title: A simple model to predict the sensitivity to change of visual acuity measurements.
abstract: BACKGROUND
  Estimates of test-retest variability (TRV) in the form of a 95% range have been suggested as providing a cutoff value (or "change-criterion") against which measured acuity changes can be judged to decide whether they are indicative of a clinically important change. This approach is based on ensuring that the specificity of the procedure is 95% in individuals with no real change. In an earlier article we investigated empirically the ability of the procedure to detect varying degrees of change (its sensitivity). In this article, we develop a simple statistical model to examine further the sensitivity of the approach.
  
  
  METHODS
  A statistical model was developed, and predictions from the model were compared with empirical visual acuity data.
  
  
  RESULTS
  The model predicts that for changes equal in size to the magnitude of the change-criterion, sensitivity will be 50%. For changes 1.65 times the change-criterion, sensitivity is 90% and increasing to 95% for changes 1.84 times the size of the change-criterion. Predicted sensitivities agreed well with those measured empirically.
  
  
  CONCLUSIONS
  The 95% range for TRV is often used to decide whether measured changes are indicative of clinically important changes. Evaluating the performance of visual acuity charts using a method analogous to that of estimating the sensitivity and specificity of a screening test highlights some limitations of this method. Use of the 95% range as a change-criterion ensures a high specificity, but a simple statistical model indicates that changes must approach twice the size of the change-criterion before they will be detected with sensitivity in excess of 95%. This has implications for the clinician attempting to assess the reliability of visual acuity charts, and in other similar tests, to detect change.
authors.affiliation: London School of Hygiene and Tropical Medicine, London, United Kingdom.
authors.forename: Simon N
authors.initials: SN
authors.lastname: Cousens
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Rosser
authors.forename: Ian E
authors.initials: IE
authors.lastname: Murdoch
authors.forename: David A
authors.initials: DA
authors.lastname: Laidlaw
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D011237:Predictive Value of Tests; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014787:Vision Tests / Q000592:standards*; D014792:Visual Acuity