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Lies, Damned Lies, and Statistics

Exponential Model Can't Show the Effect of a Stay-at-Home Order

The stay-at-home order study falls short in terms of comparisons and prediction models.

A research letter in JAMA — one of the top medical journals — claims that stay-at-home orders are associated with lower hospitalizations. The study is based on data from four states (CO, MN, OH, and VA). For each state, the authors figured out a simple exponential model that would fit the first two weeks or so of data and then projected that exponential curve forwards in time. Here’s their graph for Ohio, for example:

They then point out that actual hospitalizations after the stay-at-home orders “deviated from projected best-bit exponential growth rates.” This conclusion is nearly worthless. For one thing, the authors did not provide data from any comparison states that lacked a stay-at-home order. Worse, there is no reason to think that simple exponential curves are a good prediction of where COVID hospitalizations would have ended up.

Their model for Ohio, for example, predicts that the number of hospitalizations on a given day should be 18.8482 times e to the power of 0.2268 times the number of days since time zero. That model predicts that by May 14, 2020, the entire population of Ohio would be in the hospital, and that by May 29, 2020, there would be 292 million people in the hospital in Ohio. That prediction is obviously absurd. We simply can’t know the effect of a stay-at-home order by comparing it to a wildly unrealistic exponential model.