ROC Analysis in Radiotherapy: A TCP Model-Based Test

ABSTRACT

Several mathematical models have been proposed to describe the
dynamics of irradiated cancer cells and to evaluate the tumour control
probability (TCP). In this article, we propose a TCP model-based statistical
test for predicting the outcome of a radiation treatment. We determine the
foresight capability of prostate tumour erradication (cure) from

Cite this paper

M. Santos and U. Neves, "ROC Analysis in Radiotherapy: A TCP Model-Based Test,"*Open Journal of Applied Sciences*, Vol. 3 No. 2, 2013, pp. 186-193. doi: 10.4236/ojapps.2013.32025.

M. Santos and U. Neves, "ROC Analysis in Radiotherapy: A TCP Model-Based Test,"

References

[1] A. Dawson and T. Hillen, “Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model,” Computational & Mathematical Methods in Medicine, Vol. 7, No. 2-3, 2006, pp. 121-141. doi:10.1080/10273660600968937

[2] M. Zaider and G. N. Minerbo, “Tumour Control Probability: A Formulation Applicable to Any Temporal Protocol of Dose Delivery,” Physics in Medicine and Biology, Vol. 45, No. 2, 2000, pp. 279-293. doi:10.1088/0031-9155/45/2/303

[3] T. Hillen, G. De Vries, J. F. Gong and C. Finlay, “From Cell Population Models to Tumor Control Probability: Including Cell Cycle Effects,” Acta Oncologica, Vol. 49, No. 8, 2010, pp. 1315-1323. doi:10.3109/02841861003631487

[4] F. C. Henriquez and S. V. Castrillon, “The Use of a Mixed Poisson Model for Tumour Control Probability Computation in Non Homogeneous Irradiations,” Australasian Physical & Engineering Sciences in Medicine, Vol. 34, No. 2, 2011, pp. 267-272. doi:10.1007/s13246-011-0074-4

[5] H. Byrne and D. Drasdo, “Individual-Based and Continuum Models of Growing Cell Populations: A Comparison,” Journal of Mathematical Biology, Vol. 58, No. 4, 2009, pp. 657-687. doi:10.1007/s00285-008-0212-0

[6] J. F. Gong, M. M. Dos Santos, C. Finlay and T. Hillen, “Are More Complicated Tumour Control Probability Models Better?” Mathematical Medicine and Biology, Vol. 30, No. 1, 2011, pp. 1-19. doi:10.1093/imammb/dqr023

[7] R. Keinj, T. Bastogne and P. Vallois, “Multinomial Model Based Formulations of TCP and NTCP for Radiotherapy Treatment Planning,” Journal of Theoretical Biology, Vol. 279, No. 1, 2011, pp. 55-62. doi:10.1016/j.jtbi.2011.03.025

[8] R. Varadhan, S. K. Hui, S. Way and K. Nisi, “Assessing Prostate, Bladder and Rectal Doses during Image Guided Radiation Therapy—Need for Plan Adaptation?” Journal of Applied Clinical Medical Physics, Vol. 10, No. 3, 2009, pp. 56-74. doi:10.1120/jacmp.v10i3.2883

[9] J. Sykes, D. S. Brettle, D. R. Magee and D. I. Thwaites, “Investigation of Uncertainties in Image Registration of Cone Beam CT to CT on an Image-Guided Radiotherapy System,” Physics in Medicine and Biology, Vol. 54, No. 24, 2009, pp. 7263-7283. doi:10.1088/0031-9155/54/24/002

[10] M. Kasabasic, V. Rajevac, S. Jurkovic, A. Ivkovic, H. Sobat and D. Faj, “Influence of Daily Set-Up Errors on Dose Distribution during Pelvis Radiotherapy,” Archives of Industrial Hygiene and Toxicology, Vol. 62, No. 3, 2011, pp. 261-267. doi:10.2478/10004-1254-64-2011-2110

[11] R. Mehra, S. A. Tomlins, J. J. Yu, X. H. Cao, L. Wang, A. Menon, M. A. Rubin, K. J. Pienta, R. B. Shah and A. M. Chinnaiyan, “Characterization of TMPRSS2-ETS Gene Aberrations in Androgen-Independent Metastatic Prostate Cancer,” Cancer Research, Vol. 68, No. 10, 2008, pp. 3584-3590. doi:10.1158/0008-5472.CAN-07-6154

[12] M. Zaider and L. Hanin, “Tumor Control Probability in Radiation Treatment,” Medical Physics, Vol. 38, No. 2, 2011, pp. 574-583. doi:10.1118/1.3521406

[13] J. A. Hanley and B. J. McNeil, “The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve,” Radiology, Vol. 143, No. 1, 1982, pp. 29-36.

