Pandemic Fears: When the ‘availability heuristic’ meets ‘belief bias’

The authors of this blog were recently featured in the UMass Daily Collegian and a subsequent post of the article in the ‘Overheard at UMass’ Facebook page generated a spirited debate. That spirited debate is what we have been trying to promote with this blog. To arrive at the best policy, there should be a lively and scientifically informed debate. Science does not tell you what to do. (In the words of Sabine Hossenfelder, “science does not tell you not to pee on a high voltage line, it just tells you that urine is a good conductor”). Science provides evidence, and it is up to policy makers to review the evidence from different perspectives and make a policy decision that weighs the costs and benefits. One comment on the Facebook page criticized the authors of this blog for our lack of medical credentials. It is true that none of us is a doctor or epidemiologist. Rather, we are statisticians and scientists with expertise in data analyses. In addition, we are Cognitive Psychologists with expertise in decision making. For the most part, policy responses to this pandemic have been driven by doctors and epidemiologists, but a well-rounded and better-informed policy will emerge from a debate that includes individuals with other kinds of expertise, such as the way that human decision making can go awry in light of well-documented biases.

The most powerful and common form of decision-making error is termed the ‘availability heuristic’. This error occurs when people have an inaccurate understanding of the probabilities of events because they base their understanding on personal anecdotes or anecdotes portrayed in the news media. For example, considering the news coverage of COVID-19, it may surprise many to learn that approximately as many people die every year from smoking as died during the first year of the COVID-19 pandemic (according to the CDC, both killed approximately half a million Americans).

Considering this numerical equivalence between smoking deaths and COVID deaths, we can ask what it would require to nearly eliminate all COVID-19 deaths versus all smoking deaths. In the case of smoking, the government could ban smoking, shut-down tobacco companies, burn tobacco fields, and impose harsh penalties for smoking. What might have worked with COVID-19 was the approach taken in Wuhan, China: An extreme shelter-in-place order (no exceptions) and harsh penalties for violators, combined with forcible removal from their home for anyone suspected of COVID infection, placing them in a massive state-run quarantine hospital (shades of leprosy colonies). It is clear which of these policies is more draconian, and those who would counter “but many more could have died from COVID-19 than from smoking” must be reminded that the annual smoking death toll is repeated every year, whereas no pandemic in human history has lasted indefinitely. Moreover, the Wuhan approach violates core values of a free democratic society. Instead, most democracies attempted various forms of ‘lockdown lite’. It is not clear whether these measures ultimately changed the course of the virus, but it is certainly clear that these measures resulted in the loss of education for millions of children, a looming mental health crisis, the permanent closure of local businesses, deaths from deferred cancer screening, an enormous debt burden for the next generation, and the potential starvation of millions in East Africa as the developed world focused all resources on COVID-19.

The scientists and epidemiologists directing COVID policy claim there is substantial evidence to support mitigation policies, such as social distancing, mask mandates, and school closures. To be sure, laboratory studies (and common sense) show that people cannot infect each other if sufficiently separated and that masks greatly reduce airborne virus. The real world is messy and complicated though: law-abiding citizens with the best of intentions do not always follow guidelines, masks slip off noses, people touch their face reflexively, etc. When considering the net outcome of these lockdown-lite mitigation policies, there is little evidence to suggest that they did much beyond delay waves of infections (e.g., California appeared to do better than Florida initially, owing to more extreme restrictions in California, but eventually these two states ended up with similar COVID death rates even though California did substantially more damage to its economy, mental health of its citizens, and education of its children).

Why are people dismissive of evidence suggesting that these mitigation policies have been ineffective? This is where the availability heuristic collides with the ‘belief bias’. In decision making, ‘belief bias’ is the tendency to judge the strength of an argument based on plausibility rather than on evidence and logic. For instance, in one logic puzzle, people are told that “some college professors are intellectuals” and that “some intellectuals are liberals” and then asked whether this necessarily implies that “some college professors are liberals”. Most people respond yes and yet the first two statements do not necessarily imply the third (easily shown by drawing a Venn diagram). This occurs because the common knowledge that many professors are liberals (including the authors of this blog), clouds the ability to make an accurate judgment about the implications of the two statements. As applied to COVID-19, the commonsense notion that mask mandates and social distancing ought to stop the virus clouds rational analysis of the evidence as to whether these mitigation policies work in practice.

