title: Degeneracy and discrete receiver operating characteristic rating data.
abstract: OBJECTIVE
  Observer performance studies sometimes use too few cases for estimating diagnostic accuracy from binormal receiver operating characteristic (ROC) curves. One important problem is degenerate data sets. We compared a new algorithm, RSCORE4, with the exact-solution approach to degeneracy in ROCFIT and with the Wilcoxon statistic.
  
  
  METHODS
  Degenerate ROC solutions result from empty cells in the data matrix. We addressed this problem by adding a small constant to empty cells in a maximum-likelihood program, RSCORE4. When this method failed, the program branched to a pattern-search algorithm. We tested the program in a series of Monte Carlo studies.
  
  
  RESULTS
  RSCORE4 converged to nondegenerate solutions in every case and gave results closer to population values than ROCFIT or Wilcoxon. ROCFIT converged to exact-fit degenerate solutions, those with zero or infinite parameter values, in more than 40% of the samples. The Wilcoxon statistic was biased.
  
  
  CONCLUSIONS
  RSCORE4 seems to outperform other currently recommended methods for dealing with degeneracy.
authors.affiliation: Department of Psychology, University of Iowa, Iowa City 52242, USA.
authors.forename: D D
authors.initials: DD
authors.lastname: Dorfman
authors.forename: K S
authors.initials: KS
authors.lastname: Berbaum
mesh_terms: D000465:Algorithms; D016013:Likelihood Functions; D009010:Monte Carlo Method; D012372:ROC Curve; D011859:Radiography; D018709:Statistics, Nonparametric