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

Abstract 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.