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

Abstract

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. 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 N 0 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. 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 N 0 , the overall treatment time (OTT), the kick-off time for tumor repopulation T k 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. The value of is determined from cohorts of Mexican patients with PC a 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.