title: Sample size requirements for knowledge-based treatment planning.
abstract: OBJECTIVE
  To determine how training set size affects the accuracy of knowledge-based treatment planning (KBP) models.
  
  
  METHODS
  The authors selected four models from three classes of KBP approaches, corresponding to three distinct quantities that KBP models may predict: dose-volume histogram (DVH) points, DVH curves, and objective function weights. DVH point prediction is done using the best plan from a database of similar clinical plans; DVH curve prediction employs principal component analysis and multiple linear regression; and objective function weights uses either logistic regression or K-nearest neighbors. The authors trained each KBP model using training sets of sizes n = 10, 20, 30, 50, 75, 100, 150, and 200. The authors set aside 100 randomly selected patients from their cohort of 315 prostate cancer patients from Princess Margaret Cancer Center to serve as a validation set for all experiments. For each value of n, the authors randomly selected 100 different training sets with replacement from the remaining 215 patients. Each of the 100 training sets was used to train a model for each value of n and for each KBT approach. To evaluate the models, the authors predicted the KBP endpoints for each of the 100 patients in the validation set. To estimate the minimum required sample size, the authors used statistical testing to determine if the median error for each sample size from 10 to 150 is equal to the median error for the maximum sample size of 200.
  
  
  RESULTS
  The minimum required sample size was different for each model. The DVH point prediction method predicts two dose metrics for the bladder and two for the rectum. The authors found that more than 200 samples were required to achieve consistent model predictions for all four metrics. For DVH curve prediction, the authors found that at least 75 samples were needed to accurately predict the bladder DVH, while only 20 samples were needed to predict the rectum DVH. Finally, for objective function weight prediction, at least 10 samples were needed to train the logistic regression model, while at least 150 samples were required to train the K-nearest neighbor methodology.
  
  
  CONCLUSIONS
  In conclusion, the minimum required sample size needed to accurately train KBP models for prostate cancer depends on the specific model and endpoint to be predicted. The authors' results may provide a lower bound for more complicated tumor sites.
authors.affiliation: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
authors.forename: Justin J
authors.initials: JJ
authors.lastname: Boutilier
authors.affiliation: Radiation Medicine Program, UHN Princess Margaret Cancer Centre, 610 University of Avenue, Toronto, Ontario M5T 2M9, Canada and Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2, Canada.
authors.forename: Tim
authors.initials: T
authors.lastname: Craig
authors.affiliation: Radiation Medicine Program, UHN Princess Margaret Cancer Centre, 610 University of Avenue, Toronto, Ontario M5T 2M9, Canada; Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2, Canada; and Techna Institute for the Advancement of Technology for Health, 124-100 College Street, Toronto, Ontario M5G 1P5, Canada.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Sharpe
authors.affiliation: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada and Techna Institute for the Advancement of Technology for Health, 124-100 College Street, Toronto, Ontario M5G 1P5, Canada.
authors.forename: Timothy C Y
authors.initials: TC
authors.lastname: Chan
mesh_terms: D006801:Humans; D008297:Male; D011471:Prostatic Neoplasms / Q000532:radiotherapy; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated; D018401:Sample Size