A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

CPT: Pharmacometrics and Systems Pharmacology

Volumn 3, Issue 5, 2014, Pages

  Ribba, B ^a   Holford, N H ^b   Magni, P ^c   Troconiz I ^d   Gueorguieva, I ^e   Girard, P ^f   Sarr, C ^g   Elishmereni, M ^h   Kloft, C ⁱ   Friberg, L E ^b  

^a UNIVERSITÉ DE LYON   (France)

^b UPPSALA UNIVERSITY   (Sweden)

^c UNIVERSITY OF PAVIA   (Italy)

^d UNIVERSITY OF NAVARRA   (Spain)

^e ELI LILLY AND COMPANY   (United States)

^f EPFL   (Switzerland)

^g NOVARTIS PHARMA AG   (Switzerland)

^h Optimata Ltd   (Israel)

ⁱ FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALENDRONIC ACID; ANTINEOPLASTIC AGENT; BEVACIZUMAB; CAPECITABINE; CARBOPLATIN; CISPLATIN; DOCETAXEL; ERLOTINIB; EVEROLIMUS; FLUOROURACIL; FOLINIC ACID; GEMCITABINE; IRINOTECAN; KETOCONAZOLE; MOTESANIB; NAVELBINE; PACLITAXEL; PAZOPANIB; PEMETREXED; PREDNISONE; PROCARBAZINE; SORAFENIB; SUNITINIB; TEMOZOLOMIDE; THALIDOMIDE; VACCINE; VINCRISTINE;

CLINICAL STUDY; DRUG EFFECT; HUMAN; MATHEMATICS; NONHUMAN; POPULATION RESEARCH; PRIORITY JOURNAL; REVIEW; TREATMENT RESPONSE; TUMOR GROWTH; TUMOR MODEL;

EID: 84902511572     PISSN: None     EISSN: 21638306     Source Type: Journal    
DOI: 10.1038/psp.2014.12     Document Type: Review

References (70)

