Tag Archives: Pandemic

Case Fatality, Stale Ratios and Exaggerated Loss

14 Tuesday Jul 2020

Posted by in Analytics, Pandemic

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I hope someday I won’t feel compelled to write or worry about the coronavirus. However, as the pandemic wears on, it seems to take only a few days for issues to pile up, and I just can’t resist comment. Today I have a couple of beefs with uses of data and concomitant statements I’ve seen posted of late.

People are still quoting case fatality rates (CFRs) as if those cumulative numbers are relevant to the number of deaths we can expect going forward. They are not. Just as hair-brained are applications of cumulative hospitalization and ICU admittance rates to produce “rough and ready” estimates of what to expect going forward. Or, I’ve seen people express hospitalizations as ratios to CFR, as if those ratios will be the same going forward. Again, they are not. Let me try to explain.

The chart below shows the course of the U.S. CFR since the start of the pandemic. It’s taken from the interactive Covid Time Series site. My apologies if you have to click on the chart for decent viewing (or you can visit the site). The CFR at any date is the cumulative number of deaths to-date divided by the cumulative number of confirmed cases. It is a summary of past history, but it is not well-suited to making predictions about death rates in the future. The CFR began to taper a little before Memorial Day, and it is now at about 4% (as of July 13).

Out of curiosity, I also generated CFRs for AZ, CA, FL, GA, and TX, which now average about half of the national CFR. There’s an obvious lesson: if you must use CFRs, understand that they vary from place to place.

Again, CFRs are cumulative. Their changes over time can tell us something about recent trends, but even then they are flawed. For example, case counts have risen dramatically with more widespread testing. Those testing positive more recently are concentrated in younger age cohorts, for whom infections are much less severe. Treatment has improved dramatically as well, so there is little reason to expect the CFR’s of recently diagnosed cases to be as high as the latest CFRs shown above.

There is no easy way to calculate an unflawed “marginal” CFR for a recent period, though an effort to do so might improve the predictive value. Deaths lag behind case counts because the progression from early symptoms to death can take several weeks. Even more vexing for constructing a valid, recent fatality rate is that reporting of deaths is itself delayed, as I explained in my last post. Each day’s report of deaths captures deaths that may have occurred over a period of several weeks in the past, and sometimes many more.

Finally no CFR can capture the true mortality rate of the virus without ongoing, ubiquitous testing. As the state of testing stands, the true mortality rate must reflect undiagnosed cases in the denominator. The CDC’s latest “best” estimate of the true mortality rate is just 0.3%, and 0.05% for those aged 50 years or less. Those figures are based on serological tests for the presence of antibodies to C19 in more random samples of the population. Those findings reflect the extent of undiagnosed and/or asymptomatic cases.

The point is one shouldn’t be too blithe about throwing numbers around like 4% mortality based on the CFR, or even 1% mortality as a “nice, round number”, without heavy qualification. Those numbers are gross exaggerations of what we are likely to see going forward.

The same criticisms can be leveled at claims that hospitalizations will proceed at some fixed ratio relative to diagnosed cases, or some fixed ratio relative to deaths. Again, new cases tend to be less severe, so hospitalizations are likely to be a much lower ratio to cases than what is reflected in cumulative totals. Because of improved treatment, the ratio of deaths to hospitalizations will be much lower in the future as well.

CFRs are not a useful guide to future COVID deaths. The true mortality rate is a much better baseline, particularly for subsets of the population matching the current case load. Finally, and this is the only disclaimer I’ll bother to provide today, we all know that suffering is not confined to terminal cases, and it is not confined to the hospitalized subset. But don’t exaggerate the extent of your preferred interpretation of suffering by applying inappropriate cumulative calculations.

 

Cases Climb, Most Patients Faring Better

30 Tuesday Jun 2020

Posted by in Pandemic, Public Health

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There’s been much speculation about whether recent increases in confirmed cases of COVID-19 (first chart above) will lead to a dramatic increase in fatalities (second chart). More generally, there is curiosity or perhaps hope as to whether the virus is not as dangerous to these new patients as it was early in the pandemic. I have discussed this point in several posts, most recently here. Based on the national data (above), we’re at the point at which an upturn in deaths might be expected. Based on the experience of many individual states, however, deaths should have trended upward by now, but they haven’t done so. Cases are generally less severe and are resolving more quickly.

