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 purposeTo 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 methodsThis 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 12.5Gy (2.9–33Gy); dose was prescribed to the median 65% PTV encompassing isodose (60–100%). Assuming an α/β-value of 10Gy, 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). ResultsThere 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 11Gy (68% CI 8–14Gy) or 22Gy (14–42Gy), 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). ConclusionOur data suggest accurate modeling of local tumor control in fractionated SBRT for stage I NSCLC with the traditional LQ formalism.