1. Rodriguez-Brenes, I.A., Komarova, N.L. & Wodarz, D. Tumor growth dynamics: insights into evolutionary processes. Trends Ecol. Evol. 28, 597-604 (2013).
2. Bernard, A., Kimko, H., Mital, D. & Poggesi, I. Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development. Expert Opin. Drug Metab. Toxicol. 8, 1057-1069 (2012).
3. Bender, B.C., Schindler, E. & Friberg, L.E. Population pharmacokinetic pharmacodynamic modelling in oncology: a tool for predicting clinical response. Br. J. Clin. Pharmacol. e-pub ahead of print 18 October 2013 http://www.ncbi.nlm.nih.gov/pubmed/24134068.
4. Bonate, P. Modeling tumor growth in oncology. In Pharmacokinetics in Drug Development (eds. Bonate, P.L. & Howard, D.R.) 1-19 (Springer, New York, 2011).
5. Laird, A.K. Dynamics of tumor growth. Br. J. Cancer 13, 490-502 (1964).
6. Mayneord, W.V. On a law of growth of Jensen's rat sarcoma. Am. J. Cancer 16, 841-846 (1932).
7. Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new model of determining the value of life contingencies. Phil Trans Royal Soc London 115, 513-583 (1825).
8. Sullivan, P.W. & Salmon, S.E. Kinetics of tumor growth and regression in IgG multiple myeloma. J. Clin. Invest. 51, 1697-1708 (1972).
9. Bloom, H.J., Richardson, W.W. & Harries, E.J. Natural history of untreated breast cancer (1805-1933). Comparison of untreated and treated cases according to histological grade of malignancy. BMJ 2, 213-221 (1962).
10. Norton, L. A Gompertzian model of human breast cancer growth. Cancer Res. 48, 7067-7071 (1988).
11. Eisenhauer, E.A. et al. New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1). Eur. J. Cancer 45, 228-247 (2009).
12. Ratain, M.J. & Eckhardt, S.G. Phase II studies of modern drugs directed against new targets: if you are fazed, too, then resist RECIST. J. Clin. Oncol. 22, 4442-4445 (2004).
13. Sharma, M.R., Maitland, M.L. & Ratain, M.J. RECIST: no longer the sharpest tool in the oncology clinical trials toolbox - point. Cancer Res 72, 5145-5149 (2012).
14. US Food and Drug Administration. Innovation or stagnation: challenge and opportunity on the critical path to new medical products. (2004).
15. Bruno, R. & Claret, L. On the use of change in tumor size to predict survival in clinical oncology studies: toward a new paradigm to design and evaluate phase II studies. Clin. Pharmacol. Ther. 86, 136-138 (2009).
16. Claret, L. et al. Evaluation of tumor-size response metrics to predict overall survival in Western and Chinese patients with first-line metastatic colorectal cancer. J. Clin. Oncol. 31, 2110-2114 (2013).
17. Tham, L.S. et al. A pharmacodynamic model for the time course of tumor shrinkage by gemcitabine + carboplatin in non-small cell lung cancer patients. Clin. Cancer Res. 14, 4213-4218 (2008).
18. Wang, Y. et al. Elucidation of relationship between tumor size and survival in non-smallcell lung cancer patients can aid early decision making in clinical drug development. Clin. Pharmacol. Ther. 86, 167-174 (2009).
19. Houk, B.E., Bello, C.L., Poland, B., Rosen, L.S., Demetri, G.D. & Motzer, R.J. Relationship between exposure to sunitinib and efficacy and tolerability endpoints in patients with cancer: results of a pharmacokinetic/pharmacodynamic meta-analysis. Cancer Chemother. Pharmacol. 66, 357-371 (2010).
20. Stein, A., Wang, W. et al. Dynamic tumor modeling of the dose-response relationship for everolimus in metastatic renal cell carcinoma using data from the phase 3 RECORD-1 trial. BMC Cancer 12, 311 (2012).
21. Maitland, M.L. et al. Estimation of renal cell carcinoma treatment effects from disease progression modeling. Clin. Pharmacol. Ther. 93, 345-351 (2013).
22. Bonate, P.L. & Suttle, A.B. Modeling tumor growth kinetics after treatment with pazopanib or placebo in patients with renal cell carcinoma. Cancer Chemother. Pharmacol. 72, 231-240 (2013).
23. Claret, L., Lu, J.F., Sun, Y.N. & Bruno, R. Development of a modeling framework to simulate efficacy endpoints for motesanib in patients with thyroid cancer. Cancer Chemother. Pharmacol. 66, 1141-1149 (2010).