Of course, more testing produces more cases (though there has been a mild uptick in test positivity over the past two weeks), but that doesn’t really explain the entire increase in cases over the past few weeks. In particular, why are so many new cases in the south? After all, there is evidence that the virus doesn’t survive well in warm, humid climates with more direct sunlight.

As I have mentioned several times, heavy use of air-conditioning in the south may have contributed to the increase. Nate Silver speculates that this is the case. The weather warmed up in late May and especially June, and many southerners retreated indoors where the air is cool, dry, and the virus thrives. Managers of public buildings should avoid blasting the AC, and you might do well to heed the same advice if you live with others in a busy household. In fact, nearly all transmission is likely occurring indoors, as has been the case throughout the pandemic. At the same time, however, with the early reopening of many southern states, younger people flocked to gyms, bars and other venues, largely abandoning any pretense of social distancing. So it’s possible that these effects have combined to produce the spike in new cases.

Some contend that the protests following George Floyd’s murder precipitated the jump in confirmed cases. Perhaps they played a role, but I’m somewhat skeptical. Yes, these could have become so-called super-spreader events; there are certain cities in which the jump in cases lagged the protests by a few weeks, such as Austin, Houston, and Miami, and where some cases were confirmed to be among those who protested. But if the protests contributed much to the jump, why hasn’t New York City seen a corresponding increase? Not only that, but the protests were outside, and the protests dissuaded many others from going out at all!

The trend in coronavirus fatalities remains more favorable, despite the increase in daily confirmed cases. One exception is New Jersey, which decided to reclassify 1,800 deaths as “probable” COVID deaths about six days ago. You can see the spike caused by that decision in the second chart above. Reclassifications like that arouse my suspicion, especially when federal hospital reimbursements are tied to COVID cases, and in view of this description from Bloomberg (my emphasis):

“… those whose negative test results were considered unreliable; who were linked to known outbreaks and showed symptoms; or whose death certificates strongly suggested a coronavirus link.”

Deaths necessarily lag new cases by anywhere from a few days to several weeks, depending on the stage at the time of diagnosis and delays in test results. The lag between diagnosis and death seems to center on about 12 – 14 days. Thus far, there doesn’t appear to be an upward shift in the trend of fatal cases, but the big updraft in cases nationally only started about two weeks ago. More on that below.

Importantly, a larger share of new cases is now among a younger age cohort, for whom the virus is much less threatening. The most vulnerable people are probably taking more precautions than early in the pandemic, and shocking as might seem, there is probably some buildup in immunity in the surviving nursing home population at this point. We are also better at treatment, and there is generally plenty of hospital capacity. And to the extent that the surge in new cases is concentrated in the south, fewer patients are likely to have Vitamin D deficiencies, which is increasingly mentioned as a contributor to the severity of coronavirus infections.

I decided to make some casual comparisons of new cases versus COVID deaths on a state-by-state basis, but I got a little carried away. Using the COVID Time Series web site, I started by checking some of the southern states with recent large increases in case counts. I ended up looking at 15 states in the south and west, and I added Missouri and Minnesota as well. I passed over a few others because their trends were basically flat. The 17 states all had upward trends in new cases over the past one to two months, or they had an increase in new cases more recently. However, only four of those states experienced any discernible increase in daily deaths over the corresponding time frames. These are Arizona, Arkansas, Tennessee, and Texas, and their increases are so modest they might be statistical noise.

Again, deaths tend to lag new cases by a couple of weeks, so the timing of the increase in case counts matters. Five of the states were trending upward beginning in May or even earlier, and 13 of the states saw an acceleration or a shift to an upward trend in new cases after Memorial Day, in late May or June. Of those 13, the changes in trend occurred between one and five weeks ago. Six states, including Texas, had a shift within the past two weeks. It’s probably too early to draw conclusions for those six states, but in general there is little to suggest that fatal cases will soar like they did early in the pandemic. Case fatality rates are likely to remain at much lower levels.