[14] W. Tedeschi, H.-P. Müller, D. B. de Araujo, A. C. Santos, U. P. C. Neves, S. N. Ernè and O. Baffa, “Generalized Mutual Information Tests Applied to fMRI Analysis,” Physica A: Statistical Mechanics and Its Applications, Vol. 352, No. 2-4, 2005, pp. 629-644. doi:10.1016/j.physa.2004.12.065

[15] B. C. T. Cabella, M. J. Sturzbecher, D. B. de Araujo and U. P. C. Neves, “Generalized Relative Entropy in Functional Magnetic Resonance Imaging,” Physica A: Statistical Mechanics and Its Applications, Vol. 388, No. 1, 2009, pp. 41-50. doi:10.1016/j.physa.2008.09.029

[16] M. J. Sturzbecher, W. Tedeschi, B. C. T. Cabella, O. Baffa, U. P. C. Neves and D. B. de Araujo, “Nonextensive Entropy and the Extraction of Bold Spatial Information in Event-Related Functional MRI,” Physics in Medicine and Biology, Vol. 54, No. 1, 2009, pp. 161-174. doi:10.1088/0031-9155/54/1/011

[17] C. H. Morrell, L. J. Brant, S. Sheng and E. J. Metter, “Screening for Prostate Cancer Using Multivariate Mixed Effects Models,” Journal of Applied Statistics, Vol. 39, No. 6, 2012, pp. 1151-1175. doi:10.1080/02664763.2011.644523

[18] W. K. Sinclair, “The Shape of Radiation Survival Curves of Mammalian Cells Cultured in Vitro,” Biophysical Aspects of Radiation Quality, Technical Reports Series (International Atomic Energy Agency), No. 58, 1966, pp. 21-43.

[19] J. T. Parsons, W. Mendenhall, N. Cassisi, J. Isascs and R. R. Million, “Accelerated Hyperfractionation for Head and Neck Cancer,” International Journal of Radiation Oncology*Biology*Physics, Vol. 14, No. 5, 1988, pp. 649-658.

[20] D. J. Carlson, R. D. Stewart, X. A. Li, K. Jennings, J. Z. Wang and M. Guerrero, “Comparison of in Vitro and in Vivo Alpha/Beta Ratios for Prostate Cancer,” Physics In Medicine and Biology, Vol. 49, No. 19, 2004, Article ID: 4477. doi:10.1088/0031-9155/49/19/003

[21] S. M. Bentzen, L. S. Constine, J. O. Deasy, A. Eisbruch, A. Jackson, L. B. Marks, R. K. Ten Haken and E. D. Yorke, “Quantitative Analyses of Normal Tissue Effects in the Clinic (Quantec): An Introduction to the Scientific Issues,” International Journal of Radiation Oncology* Biology*Physics, Vol. 76, No. 3, 2010, pp. S3-S9. doi:10.1016/j.ijrobp.2009.09.040

[1] A. Dawson and T. Hillen, “Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model,” Computational & Mathematical Methods in Medicine, Vol. 7, No. 2-3, 2006, pp. 121-141. doi:10.1080/10273660600968937

[2] M. Zaider and G. N. Minerbo, “Tumour Control Probability: A Formulation Applicable to Any Temporal Protocol of Dose Delivery,” Physics in Medicine and Biology, Vol. 45, No. 2, 2000, pp. 279-293. doi:10.1088/0031-9155/45/2/303

[3] T. Hillen, G. De Vries, J. F. Gong and C. Finlay, “From Cell Population Models to Tumor Control Probability: Including Cell Cycle Effects,” Acta Oncologica, Vol. 49, No. 8, 2010, pp. 1315-1323. doi:10.3109/02841861003631487

[4] F. C. Henriquez and S. V. Castrillon, “The Use of a Mixed Poisson Model for Tumour Control Probability Computation in Non Homogeneous Irradiations,” Australasian Physical & Engineering Sciences in Medicine, Vol. 34, No. 2, 2011, pp. 267-272. doi:10.1007/s13246-011-0074-4

[5] H. Byrne and D. Drasdo, “Individual-Based and Continuum Models of Growing Cell Populations: A Comparison,” Journal of Mathematical Biology, Vol. 58, No. 4, 2009, pp. 657-687. doi:10.1007/s00285-008-0212-0

[6] J. F. Gong, M. M. Dos Santos, C. Finlay and T. Hillen, “Are More Complicated Tumour Control Probability Models Better?” Mathematical Medicine and Biology, Vol. 30, No. 1, 2011, pp. 1-19. doi:10.1093/imammb/dqr023

[7] R. Keinj, T. Bastogne and P. Vallois, “Multinomial Model Based Formulations of TCP and NTCP for Radiotherapy Treatment Planning,” Journal of Theoretical Biology, Vol. 279, No. 1, 2011, pp. 55-62. doi:10.1016/j.jtbi.2011.03.025

