{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:53:58Z","timestamp":1767178438367,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010444","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T00:00:00Z","timestamp":1662508800000}}],"reference-count":41,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T00:00:00Z","timestamp":1661385600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Inserm PlanCancer","award":["Systems RCC\" (2018-2021)"],"award-info":[{"award-number":["Systems RCC\" (2018-2021)"]}]},{"name":"the Region Nouvelle Aquitaine","award":["Metasys Project"],"award-info":[{"award-number":["Metasys Project"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Distant metastasis-free survival (DMFS) curves are widely used in oncology. They are classically analyzed using the Kaplan-Meier estimator or agnostic statistical models from survival analysis. Here we report on a method to extract more information from DMFS curves using a mathematical model of primary tumor growth and metastatic dissemination. The model depends on two parameters,\n                    <jats:italic>\u03b1<\/jats:italic>\n                    and\n                    <jats:italic>\u03bc<\/jats:italic>\n                    , respectively quantifying tumor growth and dissemination. We assumed these to be lognormally distributed in a patient population. We propose a method for identification of the parameters of these distributions based on least-squares minimization between the data and the simulated survival curve. We studied the practical identifiability of these parameters and found that including the percentage of patients with metastasis at diagnosis was critical to ensure robust estimation. We also studied the impact and identifiability of covariates and their coefficients in\n                    <jats:italic>\u03b1<\/jats:italic>\n                    and\n                    <jats:italic>\u03bc<\/jats:italic>\n                    , either categorical or continuous, including various functional forms for the latter (threshold, linear or a combination of both). We found that both the functional form and the coefficients could be determined from DMFS curves. We then applied our model to a clinical dataset of metastatic relapse from kidney cancer with individual data of 105 patients. We show that the model was able to describe the data and illustrate our method to disentangle the impact of three covariates on DMFS: a categorical one (F\u00fchrman grade) and two continuous ones (gene expressions of the macrophage mannose receptor 1 (MMR) and the G Protein-Coupled Receptor Class C Group 5 Member A (GPRC5a) gene). We found that all had an influence in metastasis dissemination (\n                    <jats:italic>\u03bc<\/jats:italic>\n                    ), but not on growth (\n                    <jats:italic>\u03b1<\/jats:italic>\n                    ).\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1010444","type":"journal-article","created":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T13:57:45Z","timestamp":1661435865000},"page":"e1010444","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":6,"title":["Practical identifiability analysis of a mechanistic model for the time to distant metastatic relapse and its application to renal cell carcinoma"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8002-0903","authenticated-orcid":true,"given":"Arturo","family":"\u00c1lvarez-Arenas","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4831-5891","authenticated-orcid":true,"given":"Wilfried","family":"Souleyreau","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4133-2525","authenticated-orcid":true,"given":"Andrea","family":"Emanuelli","sequence":"additional","affiliation":[]},{"given":"Lindsay S.","family":"Cooley","sequence":"additional","affiliation":[]},{"given":"Jean-Christophe","family":"Bernhard","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4138-5229","authenticated-orcid":true,"given":"Andreas","family":"Bikfalvi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3749-8637","authenticated-orcid":true,"given":"Sebastien","family":"Benzekry","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,8,25]]},"reference":[{"key":"pcbi.1010444.ref001","doi-asserted-by":"crossref","DOI":"10.1201\/b18041","volume-title":"Modelling survival data in medical research","author":"D Collett","year":"2015"},{"issue":"282","key":"pcbi.1010444.ref002","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1080\/01621459.1958.10501452","article-title":"Nonparametric Estimation from Incomplete Observations","volume":"53","author":"EL Kaplan","year":"1958","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"pcbi.1010444.ref003","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression Models and Life-Tables","volume":"34","author":"DR Cox","year":"1972","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"issue":"3","key":"pcbi.1010444.ref004","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1214\/08-AOAS169","article-title":"Random survival forests","volume":"2","author":"H Ishwaran","year":"2008","journal-title":"The Annals of Applied Statistics"},{"issue":"5","key":"pcbi.1010444.ref005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v039.i05","article-title":"Regularization Paths for Cox\u2019s Proportional Hazards Model via Coordinate Descent","volume":"39","author":"N Simon","year":"2011","journal-title":"J Stat