title: 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: OBJECTIVE
  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).
  
  
  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).
  
  
  CONCLUSIONS
  Our data suggest accurate modeling of local tumor control in fractionated SBRT for stage I NSCLC with the traditional LQ formalism.
authors.affiliation: Department of Radiation Oncology, University of Würzburg, Germany. Electronic address: guckenberger_m@klinik.uni-wuerzburg.de.
authors.forename: Matthias
authors.initials: M
authors.lastname: Guckenberger
authors.forename: Rainer Johannes
authors.initials: RJ
authors.lastname: Klement
authors.forename: Michael
authors.initials: M
authors.lastname: Allgäuer
authors.forename: Steffen
authors.initials: S
authors.lastname: Appold
authors.forename: Karin
authors.initials: K
authors.lastname: Dieckmann
authors.forename: Iris
authors.initials: I
authors.lastname: Ernst
authors.forename: Ute
authors.initials: U
authors.lastname: Ganswindt
authors.forename: Richard
authors.initials: R
authors.lastname: Holy
authors.forename: Ursula
authors.initials: U
authors.lastname: Nestle
authors.forename: Meinhard
authors.initials: M
authors.lastname: Nevinny-Stickel
authors.forename: Sabine
authors.initials: S
authors.lastname: Semrau
authors.forename: Florian
authors.initials: F
authors.lastname: Sterzing
authors.forename: Andrea
authors.initials: A
authors.lastname: Wittig
authors.forename: Nicolaus
authors.initials: N
authors.lastname: Andratschke
authors.forename: Michael
authors.initials: M
authors.lastname: Flentje
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D002289:Carcinoma, Non-Small-Cell Lung / Q000601:surgery*; D019583:Dose Fractionation, Radiation; D004307:Dose-Response Relationship, Radiation; D005260:Female; D006801:Humans; D016014:Linear Models; D008175:Lung Neoplasms / Q000473:pathology / Q000601:surgery*; D008297:Male; D008875:Middle Aged; D009367:Neoplasm Staging; D011336:Probability; D016634:Radiosurgery / Q000379:methods*
keywords: Biologically effective dose; Dose–response modeling; Linear-quadratic formalism; Non-small cell lung cancer; Stereotactic body radiotherapy