Heuristic estimation of the α/β ratio for a cohort of Mexican patients with prostate cancer treated with external radiotherapy techniques
Abstract
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.
Keywords: α/β ratiotime-dependent LQ modelbiochemical relapse-free survivalbRFSbiologically effective doseBEDprostate cancerPCa
References
- Cosset JM, Chargari C, Créhange G. [Which alpha/beta ratio for prostate cancer in 2019?]. Cancer Radiother. 2019; 23(4): 342–345.
- 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).
- 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).
- 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.
- Dekkers G. Accuracy Requirements and Uncertainties in Radiotherapy. IAEA Human Health Series. 2016; 31.
- 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.
- 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.
- 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.
- Arribalzaga E. Interpretación de las curvas de supervivencia. Revista chilena de cirugía. 2007; 59(1).
- Mayles P, Nahum A, Rosenwald JC. Handbook of Radiotherapy Physics: Theory and Practice. Taylor & Francis, New York 2007.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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).
- 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).
- 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.
- 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.
- Donald Chapman J, Nahum AE. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology. Taylor & Francis, New York 2015.
- Fowler J. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989; 62(740): 679–694.
- Khan FM, Gibbons JP, Sperduto PW. Treatment Planing in Radiation Oncology. 4th ed. Wolters Kluwer 2016.