Tests are crucial for controlling the covid-19 pandemic. Test result interpretation is also important. For example, a test could be negative, but covid-19 might still be present.

After getting a negative rapid test a few months ago, I tried to use Bayes rule, which is the standard approach, to calculate post-test probability.

This was not easy. I recorded my efforts here, and I have tried to collect my most updated thoughts here.

Difficulties included specifying my pretest probability, getting appropriate estimates for the test operating characteristics, and understanding my estimate in light of other available information, such as exposure and symptom status.

Based on my reading of Moons and Harrell, 2003 and the BBR diagnosis chapter, I believe there is a trap: your pretest probability cannot depend on variables that are different from those collected in the study that evaluated the test.

For variables x, this can be seen by examining

This trap is particularly problematic when certain variables, such as symptom status or exposure, make it more likely that you have the disease at baseline.

Overall, I found this to be a hard problem, based both on inherent difficulties and also on the indirect way in which I had to go about it.

There may be ways to make the entire process more direct, shifting the burden of test interpretation from the person taking the test to analysts trained in statistics who have appropriate tools and databases.

For example, as mentioned in the references above, it might be best to maintain databases that could be used to fit models for post-test probability that are specific to location and time, as well as other important covariates.

In this case, we would just need to go to a website and enter some information to get a test interpretation.