What is the difference between "positives" and "test-adjusted positives"? Why don't the lines match up when I "show cases"?
Our model attempts to correct for testing volume. The dotted black line shows actual new cases reported, the blue line shows what the model believes actual cases would have been if you correct for testing volume. If today you tested 100 people and 10 came back positive and tomorrow you tested 500 people, you might assume you'd get 5x the number of positives back (all things being equal).
For instance, California shows a marked increase in cases over most of June, but the blue test-adjusted curve doesn't react nearly as much. This is because testing volume has ramped significantly in California in the same time period. If there are more tests, there will be more positives. The model works off the blue test-adjusted curve rather than the black dotted curve. Doing so ensures that we're looking at the 'true' trend in cases. That being said, tests are not a random sample of the population and therefore it's possible (and likely) that the selection of this group changes over time to include many more people who are not symptomatic and who are simply getting a test as a precaution. This means that if anything, the blue curve may be understating the true infections going forward. Please keep this in mind when drawing conclusions.
How does the new model work?
In the simplest terms, it searches for the most likely curve of Rt that produced the new cases per day that we observe. It does this through some neat (and powerful!) math that is beyond the scope of this FAQ. In more complex terms: we assume a seed number of people and a curve of Rt over the history of the pandemic, we then distribute those cases into the future using a known delay distribution between infection and positive report. We then scale and add noise based on known testing volumes via a negative binomial with an exposure parameter for a given day to recover an observed series. We plan on publishing our code soon, so if you’re so inclined you’ll be able to run it, too.
Why do you use positive tests instead of hospitalizations or deaths to inform your model? Aren't the latter two far more reliable?
In general, hospitalizations and deaths are more reliable than tests to see the true Rt curve. However, they are also both time-shifted fairly dramatically from the time of infection. As of this time we have not included them in our model, but we are considering ways to reliably and accurately include them to ensure the model is as accurate as possible.