We’ll know much more within a week or two. It’s very encouraging that the upward trend in new cases hasn’t resulted in more deaths thus far, especially at the state level, as many states have had case counts drift upward for over a month. If it’s going to occur, it should be well underway within a week or so. Much also depends on whether new cases continue to climb in July, in which case we’ll be waiting in trepidation for whether more deaths transpire.

Suspending Medical Care In the Name of Public Health

23 Saturday May 2020

Posted by in Health Care, Pandemic

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Step back in time six months and ask any health care professional about the consequences of suspending delivery of most medical care for a period of months. Forget about the coronavirus for a moment and just think about that “hypothetical”. These experts would have answered, uniformly, that it would be cataclysmic: months of undiagnosed cardiac and stroke symptoms; no cancer screenings, putting patients months behind on the survival curve; deferred procedures of all kinds; run-of-the-mill infections gone untreated; palsy and other neurological symptoms anxiously discounted by victims at home; a hold on treatments for all sorts of other progressive diseases; and patients ordinarily requiring hospitalization sent home. And to start back up, new health problems must compete with all that deferred care. Do you dare tally the death and other worsened outcomes? Both are no doubt significant.

What you just read has been a reality for more than two months due to federal and state orders to halt non-emergency medical procedures in the U.S. The intent was to conserve hospital capacity for a potential rush of coronavirus patients and to prevent others from exposure to the virus. That might have made sense in hot spots like New York, but even there the provision of temporary capacity went almost completely unused. Otherwise, clearing hospitals of non-Covid patients, who could have been segregated, was largely unnecessary. The fears prompted by these orders impacted delivery of care in emergency facilities: people have assiduously avoided emergency room visits. Even most regular office visits were placed on hold. And as for the reboot, there are health care facilities that will not survive the financial blow, leaving communities without local sources of care.

A lack of access to health care is one source of human misery, but let’s ask our health care professional about another “hypothetical”: the public health consequences of an economic depression. She would no doubt predict that the stresses of joblessness and business ruin would be acute. It’s reasonable to think of mental health issues first. Indeed, in the past two months, suicide hotlines have seen calls spike by multiples of normal levels (also see here and here). But the stresses of economic disaster often manifest in failing physical health as well. Common associations include hypertension, heart disease, migraines, inflammatory responses, immune deficiency, and other kinds of organ failure.

The loss of economic output during a shutdown can never be recovered. Goods don’t magically reappear on the shelves by government mandate. Running the printing press in order to make government benefit payments cannot make us whole. The output loss will permanently reduce the standard of living, and it will reduce our future ability to deal with pandemics and other crises by eroding the resources available to invest in public health, safety, and disaster relief.

What would our representative health care professional say about the health effects of a mass quarantine, stretching over months? What are the odds that it might compound the effects of the suspension in care? Confinement and isolation add to stress. In an idle state of boredom and dejection, many are unmotivated and have difficulty getting enough exercise. There may be a tendency to eat and drink excessively. And misguided exhortations to “stay inside” certainly would never help anyone with a Vitamin D deficiency, which bears a striking association with the severity of coronavirus infections.

But to be fair, was all this worthwhile in the presence of the coronavirus pandemic? What did health care professionals and public health officials know at the outset, in early to mid-March? There was lots of alarming talk of exponential growth and virus doubling times. There were anecdotal stories of younger people felled by the virus. Health care professionals were no doubt influenced by the dire conditions under which colleagues who cared for virus victims were working.

Nevertheless, a great deal was known in early March about the truly vulnerable segments of the population, even if you discount Chinese reporting. Mortality rates in South Korea and Italy were heavily skewed toward the aged and those with other risk factors. One can reasonably argue that health care professionals and policy experts should have known even then how best to mitigate the risks of the virus. That would have involved targeting high-risk segments of the population for quarantine, and treatment for the larger population in-line with the lower risks it actually faced. Vulnerable groups require protection, but death rates from coronavirus across the full age distribution closely mimic mortality from other causes, as the chart at the top of this chart shows.

