Vol 26, No 5 (2021)
Research paper
Published online: 2021-04-13

open access

Page views 6543
Article views/downloads 393
Get Citation

Connect on Social Media

Connect on Social Media

Heuristic estimation of the α/β ratio for a cohort of Mexican patients with prostate cancer treated with external radiotherapy techniques

Christian S. Adame González12, José Trinidad Álvarez Romero3, Mario Moranchel y Rodríguez2, Armando Félix Leyva4, Michelle Aline Villavicencio Queijeiro5, María Yicel Bautista Hernández6
Rep Pract Oncol Radiother 2021;26(5):664-673.


BACKGROUND: The aim of the study was to Estimate and compare the radiobiological ratio α/β with the heuristic method for a cohort of Mexican patients with prostate cancer (PCa) who were treated with external radiotherapy (RT) techniques at three Hospital Institutions in Mexico City.

With the Kaplan-Meier technique and the Cox proportional hazards model, the biochemical relapse-free survival (bRFS) is determined and characterized for cohorts of Mexican patients with PCa who received treatment with external RT. Using these clinical outcomes, the radiobiological parameter α/β is determined using the heuristic methodology of Pedicini et. al.

MATERIALS AND METHODS: The α/β is calculated from the survival curves for different treatment schemes implemented at three distinct hospitals. The Pedicini’s techniques allow to determine the parameters α/β, k and N0 when treatments are not radiobiologically equivalent, therefore, are built up of a set of curved pairs for the biologically effective dose (BED) versus the ratio α/β, where the ratio is given by the intersection for each pair of curves.

RESULTS: Six different values of α/β were found: the first α/β = 2.46 Gy, the second α/β = 3.30 Gy, the third for α/β = 3.25 Gy, the fourth α/β = 3.24 Gy, the fifth α/β = 3.38 Gy and the last α/β = 4.08 Gy. These values can be explained as follows: a) The bRFS of the schemes presents a statistical variation; b) The absorbed doses given to the patient present uncertainties on the physical dosimetry that are not on the modeling; c) Finally, in the model for the bRFS of Eq. (3), there are parameters that have to be considered, such as: the number of clonogenic tumor cells N0, the overall treatment time (OTT), the kick-off time for tumor repopulation Tk and the repopulation doubling time. Therefore, the mean value to α/β for all schemes has an average value of 3.29 (± 0.52) Gy.

CONCLUSIONS: The value of = 3.29 (± 0.52) Gy is determined from cohorts of Mexican patients with PCa treated with external radiotherapy using the time-dependent LQ model, which is a higher value with respect to the “dogma” value of α/β 1.5 Gy obtained with the LQ model without temporal dependence. Therefore, there is a possibility of optimizing treatments radiobiologically and improving the results of bRFS in Mexican patients with PCa treated with external radiotherapy.

