If you’ve been reading/watching/listening to the news this past week you almost certainly heard about the COVID-19 Epidemic projections from the University of Washington. It’s a slick looking web application that provides hospital administrators and goverments with exactly what they need to know right now: what is the peak demand on healthcare, and when will it happen?
What you might not have done is dig deeply into the preprint on MedRxiv where the model is described. And, to save you the trouble I’m going to tell you what I think about it, and make a prediction about their predictions.
What I like
The model uses the reported deaths rather than cases to get localized information about the speed and trajectory of the epidemic at a state level. This is good, because the number of cases is biased low by testing issues, but society is pretty good at counting deaths. At least as long as the system isn’t overwhelmed. We also have a pretty good idea from places like Wuhan about what proportion of people that need hospital care end up dying. Again, this number underestimates the number of people who are sick, but for this application we only care about the number of people that end up in the hospital. So that’s a good idea.
They provide “uncertainty intervals”. This is good. I wish they were a bit clearer about exactly what those intervals are – or maybe that’s a bit too complicated. The underlying statistical model is Bayesian, so credible intervals, but then they get the number of hospitalizations using a “microsimulation” AKA agent based model AKA individual based model. So who knows what to call the bastardization of a credible interval with a stochastic simulation. Uncertainty interval I guess.
What I wish for
Open source code and data? Some testing of projections by using old forecasts to compare with new data?
Why I’m worried about these projections
I think they are optimistic. There are two reasons for this, one technical and one based on their assumptions about how Americans will act. They assume that Americans will behave like Chinese in response to various government interventions, and that serious travel bans are unnecessary. They also assume that any steps not already taken will be taken within a week, and last through the end of May. I don’t really have a problem with that last assumption, making forecasts requires making assumptions about future behavior of decision makers. But it would be handy if we could turn off those things at different points and see how it affects the model. I know that’s much harder than giving a set of fixed outputs.
Now for the technical reason. The underlying model of the cumulative number of deaths is a cumulative normal distribution, which gives the familiar sigmoid function that rises exponentially, hits an inflection point halfway, and then decelerates to an asymptote. I tried fitting some similar models last week, and in most cases the model underpredicted the continuing number of cases because the asymptote flattened off too quickly. I believe this will be the case for any model with these symmetric curves that is fit to data before the inflection point is reached. Although the number of active cases is starting to level off in the USA and Canada, the number of deaths is lagging behind that. So in many states the cumulative death rate has not reached the inflection point.
I predict that as the IHME group updates the model each day, the day of peak demand will be later, and the size of the demand higher, than the projection from the day before. This will continue until the increase in the number of deaths starts decelerating – when the inflection point is reached. Sticking my neck out again – I hope I’m wrong.