The current global death toll is still quite small relative to major pandemics of the past (Spanish Flu, 1918-19: ~45 million; Asian Flu, 1957-58: 1.1 million; Hong Kong flu, 1969: 1 million; Covid-19 as of May 22: 333,000). But by mid-March, people were distressed by one particular epidemiological model (Neil Ferguson’s Imperial College Model, subsequently exposed as slipshod), predicting 2.2 million deaths in the U.S. (We are not yet at 100,000 deaths). Most people were willing to accept temporary non-prescription measures to “slow the spread“. But unreasonable fear and alarm, eagerly promoted by the media, drove the extension of lockdowns across the U.S. by up to two extra months in some states, and perhaps beyond.

The public health and policy establishment did not properly weigh the health care and economic costs of extended lockdowns against the real risks of the coronavirus. I believe many health care workers were goaded into supporting ongoing lockdowns in the same way as the public. They had to know that the suspension of medical care was a dire cost to pay, but they fell in line when the “experts” insisted that extensions of the lockdowns were worthwhile. Some knew better, and much of the public has learned better.

Spanish Flu: No Guide for Covid Lockdowns

25 Saturday Apr 2020

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The coronavirus pandemic differs in a few important ways from the much deadlier Spanish flu pandemic of 1918-19. Estimates are that as much as 1/3rd of the world’s population was infected during that contagion, and the case fatality rate is estimated to have been 10-20%. The current pandemic, while very serious, will not approach that level of lethality.

Another important difference: the Spanish Flu was very deadly among young adults, whereas the Coronavirus is taking its greatest toll on the elderly and those with significant co-morbidities. Of course, the Spanish Flu infected a large number of soldiers and sailors, many returning from World War I in confined conditions aboard transport vessels. A major reason for its deadliness among young adults, however, is thought to be the “cytokine storm“, or severe inflammatory response, it induced in those with strong immune systems.

It’s difficult to make a perfect comparison between the pandemics, but the charts below roughly illustrate the contrast between the age distribution of case mortality for the Spanish Flu in 1918, shown in the first chart, and Covid-19 in the second. The first shows a measure of “excess mortality” for each age cohort as the vertical gap between the solid line (Spanish flu) and the dashed line (the average of the seven previous seasons for respiratory diseases). Excess mortality was especially high among those between the ages of 15 and 44.

The second chart is for South Korea, where the Covid-19 pandemic has “matured” and was reasonably well controlled. We don’t yet have a good measure of excess case mortality for Covid-19, but it’s clear that it is most deadly among the elderly population. Not to say that infected individuals in younger cohorts never suffer: they are a higher proportion of diagnosed cases, severe cases are of extended duration, and some of the infected might have to deal with lasting consequences.

One implication of these contrasting age distributions is that Covid-19 will inflict a loss of fewer “life years” per fatality. If the Spanish flu’s median victim was 25 years old, then perhaps about 49 life years were lost per fatality, based on life expectancies at that time. At today’s life expectancies, it might be more like 54 years. if Covid-19’s median victim is 70 years old, then perhaps 15 life-years are lost per fatality, or about 73% less. And that assumes the the median Covid victim is of average health, so the loss of life years is probably less. But what a grisly comparison! Any loss is tragic, but it is worth noting that the current pandemic will be far less severe in terms of fatalities, excess mortality (because the elderly always die at much higher rates), and in life-years lost.

Is that relevant to the policy discussion? It doesn’t mean we should throw all caution to the wind. Ideally, policy would save lives and conserve life-years. We’d always put children on the lifeboats first, after all! But in this case, younger cohorts are the least vulnerable.

The flu pandemic of 1918-19 is often held to support the logic of non-prescription public health measures such as school closures, bans on public gatherings, and quarantines. Does the difference in vulnerabilities noted above have any bearing on the “optimal” level of those measures in the present crisis? Some argue that while a so-called lockdown confers health benefits for a Spanish flu-type pandemic in which younger cohorts are highly vulnerable, that is not true of the coronavirus. The young are already on lifeboats having few leaks, as it were.