Article available in PDF format

View PDF Download PDF file


  1. Cosset JM, Chargari C, Créhange G. [Which alpha/beta ratio for prostate cancer in 2019?]. Cancer Radiother. 2019; 23(4): 342–345.
  2. Cancer Today. https://gco.iarc.fr/today/online-analysis-multi-bars?v=2018&mode=cancer&mode_population=countries&population=900&populations=484_388&key=total&sex=1&cancer=39&type=0&statistic=5&prevalence=0&population_group=0&ages_group%5B%5D=0&ages_group%5B%5D=17&nb_ite (July 24, 2020).
  3. Howlader N, Krapcho M, Miller D et al. Cancer Statistics Rev 1975–2014 — SEER Statistics. SEER Cancer Statistics Review — Bethesda (MD): National Cancer Institute. . https://seer.cancer.gov/archive/csr/1975_2014/ (July 25, 2020).
  4. Haiman CA, Chen GK, Blot WJ, et al. Characterizing genetic risk at known prostate cancer susceptibility loci in African Americans. PLoS Genet. 2011; 7(5): e1001387.
  5. Dekkers G. Accuracy Requirements and Uncertainties in Radiotherapy. IAEA Human Health Series. 2016; 31.
  6. Vogelius IR, Bentzen SM. Dose Response and Fractionation Sensitivity of Prostate Cancer After External Beam Radiation Therapy: A Meta-analysis of Randomized Trials. Int J Radiat Oncol Biol Phys. 2018; 100(4): 858–865.
  7. Datta NR, Stutz E, Rogers S, et al. Clinical estimation of α/β values for prostate cancer from isoeffective phase III randomized trials with moderately hypofractionated radiotherapy. Acta Oncol. 2018; 57(7): 883–894.
  8. Tree AC, Dearnaley DP. Seven or less Fractions is Not the Standard of Care for Intermediate-Risk Prostate Cancer. Clin Oncol (R Coll Radiol). 2020; 32(3): 175–180.
  9. Arribalzaga E. Interpretación de las curvas de supervivencia. Revista chilena de cirugía. 2007; 59(1).
  10. Mayles P, Nahum A, Rosenwald JC. Handbook of Radiotherapy Physics: Theory and Practice. Taylor & Francis, New York 2007.
  11. Miralbell R, Roberts SA, Zubizarreta E, et al. Dose-fractionation sensitivity of prostate cancer deduced from radiotherapy outcomes of 5,969 patients in seven international institutional datasets: α/β = 1.4 (0.9-2.2) Gy. Int J Radiat Oncol Biol Phys. 2012; 82(1): e17–e24.
  12. Fowler J, Chappell R, Ritter M, et al. Is alpha/beta for prostate tumors really low? Int J Radiat Oncol Biol Phys. 2001; 50(4): 1021–1031.
  13. Leborgne F, Fowler J. Late outcomes following hypofractionated conformal radiotherapy vs. standard fractionation for localized prostate cancer: a nonrandomized contemporary comparison. Int J Radiat Oncol Biol Phys. 2009; 74(5): 1441–1446.
  14. Leborgne F, Fowler J, Leborgne JH, et al. Later outcomes and alpha/beta estimate from hypofractionated conformal three-dimensional radiotherapy versus standard fractionation for localized prostate cancer. Int J Radiat Oncol Biol Phys. 2012; 82(3): 1200–1207.
  15. van Leeuwen CM, Oei AL, Crezee J, et al. The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies. Radiat Oncol. 2018; 13(1): 96.
  16. Ferreira MR, Thomas K, Truelove L, et al. Dosimetry and Gastrointestinal Toxicity Relationships in a Phase II Trial of Pelvic Lymph Node Radiotherapy in Advanced Localised Prostate Cancer. Clin Oncol (R Coll Radiol). 2019; 31(6): 374–384.
  17. Decree by which various provisions of the Mexican General Health Law are amended and added. Registry. Official Journal of the Federation DOF 17/07/2018. Accessed July 26, 2020. Mexico City, Mexico. (in Spanish).
  18. Regulation of the National Cancer Registry. Official Journal of the Federation DOF : 17/07/2018. Published online 2021:1-2. Mexico City, Mexico. (in Spanish).
  19. Adame González C, Álvarez Romero JT, Morachel Y Rodríguez M, et al. Biochemical relapse free survival rate in patients with prostate cancer treated with external radiotherapy: outcomes obtained at the CMN Siglo XXI Hospital de Oncología, CMN 20 de Noviembre and Hospital General de México of the México City. Rep Pract Oncol Radiother. 2020; 25(2): 276–281.
  20. Pedicini P, Strigari L, Benassi M. Estimation of a self-consistent set of radiobiological parameters from hypofractionated versus standard radiation therapy of prostate cancer. Int J Radiat Oncol Biol Phys. 2013; 85(5): e231–e237.
  21. Donald Chapman J, Nahum AE. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology. Taylor & Francis, New York 2015.
  22. Fowler J. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989; 62(740): 679–694.
  23. Khan FM, Gibbons JP, Sperduto PW. Treatment Planing in Radiation Oncology. 4th ed. Wolters Kluwer 2016.