title: Improved prediction of rates of visual field loss in glaucoma using empirical Bayes estimates of slopes of change.
abstract: OBJECTIVE
  To describe and test a new methodology for estimation of rates of progressive visual field loss in glaucoma.
  
  
  METHODS
  This observational cohort study enrolled 643 eyes of 368 patients recruited from the Diagnostic Innovations in Glaucoma Study, followed for an average of 6.5±2.0 years. The visual field index was used to evaluate degree of visual field loss in standard automated perimetry. Growth mixture models were used to evaluate visual field index changes over time. Empirical Bayes estimates of best linear unbiased predictions (BLUPs) were used to obtain slopes of change based on the first 5 visual fields for each eye. These slopes were then used to predict future observations. The same procedure was done for ordinary least squares (OLS) estimates. The mean square error of the predictions was used to compare the predictive performance of the different methods.
  
  
  RESULTS
  The growth mixture model successfully identified subpopulations of nonprogressors, slow, moderate, and fast progressors. The mean square error was significantly higher for OLS compared with the BLUP method (32.3 vs 13.9, respectively; P<0.001), indicating a better performance of the BLUP method to predict future observations. The benefit of BLUP predictions was especially evident in eyes with moderate and fast rates of change.
  
  
  CONCLUSIONS
  Empirical Bayes estimates of rates of change performed significantly better than the commonly used technique of OLS regression in predicting future observations. Use of BLUP estimates should be considered when evaluating rates of functional change in glaucoma and predicting future impairment from the disease.
authors.affiliation: Hamilton Glaucoma Center and Department of Ophthalmology, University of California, San Diego, La Jolla, CA 92093-0946, USA. fmedeiros@glaucoma.ucsd.edu
authors.forename: Felipe A
authors.initials: FA
authors.lastname: Medeiros
authors.forename: Linda M
authors.initials: LM
authors.lastname: Zangwill
authors.forename: Robert N
authors.initials: RN
authors.lastname: Weinreb
mesh_terms: D001499:Bayes Theorem; D018450:Disease Progression; D005189:False Positive Reactions; D005260:Female; D005500:Follow-Up Studies; D005902:Glaucoma, Open-Angle / Q000503:physiopathology*; D006801:Humans; D007429:Intraocular Pressure / Q000502:physiology; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D011237:Predictive Value of Tests; D011446:Prospective Studies; D014786:Vision Disorders / Q000503:physiopathology*; D014792:Visual Acuity / Q000502:physiology; D058609:Visual Field Tests; D014794:Visual Fields / Q000502:physiology*