Tag Archives: Co-morbidity

Coronavirus: Framing the Next Few Weeks #3

05 Sunday Apr 2020

Posted by in Pandemic, Risk Management

≈ 1 Comment

Tags

, , , , , , , , , , , , , , , , ,

There were a few encouraging signs of change over the past few days in the course of the coronavirus pandemic in the U.S. This is the third of my quaint efforts to provide perspective on the coronavirus pandemic with “tracking” or “framing” posts. The first two were: Coronavirus: Framing the Next Few Weeks, on March 22, and Framing Update on March 28. In both of those posts, I charted confirmed cases of Covid-19 in the U.S. along with optimistic and pessimistic scenarios. I speculated that over the course of a few weeks, social distancing would lead to a reduction in the daily number of new confirmed cases. Unfortunately, it’s not clear whether that curve has started to “bend” rightward, but new confirmed cases on Sunday, April 5 — the number of those testing positive — was down almost 30% from Saturday.

An updated version of the earlier chart appears below, accompanied by a table. The number of confirmed cases (red line) has mounted over the past week, as has the daily increase in confirmed cases, though yesterday’s number was better. The table below the chart shows that the growth rate of confirmed cases (the far right-hand column) has decelerated, but it had leveled off at about 14% over the few days before Sunday. If Sunday’s drop persists it would be encouraging. Unfortunately, even moderate growth rates are destructive when the base of confirmed cases is large. The faster the growth rate declines, the faster the curve will bend.

I did not make any changes to the original “Very Good” and “Pretty Bad” scenarios, deciding that it was better to keep them as a consistent benchmark. As of Sunday, the top of the “Very Good” curve would still be about 2.3x the North Korean experience as of Sunday night, normalized for population. The top of the “Pretty Bad” scenario (which is not visible in this “zoomed-in” version) would be about 1.4x the Italian experience thus far. South Korea’s curve flattened substantially several weeks ago, and now even Italy’s curve is showing a rightward bend. Let’s hope that continues.

The case count obviously depends on the volume of daily testing, which has been increasing rapidly. As I’ve noted before, there has been a backlog of test requests. In addition, every day there is an overhang of “pending” test results. Interestingly, the number of tests stabilized on Saturday and the number of pending test results plunged (see the next chart, which uses data from the Covid Tracking Project). We’ll see if those developments persist. It would represent a milestone because daily case counts will advance as long as tests do, and the effort to work through the backlog has been inflating the speed of the advance in confirmed cases.

Another interesting development coincident with the drop in pending tests has to do with the cumulative percentage of positive test results: it has stabilized after growing for several weeks. This might mean we’ve reached a point at which the most severe incoming cases are fewer, but we’ll have to see if the flattening persists or even declines, which would be wonderful.

I’ve been grappling with potential weaknesses of the data on confirmed cases: first, the U.S. got a late start on testing, so there was the backlog of patients requiring tests just discussed above. That was presumed to have exaggerated the acceleration in the daily totals for new cases. Second, it’s possible that a continuing transition to more rapid test results would exaggerate the daily counts of new cases. Third, It’s possible that testing criteria are being relaxed, which, despite reducing the positive test rate, would increase growth in the “official” confirmed case count. Suspected cases should be tested, of course, but the change in standards is another factor that distorts the shape of the curve.

Any published statistic has its shortcomings. All test results are subject to false positives and negatives. Hospitalizations of patients with a positive coronavirus diagnosis are subject to the measurement issues as well, though they might be driven more by the severity of symptoms and co-morbidities than a positive Covid diagnosis per se. And hospitalizations of Covid patients might be subject to inconsistencies in reporting, and so might ICU admittances. Coronavirus deaths are subject to vagaries: reporting a cause of death is dictated by various criteria when co-morbidities are involved, and those criteria differ from country to country, or perhaps even hospital to hospital and doctor to doctor! In fact, some go so far as to say that all deaths should be tracked for coronavirus plus its co-morbidities and then compared to an average of the past five to ten years to obtain an estimate of “excess deaths”, which could conceivably be negative or positive. Finally, recoveries are even more impacted by inconsistent reporting, especially because many recoveries occur at home.