Now that vaccines are changing the calculus at a rapid pace (the most vulnerable have been offered vaccines in the U.S., and this offer of protection is now being extended to the less vulnerable in many states), we can consider the lingering consequences of these decision biases. After a year of pandemic in which people have been consistently bombarded with messages of death and fear and constant reminders regarding mask wearing and social distancing, thoughts and behavior have been permanently altered. For example, Rutgers University recently announced not only that all students must be vaccinated before the Fall semester, but that despite this mandate, students must still wear masks, practice social distancing, and undergo regular COVID testing. Why? The CDC is currently investigating the remote possibility that vaccinated individuals are nevertheless effective spreaders of the virus. Perhaps this remote possibility is why Rutgers will impose a continuance of these mitigation policies. But even if the vaccinated can spread the disease, what possible benefit would come from these social restrictions and constant testing once all of the vulnerable and most others have been vaccinated? And at what cost? By Fall, everyone who wants a vaccine will have had the opportunity to get one and even if the virus is spreading in a silent manner among the vaccinated, the health consequences for the vaccinated will be minimal (all of the currently deployed vaccines in the U.S. are 100% effective in preventing death – “Not a single vaccinated person has died of COVID-19”).

We live in a democratic nation and individual responsibility is a pillar of our society. Once everyone has been offered a vaccine, then all restrictions should be removed (if not earlier, considering that the most vulnerable have already been offered a vaccine). The news media should stop skewing our fears by a constant focus on the worst-case examples and worst-case possibilities (evidenced in this recent study). At our core, humans are social animals, and society is the thing that emerges from our social interaction. For the last year, we have been actively suppressing that which makes us human, and it is time to stop the damage.

David Huber:

Thanks to Adrian Staub, Carlo Dallapiccola, and Rosie Cowell for helpful discussion and comments.

Will mask mandate enthusiasts please confront the data?

On March 2, Texas Governor Greg Abbott made headlines by lifting the state’s mask mandate and removing all restrictions on business capacity.  The condemnation from public health authorities was swift.  Dr. Anthony Fauci stated that this move was “inviting” another virus surge.  CNN reported that Abbott faced a “torrent of criticism,” including from President Biden, who characterized Abbott’s move as “Neanderthal thinking.”

We are now, on March 23, three weeks out from Abbott’s decision.  Here are the data on cases in Texas, from the NY Times:

On March 2, the Times reported a seven-day average of 7,259 new cases per day; as of yesterday, the seven-day average is 3,714 cases per day.  Clearly, there is no sign of a surge; far from it, the number of cases in Texas has dropped by 49%.  Note that this is much steeper drop than the 17% national decline in cases over the same period, based on the NY Times data (64,469 cases/day to 54,190 cases/day).  

Mississippi eliminated its mask mandate and business restrictions on the same day as Texas.  Almost exactly like Texas, Mississippi has seen a 50% drop in the seven-day average of new cases from March 2 (582/day) to March 22 (293/day).  Here’s the plot:

Maybe three weeks is not long enough to see the predicted rise in cases?  Three other states lifted their mask mandates earlier:  North Dakota in mid-January, and Iowa and Montana in early-to-mid February.  Here are the plots:

Not a surge in sight; in all three states, there are fewer new cases per day now than there were when the mask mandates were lifted.  

What about states that never had mask mandates in the first place?  Surely, during the periods of the worst spread of Covid-19, mask mandates must have made some difference?  The following chart shows the number of Covid-19 deaths per 100,000 people as of March 22, 2021, by state (from Statista).  I have added the arrows to indicate the 11 states that never had mask mandates.

A couple of states without mandates have had a relatively high toll (Arizona, South Dakota), and a few states without mandates have had a very low toll (Nebraska, Idaho, Alaska).  The rest are in the middle somewhere.  Overall, there is no indication that the impact of Covid-19 has been greater in states that have lacked a mask mandate.  

One year into this pandemic, policies with regard to masks and other restrictions on personal and business activity do not seem to explain the variability in the prevalence of Covid-19 between states, nor do they seem to explain changes in prevalence over time.  This is not a new observation, as the almost identical impact in Florida and California, despite their very different approaches, has been much discussed, such as in this article from March 13: 

“Nearly a year after California Gov. Gavin Newsom ordered the nation’s first statewide shutdown because of the coronavirus, masks remain mandated, indoor dining and other activities are significantly limited, and Disneyland remains closed.  By contrast, Florida has no statewide restrictions. Republican Gov. Ron DeSantis has prohibited municipalities from fining people who refuse to wear masks. And Disney World has been open since July. Despite their differing approaches, California and Florida have experienced almost identical outcomes in COVID-19 case rates.”