[8] R. Varadhan, S. K. Hui, S. Way and K. Nisi, “Assessing Prostate, Bladder and Rectal Doses during Image Guided Radiation Therapy—Need for Plan Adaptation?” Journal of Applied Clinical Medical Physics, Vol. 10, No. 3, 2009, pp. 56-74. doi:10.1120/jacmp.v10i3.2883

[9] J. Sykes, D. S. Brettle, D. R. Magee and D. I. Thwaites, “Investigation of Uncertainties in Image Registration of Cone Beam CT to CT on an Image-Guided Radiotherapy System,” Physics in Medicine and Biology, Vol. 54, No. 24, 2009, pp. 7263-7283. doi:10.1088/0031-9155/54/24/002

[10] M. Kasabasic, V. Rajevac, S. Jurkovic, A. Ivkovic, H. Sobat and D. Faj, “Influence of Daily Set-Up Errors on Dose Distribution during Pelvis Radiotherapy,” Archives of Industrial Hygiene and Toxicology, Vol. 62, No. 3, 2011, pp. 261-267. doi:10.2478/10004-1254-64-2011-2110

[11] R. Mehra, S. A. Tomlins, J. J. Yu, X. H. Cao, L. Wang, A. Menon, M. A. Rubin, K. J. Pienta, R. B. Shah and A. M. Chinnaiyan, “Characterization of TMPRSS2-ETS Gene Aberrations in Androgen-Independent Metastatic Prostate Cancer,” Cancer Research, Vol. 68, No. 10, 2008, pp. 3584-3590. doi:10.1158/0008-5472.CAN-07-6154

[12] M. Zaider and L. Hanin, “Tumor Control Probability in Radiation Treatment,” Medical Physics, Vol. 38, No. 2, 2011, pp. 574-583. doi:10.1118/1.3521406

[13] J. A. Hanley and B. J. McNeil, “The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve,” Radiology, Vol. 143, No. 1, 1982, pp. 29-36.

[14] W. Tedeschi, H.-P. Müller, D. B. de Araujo, A. C. Santos, U. P. C. Neves, S. N. Ernè and O. Baffa, “Generalized Mutual Information Tests Applied to fMRI Analysis,” Physica A: Statistical Mechanics and Its Applications, Vol. 352, No. 2-4, 2005, pp. 629-644. doi:10.1016/j.physa.2004.12.065

[15] B. C. T. Cabella, M. J. Sturzbecher, D. B. de Araujo and U. P. C. Neves, “Generalized Relative Entropy in Functional Magnetic Resonance Imaging,” Physica A: Statistical Mechanics and Its Applications, Vol. 388, No. 1, 2009, pp. 41-50. doi:10.1016/j.physa.2008.09.029

[16] M. J. Sturzbecher, W. Tedeschi, B. C. T. Cabella, O. Baffa, U. P. C. Neves and D. B. de Araujo, “Nonextensive Entropy and the Extraction of Bold Spatial Information in Event-Related Functional MRI,” Physics in Medicine and Biology, Vol. 54, No. 1, 2009, pp. 161-174. doi:10.1088/0031-9155/54/1/011

[17] C. H. Morrell, L. J. Brant, S. Sheng and E. J. Metter, “Screening for Prostate Cancer Using Multivariate Mixed Effects Models,” Journal of Applied Statistics, Vol. 39, No. 6, 2012, pp. 1151-1175. doi:10.1080/02664763.2011.644523

[18] W. K. Sinclair, “The Shape of Radiation Survival Curves of Mammalian Cells Cultured in Vitro,” Biophysical Aspects of Radiation Quality, Technical Reports Series (International Atomic Energy Agency), No. 58, 1966, pp. 21-43.

[19] J. T. Parsons, W. Mendenhall, N. Cassisi, J. Isascs and R. R. Million, “Accelerated Hyperfractionation for Head and Neck Cancer,” International Journal of Radiation Oncology*Biology*Physics, Vol. 14, No. 5, 1988, pp. 649-658.

[20] D. J. Carlson, R. D. Stewart, X. A. Li, K. Jennings, J. Z. Wang and M. Guerrero, “Comparison of in Vitro and in Vivo Alpha/Beta Ratios for Prostate Cancer,” Physics In Medicine and Biology, Vol. 49, No. 19, 2004, Article ID: 4477. doi:10.1088/0031-9155/49/19/003

[21] S. M. Bentzen, L. S. Constine, J. O. Deasy, A. Eisbruch, A. Jackson, L. B. Marks, R. K. Ten Haken and E. D. Yorke, “Quantitative Analyses of Normal Tissue Effects in the Clinic (Quantec): An Introduction to the Scientific Issues,” International Journal of Radiation Oncology* Biology*Physics, Vol. 76, No. 3, 2010, pp. S3-S9. doi:10.1016/j.ijrobp.2009.09.040