I’ll be highlighting coronavirus deaths going forward, and I’ll continue to focus mainly on the U.S. and only lightly on other countries. After all, death is obviously the most negative outcome. Again, however, the count of coronavirus deaths does not account for deaths that would have occurred over the same time frame due to co-morbidities or the effect of deaths that would not have occurred absent co-morbidities.

The predictions in the chart below are from the Chris Murray Model, upon which the White House Coronavirus Task Force has focused more recently. This model was developed by Dr. Christopher Murray at the Institute for Health Metrics and Evaluation at the University of Washington. I’ll be using the forecast starting from April 2 as the basis for my “framing” of actual deaths over the next few weeks, keeping it “frozen” at that level as a new benchmark. My apologies for the absence of dates on the horizontal axis, but the origin is at March 14 and there is only a single line up through April 1. That line represents actual cumulative Covid deaths recorded in the U.S. The red line is the mean model prediction. Deaths are expected to ramp up over the next week or so, much as we’ve seen in the confirmed case count, as deaths lag behind diagnoses by anywhere from a few days up to 17 days. This model predicts an ultimate death toll of about 94,000 at the top of the mean curve (not visible on the zoomed-in chart). Above and below that line are upper (blue) and lower (green) bounds, respectively, of a “confidence interval”. It’s unlikely we’ll see cumulative deaths breach either of those bounds. The lower bound would place the ultimate death toll at about 40,000; the upper bound would place it at just under 180,000. At this point, as of Sunday, April 5, actual deaths (black) are slightly below the mean or central tendency, but that’s difficult to see in the current chart.

The ongoing lockdowns in the U.S. and around the world are exceedingly controversial. There is a very real tradeoff between the benefits of extending the length of these lockdowns and the benefits of allowing economic activity to “restart”. But do lockdowns work? Christopher Monkton offers aggregate evidence that they truly do reduce the spread of the virus in “Are Lockdowns Working?” That they would work is intuitive, and decisions to scale them back should be made cautiously for certain “high exposure” activities, and in conjunction with isolating and trace-tracking contacts of all infected individuals, as they have done successfully in countries such as Taiwan and Singapore.

There may be signs that a bend in the U.S. case curve is in the offing, perhaps over the next week or two. That timing would roughly comport with the notion that over the past three weeks, efforts at social distancing and stay-at-home orders have allowed the U.S. to limit the spread of coronavirus through the first major “round” of infections and a much more limited second round. Perhaps these efforts will largely stanch a third and subsequent rounds of infection. Ultimately, if the number of coronavirus deaths is in the neighborhood of the mean value predicted by the Murray Model, about 94,000, that would place the severity of the toll at less than two times the severity of a bad flu season, though limiting the Covid death toll will have been achieved at much higher economic cost.

There are signs elsewhere around the globe that the pandemic may be turning a corner toward more favorable trends. See “Good News About COVID-19” at 80,000hours.org for a good review.

Coronavirus: Framing the Next Few Weeks

19 Thursday Mar 2020

Posted by in Pandemic

≈ 4 Comments

Tags

, , , , , , , , , , , , , , , , , ,

See my March 28 update here.

What follows is an exercise intended to put the coronavirus in perspective as we move through a crucial phase in the U.S. I believe it’s more informative than speculative. However, I’m relying on several pieces of information in establishing bounds on how the caseload and mortality rate will play out over the next few months: the experience abroad; domestic developments thus far; risk mitigation; prospective treatments; and some mathematics.

Pandemic Progressions

Despite all the warnings we’ve heard about exponential growth in the number of infections, that is something characterizing only the earliest stages of epidemics. These episodes invariably follow a growth curve that accelerates for a time before tapering. The total number of individuals infected eventually flattens, like the top of the dashed red line in the chart below. Think of the blue line’s height as showing the number of new positive diagnoses each day. New cases (blue) peak as the slope of the red line, total positive diagnoses, begins to decrease. The blue line is the one we’d like to flatten. That’s because once the number of new cases exceeds a certain threshold, medical resources can no longer handle the load. Nevertheless, I’ll focus on the red line and how it’s growth accelerates and then decelerates. Where are various countries on that curve? 