My view is that society should expend resources on protecting the most vulnerable, in this case the aged and those with significant co-morbidities. Health care workers and “first responders” should be on the list as well. If well-targeted and executed, a Covid-19 lockdown targeted at those groups can save lives, but it means supporting the aged and afflicted in a state of relative isolation, at least until effective treatments or a vaccine prove out. A lockdown might not change living conditions greatly for those confined to skilled care facilities, but much can be done to reduce exposure among those individuals, including a prohibition on staff working at multiple facilities.

Conversely, the benefits of a lockdown for younger cohorts at low risk of death are much less compelling for Covid-19 than might be suggested by the Spanish flu experience. In fact, it can be argued that a complete lockdown denies society of the lowest-hanging fruit of earlier herd immunity to Covid-19. Younger individuals who have more social and economic contacts can be exposed with relative safety, and thus self-immunized, as their true mortality rate (including undiagnosed cases in the denominator) is almost zero to begin with.

Then we have the economic costs of a lockdown. Idle producers are inherently costly due to lost output, but idle non-producers don’t impose that cost. For Covid-19, prohibiting the labor of healthy, working age adults has scant health benefits, and it carries the high economic costs of lost output. That cost is magnified by the mounting difficulty of bringing moribund activities back to life, many of which will be unsalvageable due to insolvency.

The lockdown question is not binary. There are ways to maintain at least modest levels of production in many industries while observing guidelines on safety and social distancing. In fact, producers are finding inventive ways of maximizing both production and safety. They should be relied upon to create these solutions. The excess mortality rates associated with this pandemic will continue to come into focus at lower levels with more widespread serological testing. That will reinforce the need for individual autonomy in weighing risks and benefits. Hazards are always out there: reckless or drunk drivers, innumerable occupational hazards, and the flu and other communicable diseases. Protect yourself in any way you see fit, but if you are healthy, please do so without agitating for public support from the rest of us, and without imposing arbitrary judgments on which activities carry acceptable risk for others.

 

A Look at Covid-19 Cases in Missouri

21 Tuesday Apr 2020

Posted by in Pandemic

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This is a quick post for Missouri readers. It’s well known that the coronavirus pandemic has differed in its severity across the world and across the country. I’ve been focusing on nationwide statistics, but I thought it would be interesting to look at my home state’s progress in getting ahead of the virus. The charts below are taken from the Covid Tracker from Microsoft/Bing.

The peak of new cases in Missouri appears to be behind us. The state reached a rough plateau around the beginning of April. There was some volatility in the daily numbers of conformed cases, but the a downward trend seemed to begin around the 10th.

Cumulative confirmed cases in Missouri are shown in the next chart (Oops… spelling!), but in log scale. The slope of the line can be interpreted as the growth rate. It’s still positive and will be as long as there are new confirmed cases, but it is getting small.

Daily Covid-19 fatalities in Missouri are shown next. They are obviously quite volatile from day-to-day, as might be expected. They seemed to reach a high about a week after new cases reached their plateau, which demonstrates the lag between diagnosis and death in the most severe cases. The trend has become more favorable over the past week, though another jump in deaths was reported today.

The following chart shows cumulative Missouri fatalities in log scale. The curve is flattening (growth rate slowing), but it might take a few weeks for fatalities to stay in the very low single digits day after day.

The St. Louis metro area has had the largest concentration of cases and fatalities in Missouri. St. Louis County, St. Louis City, and St. Charles County are ranked #1 – #3 in the state, respectively. Here are the top ten counties in terms of this grim statistic (I’m sorry for the poor alignment).

County                 Cases       Deaths

St. Louis               2,333       91 (3.90%)
St. Louis City           877       21 (2.39%)
St. Charles              458       15 (3.28%)
Jackson                   438       13 (2.97%)
Jefferson.                230         3 (1.30%)
Franklin.                  102         5 (4.90%)
Boone                       96         1 (1.04%)
Greene.                    84          7 (8.33%)
Clay                          61         1 (1.64%)
Cass                         54          6  (11.1%)

I wanted to take a closer look at the pattern of cases in the metro area over time. Last night I found daily county-level case data on my phone. I thought I’d be able to download it tonight, but the site has been uncooperative. Maybe later.

Missouri looks like it’s on the back end of the curve, at least for this wave of the pandemic. We can hope there won’t be a second wave, or if there is, that it will be more manageable.

