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////$$SUPPORTING INFORMATION
Construction of Empirical 95% Confidence Intervals
Simulations were used to construct empirical 95% confidence intervals for the prevalence of diagnosed HIV-infection and for the percentage of HIV that is undiagnosed. The step-by-step process was performed as follows:
Pairs of samples were drawn at random. Sample 1 was used to estimate the prevalence of undiagnosed HIV. For sample 1, we assumed a binomial distribution and used the estimated prevalence of undiagnosed HIV to generate the number of undiagnosed HIV cases and the corresponding sample size of the USHER Trial. For example, when estimating for the entire population, the sample size was 4,056 and when estimating for those ages 18-44, the sample size was 2,954.
Sample 2 was used to estimate the prevalence of diagnosed HIV. Again, we assumed a binomial distribution and used the estimated prevalence of diagnosed HIV. When comparing to persons demographically similar to those presenting to the BWH ED, we used the sample size from the BWH ED. When comparing to persons demographically similar to those tested in the USHER Trial, we used the sample size from the USHER Trial.
The simulation was run 1,000 times and 1,000 estimates of the prevalence of undiagnosed and diagnosed HIV were calculated.
The empirical 95% confidence interval for the prevalence of diagnosed HIV was derived as the 2.5th percentile (lower bound) and the 97.5th percentile (upper bound) of the distribution of the 1,000 estimates obtained from the simulation ADDIN EN.CITE Efron198634343417Efron, B.Tibshirani, R.Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical AccuracyStatistical ScienceStatistical Science54-75111986Institute of Mathematical Statistics08834237http://www.jstor.org/stable/2245500[25].
Using the estimates obtained in step 3, we also calculated 1,000 estimates of the proportion of HIV that is undiagnosed.
Similar to step four, the empirical 95% confidence interval for the proportion of HIV that was diagnosed was derived as the 2.5th percentile (lower bound) and the 97.5th percentile (upper bound) of the distribution of the 1,000 estimates obtained from the simulation ADDIN EN.CITE Efron198634343417Efron, B.Tibshirani, R.Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical AccuracyStatistical ScienceStatistical Science54-75111986Institute of Mathematical Statistics08834237http://www.jstor.org/stable/2245500[25].
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