Background

In 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.

Methods

Based 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.

Results

The 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.

Conclusions

As 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.

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This is a list of supplementary files associated with this preprint. Click to download.

- AdditionalFile1.docx
Additional file 1: Proof of Formulae (1) and (2) Formulae (1) and (2) were proved based on the principle of binomial distribution and interval estimation.

- AdditionalFile2ExcelcalculatingtoolSuppInfo.xls.xls
Additional file 2: Excel calculating tool The Excel calculation tool was developed to evaluate the performance of the diagnostic test when the sensitivity and/or specificity are 100%. By inputting the raw data, the results of Tables 2, 3, and 4 were obtained. The calculation process is straightforward using an Excel sheet, and hence no specialised statistical software or programming knowledge is required.

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Posted 25 Mar, 2021

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Posted 25 Mar, 2021

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Background

In 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.

Methods

Based 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.

Results

The 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.

Conclusions

As 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.

This preprint is available for download as a PDF.

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