title: On the importance of accounting for competing risks in pediatric brain cancer: II. Regression modeling and sample size.
abstract: OBJECTIVE
  To accurately model the cumulative need for radiotherapy in trials designed to delay or avoid irradiation among children with malignant brain tumor, it is crucial to account for competing events and evaluate how each contributes to the timing of irradiation. An appropriate choice of statistical model is also important for adequate determination of sample size.
  
  
  METHODS
  We describe the statistical modeling of competing events (A, radiotherapy after progression; B, no radiotherapy after progression; and C, elective radiotherapy) using proportional cause-specific and subdistribution hazard functions. The procedures of sample size estimation based on each method are outlined. These are illustrated by use of data comparing children with ependymoma and other malignant brain tumors. The results from these two approaches are compared.
  
  
  RESULTS
  The cause-specific hazard analysis showed a reduction in hazards among infants with ependymoma for all event types, including Event A (adjusted cause-specific hazard ratio, 0.76; 95% confidence interval, 0.45-1.28). Conversely, the subdistribution hazard analysis suggested an increase in hazard for Event A (adjusted subdistribution hazard ratio, 1.35; 95% confidence interval, 0.80-2.30), but the reduction in hazards for Events B and C remained. Analysis based on subdistribution hazard requires a larger sample size than the cause-specific hazard approach.
  
  
  CONCLUSIONS
  Notable differences in effect estimates and anticipated sample size were observed between methods when the main event showed a beneficial effect whereas the competing events showed an adverse effect on the cumulative incidence. The subdistribution hazard is the most appropriate for modeling treatment when its effects on both the main and competing events are of interest.
authors.affiliation: Department of Epidemiology and Public Health, Yong Loo Lin School of Medicine, National University of Singapore, Singapore. ephtbc@nus.edu.sg
authors.forename: Bee-Choo
authors.initials: BC
authors.lastname: Tai
authors.forename: Richard
authors.initials: R
authors.lastname: Grundy
authors.forename: David
authors.initials: D
authors.lastname: Machin
mesh_terms: D001932:Brain Neoplasms / Q000188:drug therapy / Q000473:pathology / Q000532:radiotherapy* / Q000601:surgery; D002648:Child; D017326:Clinical Trials, Phase III as Topic / Q000706:statistics & numerical data; D016001:Confidence Intervals; D018450:Disease Progression; D004806:Ependymoma / Q000473:pathology / Q000532:radiotherapy; D006801:Humans; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D012044:Regression Analysis; D018570:Risk Assessment; D018401:Sample Size; D013997:Time Factors