:16–32.
34. Scholzen T, Gerdes J. The Ki-67 protein: from the known and the unknown. J CellPhysiol. 2000;182:311–22.
35. Shannon CE. Communication theory of secrecy systems. Bell Syst Tech J. 1949;28:656–715.
36. Simpson EH. Measurement of diversity. Nature. 1949;163:688.
37. Jost L. Entropy and diversity. Oikos. 2006;113:363–75.
38. Moran PAP. Notes on continuous stochastic phenomena. Biometrika. 1950;37:17–23.
39. Geary RC. The contiguity ratio and statistical mapping. The Incorporated Statistician.1954;5:115–46.
40. Pepe MS, Janes H, Longton G, Leisenring W, Newcomb P. Limitations of the odds ratioin gauging the performance of a diagnostic, prognostic, or screening marker. Am JEpidemiol. 2004;159:882–90.
41. Heagerty PJ, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics.2005;61:92–105.
42. Gerlinger M, Rowan AJ, Horswell S, Larkin J, Endesfelder D, Gronroos E, et al. Intra-tumor heterogeneity and branched evolution revealed by multiregion sequencing. NewEngl J Med. 2012;366:883–92.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
δ Detectable fraction of cancer cells in the tissue 0.05Nm Min. no. advantageous mutations for cancer {3, 5, 10, 15}sp Fitness increase from a advantageous mutation {0, 0.002, 0.02, 0.2}sd Fitness decrease from a deleterious mutation {0, 0.002, 0.02, 0.2}μ Probability of mutation per cell division {0.01, 0.05, 0.1}Np Min. no. advantageous mutations for positive stain {2, 3, 5, 7, 9}tw Time over which a cell stains positive for a recent mitosis 0.01N Number of cells in lattice 100× 100Nb Radius of biopsy region {5, 20, 40}Ns Number of cells taken in scraping 1000Tb Time at which sample is taken {50, 80}
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Summary of Cox proportional hazards models for various putative biomarker schemes,for different tissue sampling schemes. Hazard ratios (HR75) are computed at time t = 75for the case Nm = 10, sp = sd = 0.2, and μ = 0.1. Statistically significant values are in bold.‘Unit change’ denotes the change in the value of each putative biomarker that increases theassociated hazard ratio by the reported factor.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Depiction of the spatial simulation, a virtual biopsy, and the successive clonal sweeps.A: Heat map of the lattice at a given point in time, with different colours representing differentnumbers of positive mutations of the cells at those points. B: Depiction of the lattice subsetinvolved in a virtual biopsy. C: Time evolution of the proportions of cells with different num-bers of positive mutations, showing successive clonal sweeps. Results are averaged from 200simulations with parameter values Nm = 10, sp = sd = 0.2 for five such genotypes (for figureclarity).
Figure 2
Prognostic value of random tissue sampling. A random sample of Ns = 103 (10% of thelesion) cells was sampled at time Tb = 80 and the prognostic value of the mitotic proportion(A), Shannon index (B) and Gini-Simpson index (C) on this sample was considered. Kaplan-Meier curves are plotted for each putative biomarker assessed, and in case, the values acrossthe simulations were separated into upper (red), upper middle (green), lower middle (blue)and lower (black) quartiles. Only biomarkers that did not require spatial information could becomputed for this tissue sampling method. P -values are for the generalized log-rank test.
Figure 3
Sampling the whole lesion improves the prognostic value. The prognostic value of sam-pling the whole lattice at time Tb = 80 was assessed. Kaplan-Meier curves are plotted for themitotic proportion (A), Shannon index (B), Gini-Simpson index (C), Moran’s I (D), Geary’s C (E),IPP (F) and INP (G). In each case, biomarker values across the simulations were separatedinto upper (red), upper middle (green), lower middle (blue) and lower (black) quartiles. P -valuesare for the generalized log-rank test.
Figure 4
Areas under ROC curves for putative biomarkers. The prognostic value of sampling a cir-cular biopsy at time Tb = 75 was assessed by considering the area under the curve (AUC) ofreceiver-operator characteristic (ROC) curves as a function of censoring time. This analysisconfirmed the time-invariant predictive value of the IPP (red line) and clonal diversity measures(blue and green lines), and lack of predictive value derived from the mitotic proportion (blackline) and proportion of cells bearing at least one abnormality (brown line). The worse-than-random performance of the proliferation and Geary’s C measures at short censoring times islikely to be attributable to the stochasticity inherent in cancer development within the model:early clonal expansions do not necessarily signify later cancer risk. Results from 1000 simu-lations for each sampling scheme, with parameter values Nm = 10, sp = sd = 0.2, μ = 0.1,
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Nb = 20 and Ns = 103. For comparison, the black dotted line denotes an AUC = 0.5 (whichwould would be achieved by a random predictor).
Figure 5
Prognostic value of early versus late biopsies. For a range of sampling times Tb, the virtualtissue was biopsied and the correlation between putative biomarker values and the time ofclinically detectable cancer was computed. Results are shown based on sampling the wholelesion (A), a circular biopsy (B) and random tissue sampling (C). For each sampling scheme,1000 simulations were run with Nm = 10, sp = sd = 0.2, μ = 0.1, Nb = 20 and Ns = 103.
Figure 6
Serial biopsies provide slightly increased additional prognostic information. Heat mapsdepicting the relative value of taking serial biopsies at different time points for the proportionof cells with at least two positive mutations (A), mitotic proportion (B), Shannon index (C), Gini-Simpson index (D), Moran’s I (E), Geary’s C (F), IPP (G) and INP (H). Positive values (warmcolours) indicate that prognostic value was improved by taking the average of biomarker valuefrom both time-points; negative values (cool colours) indicate that more information was avail-able at the second time point alone than from the averaged time points. Results are shownfrom 1000 simulations for each pair of time points, with Nm = 10, sp = sd = 0.2, μ = 0.1 andNb = 20.
Figure 7
Additional biopsies at the same time point improves prognostication with diminishingreturns. Graphs show the relationship between the correlation coefficient (between eachbiomarker value and time of clinically detectable cancer) and the number of biopsies collectedat time Tb = 50, for the proportion of cells with at least two positive mutations (A), mitotic propor-tion (B), Shannon index (C), Gini-Simpson index (D), Moran’s I (E), Geary’s C (F), IPP (G) andINP (H). Lines denote different measures based on the multiple biopsies: average biomarkervalue across biopsies (red); maximum value (green); minimum value (blue); difference betweenmaximum and minimum values (black); and variance in values (cyan). Results are shown from1000 simulations for each pair of time points, with Nm = 10, sp = sd = 0.2, μ = 0.1 and Nb = 20.
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248
Published OnlineFirst February 5, 2016.Cancer Prev Res Andrew Dhawan, Trevor Graham and Alexander G Fletcher predict cancer risk in premalignant diseaseA computational modelling approach for deriving biomarkers to
Updated version
10.1158/1940-6207.CAPR-15-0248doi:
Access the most recent version of this article at:
Manuscript
Authoredited. Author manuscripts have been peer reviewed and accepted for publication but have not yet been
E-mail alerts related to this article or journal.Sign up to receive free email-alerts
To order reprints of this article or to subscribe to the journal, contact the AACR Publications
Permissions
Rightslink site. Click on "Request Permissions" which will take you to the Copyright Clearance Center's (CCC)
.48http://cancerpreventionresearch.aacrjournals.org/content/early/2016/02/05/1940-6207.CAPR-15-02To request permission to re-use all or part of this article, use this link
Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on February 5, 2016; DOI: 10.1158/1940-6207.CAPR-15-0248