24. Frances, N., Claret, L., Bruno, R. & Iliadis, A. Tumor growth modeling from clinical trials reveals synergistic anticancer effect of the capecitabine and docetaxel combination in metastatic breast cancer. Cancer Chemother. Pharmacol. 68, 1413-1419 (2011).
25. Stein, W.D., Gulley, J.L. et al. Tumor regression and growth rates determined in five intramural NCI prostate cancer trials: the growth rate constant as an indicator of therapeutic efficacy. Clin. Cancer Res. 17, 907-917 (2011).
26. Hansson, E.K. et al. PKPD Modeling of VEGF, sVEGFR-2, sVEGFR-3, and sKIT as Predictors of Tumor Dynamics and Overall Survival Following Sunitinib Treatment in GIST. CPT Pharmacometrics Syst. Pharmacol. 2, e84 (2013).
27. Ribba, B. et al. A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy. Clin. Cancer Res. 18, 5071-5080 (2012).
28. Bonate, P.L. & Suttle, B. Effect of censoring due to progressive disease on tumor size kinetic parameter estimates. AAPS J. 15, 832-839 (2013).
29. Claret, L. et al. Model-based prediction of phase III overall survival in colorectal cancer on the basis of phase II tumor dynamics. J. Clin. Oncol. 27, 4103-4108 (2009).
30. Wharton, S.B., Chan, K.K., Anderson, J.R., Stoeber, K. & Williams, G.H. Replicative Mcm2 protein as a novel proliferation marker in oligodendrogliomas and its relationship to Ki67 labelling index, histological grade and prognosis. Neuropathol. Appl. Neurobiol. 27, 305-313 (2001). (Pubitemid 32768551)
31. Hahnfeldt, P., Panigrahy, D., Folkman, J. & Hlatky, L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59, 4770-4775 (1999). (Pubitemid 29472873)
32. Rocchetti, M. et al. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth after administration of an anti-angiogenic agent, bevacizumab, as single-agent and combination therapy in tumor xenografts. Cancer Chemother. Pharmacol. 71, 1147-1157 (2013).
33. Ribba, B. et al. A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers. Eur. J. Cancer 47, 479-490 (2011).
34. Mandonnet, E. et al. Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann. Neurol. 53, 524-528 (2003). (Pubitemid 36373265)
35. Beal, S. et al. NONMEM User's Guides (I.D. Solutions, Ellicott City, Maryland, 1989-2009).
36. Hansson, E.K. et al. PKPD modeling of predictors for adverse effects and overall survival in sunitinib-treated patients with GIST. CPT Pharmacometrics Syst. Pharmacol. 2, e85 (2013).
37. Simeoni, M., De Nicolao, G., Magni, P., Rocchetti, M. & Poggesi, I. Modeling of human tumor xenografts and dose rationale in oncology. Drug Discov. Today Technol. 10, e365-e372 (2013).
38. Lobo, E.D. & Balthasar, J.P. Pharmacodynamic modeling of chemotherapeutic effects: application of a transit compartment model to characterize methotrexate effects in vitro. AAPS PharmSci 4, E42 (2002).
39. Mager, D.E. & Jusko, W.J. Pharmacodynamic modeling of time-dependent transduction systems. Clin. Pharmacol. Ther. 70, 210-216 (2001). (Pubitemid 32868484)
40. Simeoni, M. et al. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res. 64, 1094-1101 (2004). (Pubitemid 38176915)
41. Shah, D.K., Haddish-Berhane, N. & Betts, A. Bench to bedside translation of antibody drug conjugates using a multiscale mechanistic PK/PD model: a case study with brentuximabvedotin. J. Pharmacokinet. Pharmacodyn. 39, 643-659 (2012).
42. Haddish-Berhane, N. et al. On translation of antibody drug conjugates efficacy from mouse experimental tumors to the clinic: a PK/PD approach. J. Pharmacokinet. Pharmacodyn. 40, 557-571 (2013).
43. Bueno, L. et al. Semi-mechanistic modelling of the tumour growth inhibitory effects of LY2157299, a new type I receptor TGF-beta kinase antagonist, in mice. Eur. J. Cancer 44, 142-150 (2008). (Pubitemid 350256941)
44. Friberg, L.E., Henningsson, A., Maas, H., Nguyen, L. & Karlsson, M.O. Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J. Clin. Oncol. 20, 4713-4721 (2002).
45. Hart, D., Shochat, E. & Agur, Z. The growth law of primary breast cancer as inferred from mammography screening trials data. Br. J. Cancer 78, 382-387 (1998). (Pubitemid 28336427)
46. Kola, I. & Landis, J. Can the pharmaceutical industry reduce attrition rates? Nat. Rev. Drug Discov. 3, 711-715 (2004). (Pubitemid 39173511)