I’ve been using the interactive tool at the Insights and Outliers web site to view curves like the red line above, by country. China and South Korea are at the top, where the line is flat, though I discount the Chinese numbers as quite likely manipulated. Italy is somewhere in the middle of the red curve — one hopes it will enter the deceleration phase soon, but it’s not clear from the numbers.

Setting Context

The U.S. caseload is accelerating; it will continue to accelerate until the availability of tests catches up with demand from individuals meeting the qualifications for testing. The delay in the availability of tests, which I mentioned in an earlier post, will exaggerate the acceleration in the number of diagnosed cases for another week, or perhaps a bit more. Some of those cases already existed, and we should have known about them before now. However, after starting high, the U.S. death rate from the virus is already well below the global death rate, suggesting that either 1) our testing is actually well ahead of the rest of the world; 2) our Covid-19 mortality is, and will be, lower than the rest of the world; or 3) deaths in the U.S. will increase much faster than new diagnoses over the next few weeks. I seriously doubt the latter given the high quality of U.S. health care, the time of year, and the promising treatments that have recently been approved for use.

I expect the daily number of new cases in the U.S. to fall after the “catch-up” in testing. That’s based on a combination of things: first, the time from infection to first symptoms can be up to about 14 days, but the mean is just five days. Second, in the U.S., we began to practice “social distancing” and “self-quarantine” in earnest just this past week. Among those infected before this week, those who develop symptoms serious enough to notice will know before the end of March. But people are still out trying to take care of business. Some of those people will catch the virus, and there will be secondary infections of family members or others in close proximity to individuals diagnosed earlier. It will take an additional week, accounting for overlap, for infections among that cohort to mature. Nevertheless, over the next three weeks, the number of infections transmitted to new “hosts” will fall drastically with social distancing, as each of us comes into contact with fewer people. 

Third, the transmissibility of the virus will decrease with rising temperatures, more direct sunlight, and higher absolute humidity. See my post on the topic here. I know, I know, skeptics wag their fingers and say, “Covid-19 is not the same as the flu virus”, and they’re right! It has some similarities, however: a so-called “envelope” lipid membrane, transmissability via fine aerosols or larger droplets expelled into the air by infected individuals, and symptoms that are similar, except for shortness of breath with Covid-19. And like the flu, the new virus seems to be more virulent in cold, dry environments. If you cannot avoid contact with other individuals during your workday, if you have a large family at home, or if you live in quarters with a number of other individuals, it might be a good idea to keep your humidifier on or don’t air-condition aggressively. That’s an implication of this study and this study:

“The current spread suggests a degree of climate determination with Coronavirus displaying preference for cool and dry conditions. The predecessor SARS-CoV was linked to similar climate conditions.”

Bounding Expectations

How high will the numbers go? I’ll start by establishing some “very good” and “very bad” scenarios for total confirmed cases. South Korea (where masks were used widely) has had an excellent experience thus far. The county’s cumulative confirmed cases flattened out at less than 0.017% (0.00017) of the total population. Assuming that 90% of cases are asymptomatic and undiagnosed, that would mean 0.17% (0.0017) of the South Korean population has been infected. If the U.S. experience is the same, we’d have a total of about 60,000 confirmed infections when our curve flattens. But I won’t be that optimistic — we’re at about 25,000 cases already and I think we’ll be at 60,000 cases within a week. Instead, I’ll define the “very good” scenario as 2.5x the South Korean outcome, or 150,000 confirmed cases. 

For a “very bad” scenario one might look to Italy. Unfortunately, it’s impossible to say how much higher Italy’s case load will go before flattening. If it had flattened today (it didn’t), the rate of confirmed cases for the country would be 0.077% (0.00077). That yields 0.77% of the population including the undiagnosed at 90% of cases. Applying the same percentage to the U.S. would mean just over 250,000 confirmed cases. But again, for a really bad scenario, and because we don’t yet know how Italy’s experience will play out, let’s suppose Italy’s confirmed cases quadruple: For the U.S., using the same percentage of the population would imply just over 1 million confirmed cases, or about 1.6% of the population. That yields a total infected population of 10 million.  

