title: Functional data analysis in NTCP modeling: a new method to explore the radiation dose-volume effects.
abstract: OBJECTIVE
  To describe a novel method to explore radiation dose-volume effects. Functional data analysis is used to investigate the information contained in differential dose-volume histograms. The method is applied to the normal tissue complication probability modeling of rectal bleeding (RB) for patients irradiated in the prostatic bed by 3-dimensional conformal radiation therapy.
  
  
  METHODS
  Kernel density estimation was used to estimate the individual probability density functions from each of the 141 rectum differential dose-volume histograms. Functional principal component analysis was performed on the estimated probability density functions to explore the variation modes in the dose distribution. The functional principal components were then tested for association with RB using logistic regression adapted to functional covariates (FLR). For comparison, 3 other normal tissue complication probability models were considered: the Lyman-Kutcher-Burman model, logistic model based on standard dosimetric parameters (LM), and logistic model based on multivariate principal component analysis (PCA).
  
  
  RESULTS
  The incidence rate of grade ≥2 RB was 14%. V65Gy was the most predictive factor for the LM (P=.058). The best fit for the Lyman-Kutcher-Burman model was obtained with n=0.12, m = 0.17, and TD50 = 72.6 Gy. In PCA and FLR, the components that describe the interdependence between the relative volumes exposed at intermediate and high doses were the most correlated to the complication. The FLR parameter function leads to a better understanding of the volume effect by including the treatment specificity in the delivered mechanistic information. For RB grade ≥2, patients with advanced age are significantly at risk (odds ratio, 1.123; 95% confidence interval, 1.03-1.22), and the fits of the LM, PCA, and functional principal component analysis models are significantly improved by including this clinical factor.
  
  
  CONCLUSIONS
  Functional data analysis provides an attractive method for flexibly estimating the dose-volume effect for normal tissues in external radiation therapy.
authors.affiliation: Center for Research in Epidemiology and Population Health (CESP) INSERM 1018 Radiation, Epidemiology Group, Villejuif, France; Université Paris sud, Le Kremlin-Bicêtre, France; Institut Gustave Roussy, Villejuif, France. Electronic address: mohamedamine.benadjaoud@gustaveroussy.fr.
authors.forename: Mohamed Amine
authors.initials: MA
authors.lastname: Benadjaoud
authors.affiliation: Université Paris sud, Le Kremlin-Bicêtre, France; Department of Radiation Oncology, Institut Gustave Roussy, Villejuif, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Blanchard
authors.affiliation: Center for Research in Epidemiology and Population Health (CESP) INSERM 1018 Radiation, Epidemiology Group, Villejuif, France; Université Paris sud, Le Kremlin-Bicêtre, France; Institut Gustave Roussy, Villejuif, France.
authors.forename: Boris
authors.initials: B
authors.lastname: Schwartz
authors.affiliation: Department of Radiation Oncology, CHU de la Timone, Marseille, France.
authors.forename: Jérôme
authors.initials: J
authors.lastname: Champoudry
authors.affiliation: Department of Radiation Oncology, CHU Henri Mondor, Creteil, France.
authors.forename: Ryan
authors.initials: R
authors.lastname: Bouaita
authors.affiliation: Department of Radiation Physics, Institut Gustave Roussy, Villejuif, France.
authors.forename: Dimitri
authors.initials: D
authors.lastname: Lefkopoulos
authors.affiliation: Université Paris sud, Le Kremlin-Bicêtre, France; Department of Radiation Oncology, Institut Gustave Roussy, Villejuif, France; INSERM 1030, Molecular Radiotherapy, Villejuif, France.
authors.forename: Eric
authors.initials: E
authors.lastname: Deutsch
authors.affiliation: Center for Research in Epidemiology and Population Health (CESP) INSERM 1018 Radiation, Epidemiology Group, Villejuif, France; Université Paris sud, Le Kremlin-Bicêtre, France; Institut Gustave Roussy, Villejuif, France.
authors.forename: Ibrahima
authors.initials: I
authors.lastname: Diallo
authors.affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon, France.
authors.forename: Hervé
authors.initials: H
authors.lastname: Cardot
authors.affiliation: Center for Research in Epidemiology and Population Health (CESP) INSERM 1018 Radiation, Epidemiology Group, Villejuif, France; Université Paris sud, Le Kremlin-Bicêtre, France; Institut Gustave Roussy, Villejuif, France.
authors.forename: Florent
authors.initials: F
authors.lastname: de Vathaire
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D004307:Dose-Response Relationship, Radiation; D005163:Factor Analysis, Statistical; D006471:Gastrointestinal Hemorrhage / Q000453:epidemiology / Q000209:etiology*; D006801:Humans; D015994:Incidence; D016015:Logistic Models; D008297:Male; D008875:Middle Aged; D008962:Models, Theoretical; D058958:Organs at Risk / Q000528:radiation effects; D025341:Principal Component Analysis / Q000379:methods; D011336:Probability; D011471:Prostatic Neoplasms / Q000532:radiotherapy*; D011832:Radiation Injuries / Q000150:complications*; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods; D020266:Radiotherapy, Conformal / Q000009:adverse effects* / Q000379:methods / Q000706:statistics & numerical data; D012002:Rectal Diseases / Q000453:epidemiology / Q000209:etiology*; D012007:Rectum / Q000528:radiation effects*; D012044:Regression Analysis; D012062:Relative Biological Effectiveness