Applicability of the linear-quadratic formalism for modeling local tumor control probability in high dose per fraction stereotactic body radiotherapy for early stage non-small cell lung cancer

Radiother Oncol. 2013 Oct;109(1):13-20. doi: 10.1016/j.radonc.2013.09.005. Epub 2013 Oct 30.


Background and purpose: To compare the linear-quadratic (LQ) and the LQ-L formalism (linear cell survival curve beyond a threshold dose dT) for modeling local tumor control probability (TCP) in stereotactic body radiotherapy (SBRT) for stage I non-small cell lung cancer (NSCLC).

Materials and methods: This study is based on 395 patients from 13 German and Austrian centers treated with SBRT for stage I NSCLC. The median number of SBRT fractions was 3 (range 1-8) and median single fraction dose was 12.5 Gy (2.9-33 Gy); dose was prescribed to the median 65% PTV encompassing isodose (60-100%). Assuming an α/β-value of 10 Gy, we modeled TCP as a sigmoid-shaped function of the biologically effective dose (BED). Models were compared using maximum likelihood ratio tests as well as Bayes factors (BFs).

Results: There was strong evidence for a dose-response relationship in the total patient cohort (BFs>20), which was lacking in single-fraction SBRT (BFs<3). Using the PTV encompassing dose or maximum (isocentric) dose, our data indicated a LQ-L transition dose (dT) at 11 Gy (68% CI 8-14 Gy) or 22 Gy (14-42 Gy), respectively. However, the fit of the LQ-L models was not significantly better than a fit without the dT parameter (p=0.07, BF=2.1 and p=0.86, BF=0.8, respectively). Generally, isocentric doses resulted in much better dose-response relationships than PTV encompassing doses (BFs>20).

Conclusion: Our data suggest accurate modeling of local tumor control in fractionated SBRT for stage I NSCLC with the traditional LQ formalism.

Keywords: Biologically effective dose; Dose–response modeling; Linear-quadratic formalism; Non-small cell lung cancer; Stereotactic body radiotherapy.

MeSH terms

  • Adult
  • Aged
  • Aged, 80 and over
  • Carcinoma, Non-Small-Cell Lung / surgery*
  • Dose Fractionation, Radiation*
  • Dose-Response Relationship, Radiation
  • Female
  • Humans
  • Linear Models
  • Lung Neoplasms / pathology
  • Lung Neoplasms / surgery*
  • Male
  • Middle Aged
  • Neoplasm Staging
  • Probability
  • Radiosurgery / methods*