47. Girard, P., et al. Tumor size model and survival analysis of cetuximab and various cytotoxics in patients treated for metastatic colorectal cancer. (2013).
48. Vainas, O. et al. Personalising docetaxel and G-CSF schedules in cancer patients by a clinically validated computational model. Br. J. Cancer 107, 814-822 (2012).
49. Kogan, Y., Halevi-Tobias, K., Elishmereni, M., Vuk-Pavlović, S. & Agur, Z. Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization. Cancer Res. 72, 2218-2227 (2012).
50. Gorelik, B. et al. Efficacy of weekly docetaxel and bevacizumab in mesenchymal chondrosarcoma: a new theranostic method combining xenografted biopsies with a mathematical model. Cancer Res. 68, 9033-9040 (2008).
51. Parra-Guillen, Z.P., Berraondo, P., Grenier, E., Ribba, B. & Troconiz, I.F. Mathematical model approach to describe tumour response in mice after vaccine administration and its applicability to immune-stimulatory cytokine-based strategies. AAPS J. 15, 797-807 (2013).
52. Parra-Guillen, Z.P., Berraondo, P., Ribba, B. & Trocóniz, I.F. Modeling tumor response after combined administration of different immune-stimulatory agents. J. Pharmacol. Exp. Ther. 346, 432-442 (2013).
53. Elishmereni, M., Kheifetz, Y., Søndergaard, H., Overgaard, R.V. & Agur, Z. An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers. PLoS Comput. Biol. 7, e1002206 (2011).
54. Jager, E., van der Velden, V.H., te Marvelde, J.G., Walter, R.B., Agur, Z. & Vainstein, V. Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization. PLoS One 6, e24265 (2011).
55. Terranova, N., Germani, M., Del Bene, F. & Magni, P. A predictive pharmacokineticpharmacodynamic model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination. Cancer Chemother. Pharmacol. 72, 471-482 (2013).
56. Krippendorff, B.F., Kuester, K., Kloft, C. & Huisinga, W. Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis. J. Pharmacokinet. Pharmacodyn. 36, 239-260 (2009).
57. Wong, H. et al. Antitumor activity of targeted and cytotoxic agents in murine subcutaneous tumor models correlates with clinical response. Clin. Cancer Res. 18, 3846-3855 (2012).
58. Rocchetti, M., Simeoni, M., Pesenti, E., De Nicolao, G. & Poggesi, I. Predicting the active doses in humans from animal studies: a novel approach in oncology. Eur. J. Cancer 43, 1862-1868 (2007). (Pubitemid 47243652)
59. Keizer, R.J., Schellens, J.H., Beijnen, J.H. & Huitema, A.D. Pharmacodynamic biomarkers in model-based drug development in oncology. Curr. Clin. Pharmacol. 6, 30-40 (2011).
60. Almufti, R. et al. A critical review of the analytical approaches for circulating tumor biomarker kinetics during treatment. Ann. Oncol. 25, 41-56 (2014).
61. Kronik, N., Kogan, Y., Elishmereni, M., Halevi-Tobias, K., Vuk-Pavlović, S. & Agur, Z. Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models. PLoS One 5, e15482 (2010).
62. Komarova, N.L. & Wodarz, D. Effect of cellular quiescence on the success of targeted CML therapy. PLoS One 2, e990 (2007).
63. Kronik, N., Kogan, Y., Vainstein, V. & Agur, Z. Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics. Cancer Immunol. Immunother. 57, 425-439 (2008).
64. Swanson, K.R., Alvord, E.C. Jr & Murray, J.D. Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br. J. Cancer 86, 14-18 (2002). (Pubitemid 34146334)
65. Swanson, K.R., Bridge, C., Murray, J.D. & Alvord, E.C. Jr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216, 1-10 (2003).
66. Harpold, H.L., Alvord, E.C. Jr & Swanson, K.R. The evolution of mathematical modeling of glioma proliferation and invasion. J. Neuropathol. Exp. Neurol. 66, 1-9 (2007).
67. Ribba, B., Colin, T. & Schnell, S. A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor. Biol. Med. Model. 3, 7 (2006).
68. Lignet, F. et al. Theoretical investigation of the efficacy of antiangiogenic drugs combined to chemotherapy in xenografted mice. J. Theor. Biol. 320, 86-99 (2013).
69. Vigneaux, P., Louvet, V. & Grenier, E. Extending Monolix to use models with partial differential equations. (2013).
70. Barthelemy, C. & Lavielle, M. New methods for complex models defined by a large number of ODEs. Application to a glucose/insulin model. (2013).