# Two Source Capture Recapture

We will use the study Population Size, HIV, and Behavior Among MSM in Luanda, Angola: Challenges and Findings in the First Ever HIV and Syphilis Biological and Behavioral Survey, where they reported the results of a two source capture recapture with unique objects. They reported $n_1=792$ people were given the unique object, $n_2=353$ participated in the second capture, with $n_{12}=45$ recaptures.

Plugging these number into the confidence interval calculator results in an interval of $(4566.095,7859.505)$.

# Proportion Confidence Interval Example

We will start with the study High levels of used syringe use and unsafe sex among people who inject drugs in Kumasi, Ghana: an urgent call for a comprehensive harm reduction approach, which reports a 3% HIV prevalence rate with a sample size of 211. We will use a design effect of 1.5, and so $n=211/1.5=141$. This leads to a positive count of

\[n_+ = .03 * 141 = 4\]Plugging $n_+=4$ and $n=141$ this into the calculator results in a Clopper-Pearson interval of $(0.0078, 0.0710)$.