Games with Models, April 16 Data


OK, let’s take a risk and have some fun.  Yesterday, I noted a few things about the COVID-19 model that the governor is using to make decisions:

  • She doesn’t show a best-case scenario.
  • She shows roughly four times as many hospitalizations right now than there actually are.
  • She doesn’t explain the assumptions that lead her to project a nine-times increase over the next few weeks.

As I keep insisting, American citizens aren’t children.  We’re adults who deserve a role in public decision-making based on honest facts presented by our government.  So, what should the governor be doing?

Well, all of her assumptions should be placed on the table, to the finest detail, even though most Rhode Islanders would have no interest in it.  No doubt, the state government is looking to good, smart people for its answers, but our state is full of good, smart people, and it is foolish to rely entirely on only a handful of them.

Then, if we’re going to have a public proclamation of the death count every day, it should also include a comparison with the projection and an explanation about how the new data affects the projections going forward.  This approach gives a great deal of perspective.  I’ve been running a very simple (actually, simplistic) model, which has pointed to much lower numbers than the government is predicting.  And just about every day, the actually numbers have come in lower than I would have predicted.  Meanwhile, a common refrain in my social media interactions has been that I ought to shut up and let the experts do what needs to be done without input from the public.

This brings to mind an episode of the EconTalk podcast released back in that other world, 2019.  Psychologist Gerd Gigerenzer explained the thinking behind his book, Gut Feelings, which suggests that simple heuristics (or rules of thumb) are often preferable to complex models.  Think about it.  Every detail in a complex model builds in new assumptions that might or might not be correct.

A rule of thumb gives a very broad range of possibilities based generally on experience, but builders of complex models will often ignore that experience if the math of their assumptions says something different.  Thus, we get decisions about our state’s entire economy and our children’s education based on a model that doesn’t accurately illustrate the experience of the past week, let alone the future.

So in the name of science, I’ll take the risk of laying out the model I’ve been playing with.  I’m not making any claims about being an expert, so don’t take this as a prediction.  It’s more like a hobbyist trying to see how close he can get to a working machine.  The appropriate (scientific) approach of those who disagree would be to point out what I might be missing and to show how that would change the results.  As a hobbyist, I’d love to improve my understanding and my ability to improve my own projections.

Here’s how it’s built.  Regarding total cases:

  • I’ve taken the actual cases of COVID-19 as reported by the state government. (This should make my projections too high, at the moment, because we had an increase in testing during that time inflating the trend.)
  • To project the future trends, I multiply today’s results by the average daily increase of the past week, which I adjust for (i.e., multiply by) the change in the 14-day infection rate for the past week versus the week before.

Another bit of data the governor hasn’t provided is some estimate of “active” cases.  At what point should we stop counting people as “infected” and start thinking that they are healthy and (probably) immune? For my model:

  • I assume that a case is “active” for an average of 14 days. (Some people are sick for longer, but 14 days plus three days of being symptom free has generally been the guideline for returning to work.  This assumption might overstate the number of active cases because people probably aren’t generally tested until they’ve had symptoms for a day or two, and then it has taken some days to get results back.)
  • Thus, for each day, the “active” cases equal the total cases for that day minus the total cases two weeks prior.

As of the data released on April 16, the total cases numbered 3,838, and the active cases numbered 3,181.  By this simplistic trend, the peak for active cases will come next Tuesday, with 3,896 active cases.

To project future hospitalizations:

  • I calculate hospitalizations’ percentage of active cases each day.
  • Then I average that ratio for the past week and apply it to my projections of active cases going forward.
  • This method doesn’t work well for the down slope (because the average ratio of hospitalizations to active cases starts to go up even as the active cases goes down), so I halted the chart shortly after the peak.

The results for hospitalizations are shown in the following chart.  It predicts that the governor will announce 282 people in the hospital when she gives her statement this afternoon and that Rhode Island will hit its peak next Wednesday, with 321 people in the hospital dealing with COVID-19.


Now, this could be completely wrong, and if so, I look forward to trying to figure out what I missed.  Each day, I’ll post an updated chart that shows how reality and new projections relate to earlier charts.

One of the things I like about this approach is that it is entirely based on observed trends, so it points directly to the key question:  If the future is going to be different, what is going to change?  In that context, I’ll end with a list of what three models are projecting to happen between now and the peak of hospitalizations:

  • RI Dept. of Health: from 245 to 2,250 in 17 days.
  • IHME: from 245 to 942 in 16 days.
  • Me: from 245 to 321 in 6 days.

