2

Like many, I've been watching and tinkering with COVID-19 statistics for the past 8+ months. One thought I keep coming back to is that there must be some smart Bayesian approach to blending (a) known infection rate (positive tests / population) and (b) positivity rate (positive tests / total tests) to estimate true infection rate.

Here in the US, there are massive disparities between states/regions on levels of testing - and our Liar in Chief often blames rising case rates on "more testing", which is very dubious.

I'm not highly practiced with Bayesian methods but seems like knowing (a) known infection rate, (b) positivity rate, plus (c) true positive rate and false negative rate of tests in use, and (d) likelihood of an infected person deciding to get tested should be enough to arrive at a true infection rate for a population.

Early in the pandemic, public health officials talked about a 2x or 5x or 10x multiplier between known infections and likely actual infections, but this would vary wildly based on testing rates.

This seems like it'd be both insightful and a good example of the power of Bayesian thinking. Anyone care to help formulating the problem?

For sake of example, let's take State1 and State2 with these assumptions

                             State1     State2
Known Infection Rate            0.1%    0.5%
Positivity Rate                  20%    5%
True Positive Rate               80%    80%
False Positive Rate               0%    0%
Prob of infected person testing  50%    80%
Chad Gray
  • 21
  • 2
  • 1
    I see no reason to suppose that the positivity rate supplies reliable information about infection rates. The confounding effect of the rate at which tests are given (your item (d)), which seems almost impossible to estimate in light of the absence of any uniform rules, criteria, or procedures for testing, is going to dominate the uncertainty in the result. – whuber Oct 28 '20 at 17:44

0 Answers0