"It is really confusing to apply one of the init..."

A study of Chinese blood donors 2 found that roughly 1 in 100,000 of them had HIV \(as determined by a very reliable gold\-standard test\)\. The non\-gold\-standard test used for initial screening had a sensitivity of 99\.7% and a specificity of 99\.8%, meaning respectively that $\\mathbb P({positive}\\mid {HIV}) \= .997$ and $\\mathbb P({negative}\\mid \\neg {HIV}) \= .998$, i\.e\., $\\mathbb P({positive} \\mid \\neg {HIV}) \= .002.$

It is really confusing to apply one of the initial steps of a study as evidence to a prior which is the result (last step) of the same study.