title: Deterministic rather than stochastic factors explain most of the variation in the expression of skin telangiectasia after radiotherapy.
abstract: BACKGROUND
  The large patient-to-patient variability in the grade of normal tissue injury after a standard course of radiotherapy is well established clinically. A better understanding of this individual variation may provide valuable insights into the pathogenesis of radiation damage and the prospects of predicting the outcome.
  
  
  OBJECTIVE
  To estimate the relative importance of the stochastic vs. patient-related components of variability in the expression of radiation-induced normal tissue damage.
  
  
  METHODS
  The study data were selected from the dose fractionation studies of Turesson in Gothenburg. Patients treated with bilateral internal mammary fields, who completed at least 10 years of follow-up, were included. The material included 22 different fractionation schedules (11 on each side). Telangiectasia was graded on an arbitrary 6-point scale using clinical photographs of the irradiated fields. For each field, in each patient, a curve showing the grade of telangiectasia as a function of time was constructed. A measure of radioresponsiveness was obtained from the difference between the area under the curve (AUC) for a specific field in an individual patient minus the mean AUC of fields receiving the same dose fractionation schedule. As a confirmatory procedure, the same analysis was repeated with a weighted area under the curve (WAUC) approach, in which the time spent at or above each of the 5 nonzero grades was calculated for each field in each patient. These times were used as explanatory variables in a linear regression analysis of biological equivalent dose to establish statistically the weight of each grade providing the optimal relationship between dose and effect. Using these regression coefficients, the weighted area under the grade-time curve (WAUC) was estimated.
  
  
  RESULTS
  The AUC was significantly correlated with the isoeffective dose in 2-Gy fractions (ID2). An analysis of variance components, using the maximum likelihood method, showed that 90% (with 95% confidence limits 65% and 100%) of the variance in radioresponsiveness in the right-sided field was explained by the radioresponsiveness on the left-sided field. Through the linear regression analysis between the AUC and the ID2, it was estimated that patients with a reaction that is 1 SD from the population mean would require a dose modification of approximately 23 Gy (from the group mean of 56 Gy) to give them a level of reaction similar to the group average. Similarly, the WAUC was significantly correlated with the ID2, and 81% (with 95% confidence limits 49% and 100%) of the variance in radioresponsiveness in the right-sided field was explained by the radioresponsiveness on the left-sided field. Patients with a reaction that is 1 SD from the population mean would require a dose modification of approximately 21 Gy (from the group mean of 56 Gy) to give them a level of reaction similar to the group average.
  
  
  CONCLUSIONS
  For a given fractionation schedule, patient-related factors explain 81-90% of the patient-to-patient variation in telangiectasia level seen after radiotherapy. The remaining 10-19% are explained by stochastic effects. This observation encourages further research into genetic or phenotypic assays of normal tissue radioresponsiveness.
authors.affiliation: Group for Biostatistics in Oncology, Gray Laboratory, Northwood, Middlesex, UK.
authors.forename: Akmal
authors.initials: A
authors.lastname: Safwat
authors.forename: Søren M
authors.initials: SM
authors.lastname: Bentzen
authors.forename: Ingela
authors.initials: I
authors.lastname: Turesson
authors.forename: Jolyon H
authors.initials: JH
authors.lastname: Hendry
mesh_terms: D000704:Analysis of Variance; D019540:Area Under Curve; D019583:Dose Fractionation, Radiation; D005500:Follow-Up Studies; D006801:Humans; D016013:Likelihood Functions; D011832:Radiation Injuries / Q000150:complications* / Q000473:pathology; D011853:Radiobiology; D012044:Regression Analysis; D017445:Skin Diseases, Vascular / Q000209:etiology* / Q000473:pathology; D013684:Telangiectasis / Q000209:etiology* / Q000473:pathology