I’ve illustrated these “very good” and “very bad” scenarios in the chart below as Gompertz curves, a form of sigmoid function or s-curve. First, a couple of caveats: Please note that this represents a “first wave” of the virus, as it were. I do not dismiss the possibility of a second wave should we relax our nonprescription safeguards prematurely, and obviously the chart does not speak to a return of the virus in the fall. Also, these are just two examples that allow us to examine the implications of extreme outcomes. I could have varied the timing, growth, and end-outcome in other ways, but I think the following is instructive.

The chart shows cumulative confirmed cases for each scenario. It also shows the actual confirmed case total through March 21st, which is the shorter red line at the bottom. The data plotted begins on March 6, when there were 248 cases confirmed. The horizontal axis shows days elapsed since then. The accompanying table shows the same information through March 28th, a week from today. 

There are a few things to note about the chart and table:

  1. The actual curve is still below the “very good” curve. If our experience proves to be marginally worse than the “very good” scenario, then we’ve already “caught-up” in terms of testing for Covid-19: the actual increase today is larger than the highest daily increases under that scenario. If our experience approaches the “very bad” scenario, then we are eight days behind in our testing. That is, today’s actual increase is about what that scenario would have predicted eight days ago.
  2. Under the “very good” scenario, the daily increase in cases would peak by Friday, March 27. We’ve already exceeded that level of daily increase, but it will be encouraging if the daily increase doesn’t accelerate much more over the next few days. Under the “very bad” scenario, and given a full “catch-up”, the daily increase would peak about a week from now at approximately 37,000. That would be delayed if the catch-up process is more protracted.
  3. New cases flatten out within a couple of months under both scenarios. Under the “very good” scenario, new cases fall below 1,000 per day by April 21. Under the “very bad’ scenario, they don’t reach that level until Mid-May.
  4. In the next week (by March 28th), we will know a lot more about where we’re trending relative to these scenarios. I plan to provide an update later in the week or next weekend. 

While it can’t be seen from the chart or the table, once the “catch-up” ends, if there really is a catch-up involved, the daily increase in cases might fall abruptly. That would be encouraging.

Other Thoughts

It’s also important to note that the experience within the U.S. might be as varied as what we see around the globe. For example, New York and Washington state seem to be hot spots. Cities with large international ports and flights are more likely to suffer relatively high infection rates. In contrast, St. Louis probably won’t have a comparable incidence of infection, as there are so few international flights terminating there. 

The global death rate from Covid-19 has been widely quoted as somewhere around 4%, but that came into question with the revelation of low mortality aboard the Diamond Princess, despite the many seniors aboard. And it appears that the death rate from coronavirus is declining in the U.S. This was noted here at Endless Metrics several days ago. It’s also discussed in some detail by Aaron Ginn in this excellent this Medium article. Again, the death rate will decline as our testing “catches-up”, if indeed it must, and it will decline with spring weather as well as treatments if they are effective. Ultimately, I’ll be surprised if it comes in at more than 1% of confirmed cases in the U.S., and I won’t be surprised if it’s much less. At 1% under the “very bad” scenario, the U.S. would have about 10,000 deaths associated with coronavirus, the large majority of which would be individuals older than 70 years of age with significant co-morbidities.  

Conclusion

I hope this exercise proves useful to others in establishing a framing for what will ensue over the next few weeks. However, even the “very bad” scenario discussed above involves an infected share of the population of much less than we’ve heard we’re in for. Yet that scenario is far worse than Italy’s experience thus far, which most people consider pretty bad. For this reason, I am increasingly convinced that this pandemic will not prove to be the widespread calamity we’re still being told to expect. Those warning us might be alarmists, or perhaps they simply lack a sufficient level of numeracy.

This post was partly inspired by The Math of Epidemics by Willis Eschenbach, as well as Scott Alexander’s March 2nd post at Slate Star Codex. Also, see the Medium article by Aaron Ginn. It is a thorough examination of many aspects of the pandemic and very much aligned with my views. (Something is wrong with the link … I’ll try to fix it later.)

 

 

at WUWT