title: A probabilistic model for the MRMC method, part 2: validation and applications.
abstract: OBJECTIVE
  We have previously described a probabilistic model for the multiple-reader, multiple-case paradigm for receiver operating characteristic analysis. When the figure of merit is the Wilcoxon statistic, this model returns a seven-term expansion for the variance of this statistic as a function of the numbers of cases and readers. This probabilistic model also provides expressions for the coefficients in the seven-term expansion in terms of expectations over the internal noise, readers, and cases. Finally, this probabilistic model sets bounds on both the overall variance of the Wilcoxon statistic and the individual coefficients.
  
  
  METHODS
  In this article, we will first validate the probabilistic model by comparing variances determined by direct computation of the expansion coefficients to empirical estimates of the variance using independent sampling. Validation of the probabilistic model will enable us to use the direct estimates of the expansion coefficients as a gold standard to compare other coefficient-estimation techniques. Next, we develop a coefficient-estimation technique that employs bootstrapping to estimate the Wilcoxon statistic variance for different numbers of readers and cases. We then employ constrained, least-squares fitting techniques to estimate the expansion coefficients. The constraints used in this fitting are derived directly from the probabilistic model.
  
  
  RESULTS
  Using two different simulation studies, we show that the novel (and practical) bootstrapping/fitting technique returns estimates of the coefficients that are consistent with the gold standard.
  
  
  CONCLUSIONS
  The results presented also serve to validate the seven-term expansion for the variance of the Wilcoxon statistic.
authors.affiliation: College of Optical Sciences, The University of Arizona, 1630 East University Blvd., Tucson, AZ 85721, USA. kupinski@radiology.arizona.edu
authors.forename: Matthew A
authors.initials: MA
authors.lastname: Kupinski
authors.forename: Eric
authors.initials: E
authors.lastname: Clarkson
authors.forename: Harrison H
authors.initials: HH
authors.lastname: Barrett
mesh_terms: D000704:Analysis of Variance; D003198:Computer Simulation / Q000706:statistics & numerical data; D003952:Diagnostic Imaging / Q000706:statistics & numerical data*; D008432:Mathematical Computing; D015233:Models, Statistical; D015588:Observer Variation; D012372:ROC Curve; D018709:Statistics, Nonparametric