Softw"},{"issue":"1","key":"pcbi.1010444.ref006","doi-asserted-by":"crossref","first-page":"11707","DOI":"10.1038\/s41598-017-11817-6","article-title":"Predicting clinical outcomes from large scale cancer genomic profiles with deep survival models","volume":"7","author":"S Yousefi","year":"2017","journal-title":"Scientific Reports"},{"key":"pcbi.1010444.ref007","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1200\/CCI.19.00133","article-title":"Machine Learning and Mechanistic Modeling for Prediction of Metastatic Relapse in Early-Stage Breast Cancer","author":"C Nicol\u00f2","year":"2020","journal-title":"JCO Clinical Cancer Informatics"},{"key":"pcbi.1010444.ref008","doi-asserted-by":"crossref","DOI":"10.1038\/nrdp.2017.9","article-title":"Renal cell carcinoma","volume":"3","author":"JJ Hsieh","year":"2017","journal-title":"Nature Reviews Disease Primers"},{"key":"pcbi.1010444.ref009","article-title":"SEER Cancer Statistics Review, 1975-2016","author":"N Howlader","year":"2019","journal-title":"National Cancer Institute Bethesda, MD"},{"key":"pcbi.1010444.ref010","unstructured":"Society AC. Key Statistics about kidney cancer; 2016. http:\/\/www.cancer.org\/cancer\/kidney-cancer.html."},{"issue":"13","key":"pcbi.1010444.ref011","doi-asserted-by":"crossref","first-page":"2844","DOI":"10.1002\/cncr.24338","article-title":"Natural history, growth kinetics, and outcomes of untreated clinically localized renal tumors under active surveillance","volume":"115","author":"PL Crispen","year":"2009","journal-title":"Cancer"},{"issue":"24","key":"pcbi.1010444.ref012","first-page":"7067","article-title":"A Gompertzian model of human breast cancer growth","volume":"48","author":"L Norton","year":"1988","journal-title":"Cancer Research"},{"issue":"8","key":"pcbi.1010444.ref013","doi-asserted-by":"crossref","first-page":"e1003800","DOI":"10.1371\/journal.pcbi.1003800","article-title":"Classical mathematical models for description and prediction of experimental tumor growth","volume":"10","author":"S Benzekry","year":"2014-08","journal-title":"PLoS Computational Biology"},{"issue":"2","key":"pcbi.1010444.ref014","doi-asserted-by":"crossref","first-page":"e1007178","DOI":"10.1371\/journal.pcbi.1007178","article-title":"Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors","volume":"16","author":"C Vaghi","year":"2020","journal-title":"PLoS Computational Biology"},{"issue":"1","key":"pcbi.1010444.ref015","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1186\/1471-2407-13-283","article-title":"Detection of cancer before distant metastasis","volume":"13","author":"FAW Coumans","year":"2013","journal-title":"BMC Cancer"},{"issue":"1","key":"pcbi.1010444.ref016","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1038\/bjc.1966.9","article-title":"The growth rate of human tumours","volume":"20","author":"GG Steel","year":"1966","journal-title":"British Journal of Cancer"},{"issue":"12","key":"pcbi.1010444.ref017","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/0014-2964(80)90034-1","article-title":"Growth of testicular neoplasm lung metastases: Tumor-specific relation between two Gompertzian parameters","volume":"16","author":"R Demicheli","year":"1980-12","journal-title":"European Journal of Cancer"},{"issue":"1","key":"pcbi.1010444.ref018","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1148\/radiology.139.1.7208937","article-title":"Predictive value and threshold detectability of lung tumors","volume":"139","author":"HL Kundel","year":"1981","journal-title":"Radiology"},{"issue":"2","key":"pcbi.1010444.ref019","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1148\/radiol.2372041887","article-title":"Guidelines for Management of Small Pulmonary Nodules Detected on CT Scans: A Statement from the Fleischner Society1","volume":"237","author":"H MacMahon","year":"2005","journal-title":"Radiology"},{"key":"pcbi.1010444.ref020","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1137\/S1052623496303470","article-title":"Convergence Properties of the Nelder\u2013Mead Simplex Method in Low Dimensions","volume":"9","author":"JC Lagarias","year":"1998","journal-title":"SIAM Journal on Optimization"},{"key":"pcbi.1010444.ref021","first-page":"239","article-title":"A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code","volume":"21","author":"MD McKay","year":"1979","journal-title":"Technometrics"},{"key":"pcbi.1010444.ref022","article-title":"The growth rate of \u201cclinically significant\u201d renal cancer","author":"ON Gofrit","year":"2015","journal-title":"SpringerPlus"},{"issue":"3","key":"pcbi.1010444.ref023","article-title":"A Comparison of Radiologic Tumor Volume and Pathologic Tumor Volume in Renal Cell Carcinoma (RCC)","volume":"10","author":"SM Choi","year":"2015","journal-title":"Plos One"},{"issue":"4","key":"pcbi.1010444.ref024","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1148\/rg.2019180178","article-title":"Current Challenges in Diagnosis and Assessment of the Response of Locally Advanced and Metastatic Renal Cell Carcinoma","volume":"39","author":"A Diaz de Leon","year":"2019","journal-title":"RadioGraphics"},{"key":"pcbi.1010444.ref025","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1006\/jtbi.2000.1075","article-title":"A Dynamical Model for the Growth and Size Distribution of Multiple Metastatic Tumors","volume":"203","author":"K Iwata","year":"2000","journal-title":"Journal of Theoretical Biology"},{"issue":"4665","key":"pcbi.1010444.ref026","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1126\/science.6382606","article-title":"Growth