 

 

 

 

 

Lockdown Illusions

16 Thursday Apr 2020

Posted by in Federalism, Liberty, Pandemic

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Analytical sins have occurred with great regularity in popular discussions of the Covid-19 pandemic and even in more scholarly quarters. Among my pet peeves are cavalier statements about the number of cases or deaths in one country or state versus another without adjusting for population. Some of this week’s foibles also deal comparisons of the pandemic and public policy across jurisdictions, but they ignore important distinctions.

No matter how you weigh the benefits and costs of lockdowns or stay-at-home orders, there is no question that maximizing social distance can reduce the spread of the virus. But stories like this one from Kansas dispute even that straightforward conclusion. As evidence, the author presents the following table:

Now, I fully support the authority of states or local areas to make their own decisions, but this table does not constitute valid evidence that stay-at-home orders don’t reduce transmission. There are at least three reasons why the comparisons made in the table are invalid:

  1. The onset of coronavirus in these states lagged the coastal states, primarily because…
  2. These are all interior states with few direct arrivals of international travelers;
  3. These states are all more or less rural with relatively low population densities, ranking 40, 41, 42, 46, 48, 49, 52, 53, and 55 in density among all states and territories.

All of these factors lead to lower concentrations of confirmed cases and Covid deaths (though the first applies only on the front-end of the epidemic). The last two points provide strong rationale for less restrictive measures to control the spread of the virus. In fact, population density bears a close association with the incidence of Covid-19, as the table at the top of this post shows. Even within low-density states, residents of urban areas are at greater risk. That also weighs heavily against one-size-fits-all approaches to enforced distancing. But instead, the authors fall over themselves in a clumsy attempt to prove a falsehood.

Even highly-educated researchers can race to wholly unjustified conclusions, sometimes fooled by their own clever devices and personal mood affiliation. This recent study directly controls for the timing of stay-at-home orders at the county level. The researchers attempt to control for inherent differences in county transmission and other factors via “fixed effects” on case growth (which are not reported). This is an excuse for “assuming away” important marginal effects that local features and conditions might play in driving the contagion. The authors conclude that stay-at-home orders are effective in reducing the spread of coronavirus, which is fine as far as it goes. But they also leap to the conclusion that a uniform, mandatory, nationwide lockdown is the wisest course. Not only does this neglect to measure the differential impact of lockdowns by easily measured differences across counties, it also assumes that the benefits of lockdowns always exceed costs, regardless of density, demographics, and industrial composition; and that a central authority is always the best judge as to the timing and severity of a mandate.

The national crisis engendered by the coronavirus pandemic required action at all levels of government and by private institutions, not a uniform set of rules enforced by federal police power. State and local police power is dangerous enough, but better to have decisions made by local authorities who are more immediately accountable to citizens. Government certainly has a legitimate role to play in mitigating behaviors that might impose external costs on others. Providing good information about the risks of a virus might be a pivotal role for government, though governments have not acquitted themselves well in this regard during the Covid crisis.

It’s also important for federal, state and local authorities to remember that private governance is often more powerful in achieving social goals than public rule-making. People make innumerable decisions every day that weigh benefits against risks, but public authorities are prone to nudging or pushing private agents into over-precautionary states of being. It’s about time to start easing up.

 

Coronavirus “Framing” Update #4

13 Monday Apr 2020

Posted by in economic growth, Pandemic

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It’s beginning to look like we’ve turned a corner in mitigating the spread of the coronavirus. I hope I’m not speaking too soon.

It’s time to update some of the charts and thoughts about where the epidemic is trending in the U.S. Here’s the first of these “framing” posts I published on March 18th. The last update from about a week ago is here. The demand for tests seems to be tapering a little, and the percentage of tests that are positive has leveled and even dropped a bit. The number of confirmed cases continues to mount, but the daily increases are slowing, as is the growth rate of the cumulative count. Finally, the daily increase in the number of deaths is also slowing, and total deaths have risen more slowly than one prominent model predicted on the date at which I chose to “freeze” it for my own expositional purposes: April 2. The charts appear further below.