One possibility, of course, is that mask mandates and business restrictions don’t have much effect on the spread of Covid-19 because people’s behavior is mostly governed by their own judgment and proclivities, whatever the official rules may be; however, there is at least some evidence that mask mandates do increase mask wearing.  The other possibility is that mask wearing itself is simply not very effective in preventing community spread, in the real world, contrary to what we have been told since near the beginning of the pandemic.  Indeed, the only randomized, controlled trial that I have heard of, which was carried out in Denmark, did not find a statistically significant reduction in Covid-19 cases due to mask wearing. 

Whichever of these explanations turns out to be right – or if both are partly right – an important question is whether the supporters of mask mandates and business restrictions will start to change their views about the efficacy of these measures or, if not, will be held accountable for them by the media.  I am afraid that there is little sign of this happening, yet.  On February 26, CDC Director Rochelle Walensky stated that “Now is not the time to relax restrictions.”  But why, exactly?  It is long past time for public health and other governmental authorities to point to the actual data demonstrating the efficacy of these restrictions.  They are often espoused as ‘common sense.’  Perhaps this is a correct characterization – it does seem like mandating mask-wearing and business closures should work – but we now have more than enough data to demonstrate whether they actually do. 

I’ll note that I would welcome any argument as to why the above data should not be taken at face value.  Please reply with a comment.  

I’ll also note, however, that we should all try not to cherry-pick data from a particular time, or a particular place, that are favorable to a case for or against mask mandates. For example, on December 4 Vox published a graph very much like the one above, but showing that many of the states without mask mandates had among the highest rates of new cases in the month of October. But why focus on October? Presumably because the data from this particular month happen to fit that article’s narrative. Indeed, these were not even the most recent data at the time of publication. As the plot in the present article clearly shows, states without mask mandates have not been hit particularly hard overall, which implies that we could have focused on other months when the states without mandates did better than average. The graph I’ve shown here covers the entire pandemic; we are not picking and choosing a time period that favors any one case.

Similarly, we should avoid cherry-picking specific comparisons that make a state’s policies look good or bad. I pointed out in a previous post that the frequent comparison of Sweden’s pandemic impact to the impact in Norway and Finland, which makes it look like Sweden’s less restrictive policies have been a mistake, is quite misleading, because Sweden’s pandemic impact has actually been quite typical for European countries.

Adrian Staub (

Thanks, as usual, to Rosie Cowell, Carlo Dallapiccola, and Dave Huber.

Bringing it back home: The pandemic response and business closures in Northampton

There have been many attempts to estimate the number of small businesses in the U.S. that have closed as a result of our collective response to the Covid-19 pandemic, including here and here, and some thoughtful reflections on what these losses mean for both business owners and communities, including here.  

Most stories of this sort refer to the impact of the pandemic on businesses, rather than attributing this impact to specific policy decisions, such as forced closures of retail establishments and restaurants.  This framing makes the events of the last year seem as unavoidable as damage from a natural disaster. But just as it is the decision to close schools – not the pandemic itself – that has caused children to miss a year of education, it is a series of specific policy decisions that has resulted in the loss of so many small businesses.  Whether these policy choices will turn out to have been the right ones will, in the end, depend both on the course of the Covid-19 pandemic itself, and on the damage we will have done to our communities and institutions.

Estimates of tens or hundreds of thousands of small business closures are pretty abstract.  I’ve noticed that there does not seem to be a history being written, in real time, as we lose businesses locally.  I’d like to remember these places.  I live in Northampton, and below is a map of downtown, on which I have marked all the businesses I know of that have closed permanently since March of 2020.  

This map doesn’t include closed businesses outside the downtown area (Freckled Fox Cafe, in Florence; Webster’s Fish Hook, on Damon Road), nor does it include business that have moved elsewhere (Guild Art Supply and Pierce’s Frame Shop, both moved to Easthampton). The map also doesn’t include establishments that are temporarily closed, hoping to re-open when restrictions abate (Sylvester’s Restaurant; Packard’s Bar; Ye Ol’ Watering Hole). Obviously, the longer that restrictions on business activity are in place, the less likely it is that these places will re-open.

If you know of other businesses that should be on this map, or if I’ve made errors, please do not hesitate to let me know by email or by a comment on this blog.  

Adrian Staub (

Thanks as always to Carlo Dallapiccola, Rosie Cowell, and Dave Huber.

Oops, We Forgot the Democracy: Covid-19 Policy and Our Response to Crises

Last summer, I wrote an opinion piece for the Daily Hampshire Gazette entitled, “Greater balance needed in Covid-19 policy,” which was published on August 11.

