Probabilistic Factors Involved in Disease and Virus Testing

[PeroK]

Introduction
This Insight looks at the various probabilistic factors and related terminology involved in disease and virus testing.
As we all know, tests are rarely 100% reliable.  The frequency of false positives and false negatives, however, not only depend on the tests themselves, but also on the prevalence of the disease or virus within the population.  To see this, imagine the two extremes where a) no one has the virus, and b) everyone has the virus.  In the first case, all positives must be false.  And, in the second, all negatives must be false.
This provides the motivation for doing a proper analysis of the probabilities involved to see more precisely what can be concluded from a test result given all the available data.
Note that this insight provides a simple probabilistic analysis.  In many practical cases, some or all of the data is unknown, which leads to the more advanced techniques of hypothesis testing.
We assume throughout that we have a single test for a virus...

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[Greg Bernhardt]

Very interesting, who knew testing was so complex!

 

[Orodruin]

Nice writeup!
I think a couple of graphs would be useful though, like the PPV/NPV as a function of prevalence for a couple of values of p/q, to really drive the message home.