The epidemiological modelers have taken a real beating from many observers as their estimated virus growth curves have shifted downward. Their initial projections were way too high, and they have continued to overshoot in subsequent model revisions. In fairness, however, they didn’t have a lot to go on during the early stages of the pandemic, and conservatism was probably seen as a must. The variety and extent of mitigation measures was also an unknown, of course.

I build “event” models for a living, though the events I study are economic and are obviously much different kinds of risks than coronavirus infection. I seldom face situations in which so little historical data is available, so I can appreciate the modeling challenge presented by Covid-19: it was pretty close to an unwinnable situation. Nevertheless, until recently the projections were outrageously high. There comes a time when accurate, rather than conservative, projections are demanded. The confidence intervals produced by the modelers are really not worthy of the name. Partly on that basis, a very recent paper gave the model produced by the Institute for Health Metrics and Evaluation very poor marks (IMHE, which I called the Murray Model last week):

“In excess of 70% of US states had actual death rates falling outside the 95% prediction interval for that state…”

That’s nothing short of pathetic.

That brings me to the “framing” exercise I’ve been performing for nearly four weeks. It is not a modeling exercise. The “very good” and “pretty bad” scenarios I charted for the confirmed Covid-19 case count in the U.S. were not intended as confidence intervals except perhaps in spirit. The intent was to provide perspective on developments as they unfolded. Where to place those bounds? They were based on multiples of the Italian experience (pretty bad) and the South Korean experience (very good) as of March 18, normalized for U.S. population. Here’s the latest version of that chart, where Day 1 was March 4th:

The curve may be just starting to bend to the right. Let’s hope so. The daily growth rate of new cases has dropped below 5%. Below, it’s clear that the daily count of new confirmed cases plateaued in early April, and the last few days show an encouraging reduction.

I also think it’s telling that after a few weeks of “excess demand” for tests, demand seems to be falling. The chart below showed the sharp reduction in the “pending test” count about a week ago. It corresponded with the spike in daily tests, which have stabilized since then and may be trending down (lower panel).

The next chart shows that the cumulative share of tests with a positive diagnosis has flattened. The lower panel hints at a taper in the daily share of positive tests, which would be welcome. However, I do not necessarily expect that percentage to decline too much if the number of tests continues to fall. In fact, more testing will almost certainly be required in order to “restart” the economy. Then, we should see a reduction in the percentage of positive tests if all goes well.

The last chart highlights the IMHE model discussed above. The chart extends from March through June, though the unlabeled date axis is not cooperating with me. The mean model prediction of U.S. cumulative deaths attributed to Covid-19 is shown in red. The upper and lower bounds of the confidence interval are the blue and green lines. Again, I “froze” this forecast as of April 2 to serve as another “framing” device. Actual deaths are traced by the black line, which goes through April 13th. It is trending below the mean forecast, and IMHE has reduced their mean forecast of the death toll by about a third since April 2nd (to 60,000). Actual deaths may well come in below that level.

I hope my optimism based on these nascent developments is not unwarranted. But they are consistent with state-by-state reports of more positive trends in the data. It is time to start planning for a return to more normal times, but with a new eye toward mitigating risk that will probably involve isolating vulnerable groups when appropriate, more work at home, widespread testing, and a few other significant changes in social and business practices. It remains to be seen how easily certain industries can return to previous levels, such as hospitality, or how soon crowds can return to sporting events, concerts, and theaters. That might have to await greater levels of “herd immunity”, an effective vaccine, and fast testing.

Coronavirus: Framing the Next Few Weeks

19 Thursday Mar 2020

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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 

The Federal Reserve and Coronatative Easing

09 Monday Mar 2020

Posted by in Monetary Policy, Pandemic

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Laughs erupted all around when the Federal Reserve reduced its overnight lending rate by 50 basis points last week: LIKE THAT’LL CURE THE CORANAVIRUS! HAHAHA! It’s easy to see why it seemed funny to people, even those who think the threat posed by Covid-19 is overblown. But it should seem less silly with each passing day. That’s not to say I think we’re headed for disaster. My own views are aligned with this piece by Michael Fumento: it will run its course before too long, and “viruses hate warm weather“. Nevertheless, the virus is already having a variety of economic effects that made the Fed’s action prudent.

