A New Approach for Extreme Proportion Calculation: Median Estimate and Its Application to Evaluate Performance of HIV Assays With 100% Test Sensitivity or Specificity

Abstract BackgroundIn the evaluation of performance of HIV assays, extreme sample proportions often occur, with test sensitivity and/or specificity of 100%, which making it challenging to assess the assays accuracies. To overcome these challenges, we propose using median estimate as an evaluation indicator for such testing.MethodsBased on the principles of binomial distribution and confidence interval, median estimate was defined as \(p={0.5}^{\frac{1}{n}}\), which means that, when the sample size n is equal to the event number x, namely the sample proportion (e.g., test sensitivity) is 100%, the 50th percentile (median) of p (the estimate of population proportion) is \({0.5}^{\frac{1}{n}}\). After demonstrating the mathematical proof of the median estimate, the key programming commands of commercial software SAS and free software R were given. Subsequently, we developed an Excel-based calculation tool that allows users to fill in data in an Excel sheet without writing any program. Six cases of HIV screening and diagnostic tests and HIV infections incidence data were selected from related articles and World Health Organization reports published between 2009 and 2020.ResultsThe median estimates, which were proved in the range from \(\frac{n-1}{n}\) to 1 and within the confidence interval range, showed statistical plausibility. Six HIV testing cases were presented to illustrate its application and elaborate on the relationship between the median estimate and the conventional simple estimate. These cases demonstrate that, when extreme proportions occurred (i.e., false positive and/or false negative in testing were zero), the conventional simple estimates of sensitivity, specificity, positive predictive value, and negative predictive value were 100% regardless of the sample size and prevalence. In contrast, the corresponding median estimates varied depending on the sample size and prevalence.ConclusionsAs evaluation indicators of HIV assays with extreme proportions, median estimates were more effective than conventional simple estimates. However, simple estimates objectively expressed the results of HIV testing. Because the correlation between median estimates and simple estimates was seamless, the two types of indicators were complementary in the evaluation of testing with extreme proportions. Hence, using both types of estimates could help evaluate HIV assays with extreme proportions more comprehensively.