The linear-quadratic (LQ) model is inappropriate for high doses per fraction owing to _/_ ratio is not a constant: evidence deduced from radiothera...

Date 24 November 2018
Event ESMO Asia 2018 Congress
Session Poster display - Cocktail
Topics Prostate Cancer
Radiation Oncology
Presenter Ming Cui
Citation Annals of Oncology (2018) 29 (suppl_9): ix67-ix73. 10.1093/annonc/mdy434
Authors M. Cui1, S.X. Gao2
  • 1Department Of Radiation Oncology, Peking University First Hospital, 100034 - Beijing/CN
  • 2Radiotherapy Department, Peking University First Hospital, Beijing/CN



It had been demonstrated that the linear-quadratic (LQ) model was inappropriate for high doses per fraction on cell lines or animals. Our study used mathematics statistics with clinical data in prostate cancer (PCa) patients to estimate the α/β ratio in different fractionated dose to further validate whether LQ is inappropriate for high doses per fraction.


We searched eligible articles from PubMed and extracted following data from the articles: the number of PCa patients, total dose, the number of fractions or the dose per fraction and 5-year biochemical relapse-free survival (bRFS). We estimated the values of α/β according to formulas of LQ models using maximum-likelihood methods in mathematics statistics with Stata 12.0.


There were 44 articles of 16367 prostate cancer patients included in this study. In all 16367 prostate cancer patients, the α/β ratio was calculated as 1.35Gy (95%CI: 1.18-1.52, P < 0.001). Subgroup analysis for patients who received conventionally fractionated radiotherapy, moderately hypofractionated radiotherapy and stereotactic body radiotherapy (SBRT), the α/β ratios were 1.77Gy (95%CI: 0.864-2.68, P < 0.001), 2.41Gy (95%CI: 0.506-4.31, P = 0.013) and 4.07Gy (95%CI: -34.3-42.5, P = 0.835), respectively. The results showed that α/β ratio turned higher and higher when the dose per fraction increased meaning α/β ratio was not a constant.


We demonstrated that the LQ model was inappropriate for high doses per fraction owing to α/β ratio was not a constant. Therefore, to make the conversion of the conventionally fractionated radiation doses to high doses per fraction equivalent using the standard LQ model, we could use a higher α/β ratio when did computation.

Editorial acknowledgement

Clinical trial identification

Legal entity responsible for the study

Xian-Shu Gao.


Has not received any funding.


All authors have declared no conflicts of interest.