In the piece, I wrote that Covid-19 policy was focusing on “stopping the virus to the exclusion of all other concerns,” and that if we continued to discount the resulting costs to society—job losses, failure of small businesses, disruption to young people’s education and social development, and degradation of our civic and social life—we would “pay a heavy price for it.”

Unfortunately, the past six months have not brought a change in approach, with the social isolation measures we have now all grown accustomed to—restrictions on businesses, event cancellations, stay-at-home policies, staying six feet apart and wearing masks in public—all firmly locked in place.  And some of the costs of these policies are starting to become apparent.  We now have evidence of deaths likely related to social isolation: here, here, and hereResearch studies confirm the terrible toll on children and adolescents.  Governments around the world have taken on massive debt to keep their economies afloat—debt that will someday have to be paid back.  Working class people in this country are suffering from Depression-like economic conditions.  And the poor in developing countries are descending into even more crushing poverty, and are at elevated risk of starvation.

Of course, we won’t know the full cost of the social isolation policies adopted in response to Covid-19 for quite some time, as many of the worst effects will take years to manifest.

While all of this is deeply troubling, as I think about how our society will emerge from the pandemic and the lockdowns, what concerns me even more is the failure of democratic process that led to such unbalanced policy, and what this failure implies about our response to future crises.

The fact is that I don’t know for sure what the right balance is now, or what it should have been at the outset of the pandemic.  I am convinced that sacrificing our children’s education and social development has been an egregious mistake.  And I believe that we are still undervaluing the long-term costs of our current policies.  It is, after all, human nature to respond more strongly to immediate threats than to more distant ones.

But the truth is that there is no single correct answer to the dilemma of how to weigh the costs and benefits of various policy options and balance them against each other.  Different people will arrive at different answers based on their own values and interests.  That is what democracy is for—to balance differing values and competing interests, to create the space for an open and respectful debate, and to make the most accurate, up-to-date information as widely accessible as possible.  When democracy works, it gives us the best chance to adopt policies that meet the needs and reflect the values of the American people.

Clearly, our democracy did not work this way with respect to Covid-19.  Liberals have of course blamed the incompetence and irresponsibility of the Trump administration for nearly everything that has gone wrong with Covid-19 policy.  But without defending Trump, I think it is time for the mostly-liberal professional class that designed, implemented, and advocated for social isolation policies to engage in some introspection about its own behavior.

Instead of having an open, reasoned policy debate, and a fair balancing of values and interests, this professional class of “experts” arrogated decision making power to itself, while failing to acknowledge the influence of its own class biases and interests on the policies it adopted.  And since the lockdowns began, we have seen mainstream media organs such as the New York Times abandon intellectual honesty, and instead act as cheerleaders for “expert”-determined policies, while seemingly regarding frightening people into compliance with these policies as a public service they are providing.

It is true that social isolation polices have sparked widespread opposition in some parts of the country.  But this opposition has largely been grounded in knee jerk defiance of liberal elites, blind loyalty to our former president, and scorn for expert opinion, rather than a willingness to challenge and engage with it.

Covid-19 is not the last crisis of its kind that our society will face.  Scientists have been warning for decades that the combined effects of climate change and globalization will make pandemics more frequent occurrences.  What if we face a new viral threat every five to ten years?  Will we live in a permanent state of lockdown?

Moreover, it seems likely that we will experience a series of economic and ecological crises in the coming years.  If we respond to every new crisis the way we have responded to Covid-19, with panicked overreaction, a single-minded focus on eradicating the immediate threat with no thought for the long-term consequences, and an unwillingness or inability to face up to hard choices, we will leave our children and grandchildren with a society that is sadly diminished, and hardly worth living in.  If our only political choices are the self-satisfied consensus of the experts, or a defiant, anti-intellectual opposition, if every new crisis tears the country further apart, we will weaken our democracy, perhaps to the breaking point.

I will admit I am pessimistic that we will change course on Covid-19 policy anytime soon, not as long as vaccine rollouts give people hope that life will return to something resembling normal by this summer.

But the advent of this blog gives me hope that we may find our way towards both a better decision making process and better policy outcomes in the future.  I am no under no illusion that the blog will appeal to supporters of our former president—nor is it primarily a space for political debate.  But for those who are also troubled by the issues I raised in the Gazette last summer, it should serve as a welcome space for developing an accurate understanding of the science of Covid-19, for holding the experts and the media accountable, and perhaps in the not-too-distant future, for a re-evaluation of Covid-19 policy, which may then form the basis for a better approach to future crises.

