A simple model to predict the sensitivity to change of visual acuity measurements.

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.