Let’s see what happens!

  • Mario

    I appreciate the exercise here. I’ve tried to do it for myself, but it’s really tough without knowing how long the cases will continue to grow. If we have already reached the peak in case growth, I’d put the number at 381 on the 27th. If it grows until next Tuesday, like you hypothesized, it’s 462 on the 29th. If the IHME model is right about the timing of the peak (probably the best available guess), I’d put the number at 515 or so, which is right in their range. Obviously, it just gets worse from there.

    • OceanStateCurrent

      So you think peak hospitalization lags peak cases by a week or more? Why is that? (And I assume by “peak case growth,” you mean active cases…)

      • Mario

        By case growth, I only mean the new day-over-day case increase. I thought it might have peaked back on the 11th with 334, but no such luck. I don’t bother trying to figure out how many active infections there are, like you said, it isn’t reported. The more I assume, the more bias I add. Just using new cases on its own trades on actual viral modeling in exchange for reliability. It’s mostly clean, and using a 3-day average fixes most of the weather/holiday/weekend issues. I hadn’t been trying to model case growth at all, only looking to see if I could predict the daily number of deaths, which I think I have a handle on except that they’ve been boosting the number with extras from past days.

        Having a lag between the new cases and hospitalizations wasn’t a conscious choice, I just found that that worked best. I do think it makes sense, from what I’ve seen people can suffer through an infection for days at home before the symptoms get bad enough to require hospitalization, (if they ever do). I think that may be partly why the numbers don’t seem to be as bad as they are saying, that the latest increase in cases hasn’t even translated into hospitalizations yet. If the current hospitalizations only reflect ~150 new cases per day rather than the current 300, the official models look a little better.

        I’m rooting for your numbers to be the right ones, though.

        • ShannonEntropy

          I don’t bother trying to figure out how many active infections there are, like you said, it isn’t reported

          The ProJo reports the numbers every day

          Yesterday the 17th, 366 new cases were recorded

          There are now 4,177 positive case; 118 deaths; 252 people hospitalized; 34,402 cases in Mass; 686,991 cases and 28,998 deaths in the US

          I donut really understand your math model, but plug these numbers into it and tell us what you get

          • Justin Katz

            The distinction is active infections. The numbers reported are for total cases, as if nobody ever gets better. I’m estimating that 711 people have been reported as having it but are now free and clear.

        • Justin Katz

          OK, I see. You did say “peak in case growth,” so you’re looking at rate of increase. I didn’t read closely enough. I’ve been tracking the daily rate of increase, and that has been continually down, with a periodic aberration. A peak in the absolute number of new cases is a more conservative approach and a harder threshold to hit, but more reasonably cautious for that.

          For the record, my spreadsheet is suggesting today’s increases will be 298 new cases, 289 hospitalizations (total, so increase of 37), and 8 new deaths.

  • ritaxednorep

    Using hospitalizations isn’t a good predictor. Hospitalizations come later in the game. The CDC has been collecting data on total patient visits for years, it’s the metric to use because it has a history. Nationwide and in Rhode Island, it’s been dropping like a rock for weeks.
    Here’s a link: Look at the chart for ILINET.

    If you click to the Rhode Island link, the data there is two weeks old. The CDC get’s their data from a number of local “sentinels” that report directly to the CDC, so the CDC charts are as current as possible. For some reason, the state’s Dept. of Health is not publishing current data. Gina is our only source of data? That’s suspicious to me.

    If you look below that you’ll see that the CDC has us listed in the 24 states catagorized with “minimal” spread. You don’t need to do a lot of modeling yourself, the CDC has already done in and is reporting positive news for Rhode Island.

    We need to get onto step one asap. Gina needs to stop dawdling and get the lead out.

    • Justin Katz

      The difficulty I’ve been having with the CDC data is that I can’t tell where they’ve attempted to back COVID-19 numbers out of the flu numbers.

      • ritaxednorep

        Justin, you don’t have to. Dr. Birx used those same charts the other day in the press briefing. If she’s using those, that’s what the feds are using. The CDC is tracking over 225 different viruses and Covid is only one of them. What that shows is that the Flu season is over and the hospital beds needed for that are now available, if needed. The latest data on the Rhode Island Dept of Health web site even though two weeks old shows things moving in a very positive direction.

    • ritaxednorep

      I put in the proper link to the CDC web page. I had yours in before as a mistake. It’s now correct .