Of course, the Fed did not cut its rate to cure the virus. The rate move was intended to deal with some of the economic effects of a pandemic. The spread of the virus has been concentrated in a few countries thus far: China, Iran, Italy, and South Korea. Fairly rapid growth is expected in the number of cases in the U.S. and the rest of the world over the next few weeks, especially now with the long-awaited distribution of test kits. But already in the U.S., we see shortages of supplies hitting certain industries, as shipments from overseas have petered. And now efforts to control the spread of the virus will involve more telecommuting, cancellation of public events, less travel, less dining out, fewer shopping trips, missed work, hospitalizations, and possibly widespread quarantines.

The upshot is at least a temporary slowdown in economic activity and concomitant difficulties for many private businesses. We’ve been in the midst of a “flight to safety”, as investors incorporate these expectations into stock prices and interest rates. Firms in certain industries will need cash to pay bills during a period of moribund demand, and consumers will need cash during possible layoffs. All of this suggests a need for liquidity, but even worse, it raises the specter of a solvency crisis.

The Fed’s power can attempt to fill the shortfall in liquidity, but insolvency is a different story. That, unfortunately, might mean either business failures or bailouts. Large firms and some small ones might have solid business continuation plans to help get them through a crisis, at least one of short to moderate duration, but many businesses are at risk. President Trump is proposing certain fiscal and regulatory actions, such as a reduction in the payroll tax, wage payment assistance, and some form of mandatory paid leave for certain workers. Measures might be crafted so as to target particular industries hit hard by the virus.

I do not object to these pre-emptive measures, even as an ardent proponent of small government, because the virus is an externality abetted by multiplicative network effects, something that government has a legitimate role in addressing. There are probably other economic policy actions worth considering. Some have suggested a review of laws restricting access to retirement funds to supplement inadequate amounts of precautionary savings.

Last week’s Fed’s rate move can be viewed as pre-emptive in the sense that it was intended to assure adequate liquidity to the financial sector and payment system to facilitate adjustment to drastic changes in risk appetites. It might also provide some relief to goods suppliers who find themselves short of cash, but their ability to benefit depends on their relationships to lenders, and lenders will be extremely cautious about extending additional credit as long as conditions appear to be deteriorating.

In an even stronger sense, the Fed’s action last week was purely reactive. Scott Sumner first raised an important point about ten days before the rate cut: if the Fed fails to reduce its overnight lending target, it represents a de facto tightening of U.S. monetary policy, which would be a colossal mistake in a high-risk economic and social environment:

“When there’s a disruption to manufacturing supply chains, that tends to reduce business investment, puts downward pressure on demand for credit. That will tend to reduce equilibrium interest rates. In addition, with the coronavirus, there’s also a lot of uncertainty in the global economy. And when there’s uncertainty, there’s sort of a rush for safe assets, people buy treasury bonds, that puts downward pressure on interest rates. So you have this downward pressure on global interest rates. Now while this is occurring, if the Fed holds constant its policy rate, it targets the, say fed funds rate at a little over 1.5 percent. While the equilibrium rates are falling, then essentially the Fed will be making monetary policy tighter.

… what I’m saying is, if the Fed actually wants to maintain a stable monetary policy, they may have to move their policy interest rate up and down with market conditions to keep the effective stance of monetary policy stable. So again, it’s not trying to solve the supply side problem, it’s trying to prevent it from spilling over and also impacting aggregate demand.”

The Fed must react appropriately to market rates to maintain the tenor of its policy, as it does not have the ability to control market rates. Its powers are limited, but it does have a responsibility to provide liquidity and to avoid instability in conducting monetary policy. Fiscal actions, on the other hand, might prove crucial to restoring economic confidence, but ultimately controlling the spread of the virus must be addressed at local levels and within individual institutions. While I am strongly averse to intrusions on individual liberty and I desperately hope it won’t be necessary, extraordinary measures like whole-city quarantines might ultimately be required. In that context, this post on the effectiveness of “non-pharmaceutical interventions” such as school closures, bans on public gatherings, and quarantines during the flu pandemic of 1918-19 is fascinating.