self-incitement in murine melanoma B16: a phenomenological model","volume":"225","author":"Z Bajzer","year":"1984","journal-title":"Science"},{"key":"pcbi.1010444.ref027","doi-asserted-by":"crossref","first-page":"e1004626","DOI":"10.1371\/journal.pcbi.1004626","article-title":"Computational Modelling of Metastasis Development in Renal Cell Carcinoma","volume":"11","author":"E Baratchart","year":"2015","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1010444.ref028","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1051\/mmnp\/20127114","article-title":"Modeling the Impact of Anticancer Agents on Metastatic Spreading","volume":"7","author":"S Benzekry","year":"2012","journal-title":"Mathematical Modelling of Natural Phenomena"},{"key":"pcbi.1010444.ref029","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1200\/CCI.20.00092","article-title":"Development and Validation of a Prediction Model of Overall Survival in High-Risk Neuroblastoma Using Mechanistic Modeling of Metastasis","author":"S Benzekry","year":"2021","journal-title":"JCO Clinical Cancer Informatics"},{"key":"pcbi.1010444.ref030","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1158\/0008-5472.CAN-15-1389","article-title":"Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach","volume":"76","author":"S Benzekry","year":"2015","journal-title":"Cancer Research"},{"key":"pcbi.1010444.ref031","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-019-49407-3","article-title":"Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer","volume":"9","author":"M Bilous","year":"2019","journal-title":"Scientific Reports"},{"key":"pcbi.1010444.ref032","doi-asserted-by":"crossref","first-page":"4931","DOI":"10.1158\/0008-5472.CAN-15-3567","article-title":"Mathematical Modeling of Cancer Immunotherapy and Its Synergy with Radiotherapy","volume":"76","author":"R Serre","year":"2016","journal-title":"Cancer Research"},{"issue":"3","key":"pcbi.1010444.ref033","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/1026022021000001454","article-title":"Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology","volume":"7","author":"LG Hanin","year":"2002","journal-title":"Discrete Dynamics in Nature and Society"},{"issue":"6","key":"pcbi.1010444.ref034","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1007\/s00285-015-0928-6","article-title":"A \u201cuniversal\u201d model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases","volume":"72","author":"L Hanin","year":"2015","journal-title":"Journal of Mathematical Biology"},{"key":"pcbi.1010444.ref035","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.urology.2015.10.051","article-title":"Size and Volumetric Growth Kinetics of Renal Masses in Patients With Renal Cell Carcinoma","volume":"90","author":"SW Lee","year":"2016","journal-title":"Urology"},{"key":"pcbi.1010444.ref036","doi-asserted-by":"crossref","first-page":"171051","DOI":"10.1148\/radiol.2018171051","article-title":"Tumor Surface Regularity at MR Imaging Predicts Survival and Response to Surgery in Patients with Glioblastoma","volume":"288","author":"J P\u00e9rez-Beteta","year":"2018","journal-title":"Radiology"},{"issue":"7","key":"pcbi.1010444.ref037","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1097\/00000478-198210000-00007","article-title":"Prognostic significance of morphologic parameters in renal cell carcinoma","volume":"6","author":"SA Fuhrman","year":"1982","journal-title":"The American Journal of Surgical Pathology"},{"issue":"1","key":"pcbi.1010444.ref038","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.critrevonc.2007.07.004","article-title":"The inflammatory micro-environment in tumor progression: The role of tumor-associated macrophages","volume":"66","author":"P Allavena","year":"2008","journal-title":"Critical Reviews in Oncology\/Hematology"},{"issue":"530","key":"pcbi.1010444.ref039","doi-asserted-by":"crossref","first-page":"eaax6337","DOI":"10.1126\/scitranslmed.aax6337","article-title":"Mannose receptor (CD206) activation in tumor-associated macrophages enhances adaptive and innate antitumor immune responses","volume":"12","author":"JM Jaynes","year":"2020","journal-title":"Science Translational Medicine"},{"key":"pcbi.1010444.ref040","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/1823726","article-title":"GPRC5A: An Emerging Biomarker in Human Cancer","volume":"2018","author":"X Jiang","year":"2018","journal-title":"BioMed Research International"},{"issue":"3","key":"pcbi.1010444.ref041","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/s11538-017-0388-9","article-title":"Suppression of Metastasis by Primary Tumor and Acceleration of Metastasis Following Primary Tumor Resection: A Natural Law?","volume":"80","author":"L Hanin","year":"2018","journal-title":"Bulletin Mathematical Biology"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010444","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T00:00:00Z","timestamp":1662508800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T13:37:42Z","timestamp":1662557862000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010444"}},"subtitle":[],"editor":[{"given":"Feng","family":"Fu","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,8,25]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8,25]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010444","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,25]]}}}