Michael Alterman

Michael Alterman holds an A.B. in Social Studies from Harvard College, and an M.A. in Urban and Environmental Policy from Tufts University.  He lives in Chesterfield, and is a student of American history and politics.

What does a positive COVID test mean?

On January 20th 2021, the WHO issued new guidance for the use of gold-standard PCR testing for detection of SARS-CoV-2 (COVID-19). Considering this new guidance, and in light of the massive degree of testing currently taking place in the U.S., and Massachusetts in particular, I discuss what it means to receive a positive COVID test result.

Most medical tests are performed after a patient shows up in a doctor’s office or the emergency room and the test is chosen based on the patient’s symptoms. In such cases, a doctor uses the test as a diagnostic tool, attempting to identify the root cause of the symptoms. But in some cases, medical tests are used in the absence of symptoms, as a screening tool. This is common with cancer screening because the prognosis is better if cancers are identified before they cause symptoms. Asymptomatic screening for infectious diseases is less common, with HIV screening a notable exception. However, even HIV screening fails to come close to the level of screening that is currently deployed for COVID-19. The numbers screened for COVID-19 are staggering. For instance, among countries with a population greater than 10 million, the United States ranks second in the world in its rate of testing, with 878,000 tests per million (the UK ranks first, with 968,000 per million). In other words, there has been nearly one test for every individual in the U.S. (retrieved from worldometers on January 20th 2021). Among states, Massachusetts ranks third (after Rhode Island and Alaska), with 1.819 million tests per million. Hence, in the state of Massachusetts, everyone has been tested nearly twice on average. However, screening for COVID-19 is not uniformly applied; in truth, many people have never been tested, while others (e.g., college students) are tested every week, or even twice per week.

Because this level of screening is unprecedented, it is worth considering the two types of errors that can occur with a medical test. Most doctors and labs are concerned with the false negative rate (which is one minus the ‘specificity’). The false negative rate is the probability that the test fails to detect the disease when the disease is present. This is considered the bad kind of error because a failure to detect would allow the cancer to grow, or, in the case of COVID-19, allow the individual to continue about their daily activities, potentially infecting others. The other kind of error is a false positive, which is a positive test even though the individual does not have the disease. In this case, the cost is financial and emotional, including: 1) an unnecessary quarantine, with consequences for employment; 2) a cost to friends and family who will also undergo contact tracing and testing, and likely quarantine; and 3) a cost to mental health owing to fear, social isolation, and unwarranted shame if the local community blames the individual for perceived reckless behavior.

These different kinds of errors are defined in terms of known states of the world (the “ground truth” of whether a person is infected or not). Therefore, determination of the false negative and false positive rates requires testing of people who have been independently verified as having or not having the disease, respectively. In the mathematical language of conditional probabilities, these are expressed as p(negative test | disease) or p(positive test | no disease), read as the probability (p) of a negative test result given that you have the disease or the probability of a positive test result given that you do not have the disease. But in truth, this is not what we want to know. Instead, what we want to know is p(disease | positive test) – i.e., the probability that an individual has the disease if they receive a positive test result. Fortunately, we can use a mathematical trick termed ‘Bayes rule’ to reverse the conditional probabilities. Without going into the mathematics of it, what we require for doing this are three things: 1) the false negative rate; 2) the false positive rate; and 3) the prevalence of the disease in the population.

Paradoxically, Bayes rule says that the thing we want to know (i.e., how to interpret a positive test result), depends on how many people have the disease in general. If a disease is highly prevalent (e.g., 25% of the population has herpes), then there is greater certainty that a positive test result is an indicator of infection. But if the prevalence is low, even a highly accurate test – in the sense of delivering low false positive and false negative rates – can be misleading. In their new guidance, the WHO reminds PCR users that:

disease prevalence alters the predictive value of test results; as disease prevalence decreases, the risk of false positive increases (2). This means that the probability that a person who has a positive result (SARS-CoV-2 detected) is truly infected with SARS-CoV-2 decreases as prevalence decreases, irrespective of the claimed specificity.

Consider an exceptionally accurate and sensitive test; one with a 0% false negative rate and only a 1% false positive rate (of note, many PCR tests appear to have a false positive rate lower than 1% — this value is used for illustrative purposes). In other words, a test that always detects the disease when it exists and rarely produces a false positive. Now consider what will occur if this exceptionally accurate test is massively deployed in the context of 1% prevalence (which is a prevalence that that is likely higher than the current prevalence of active COVID-19 infections). Paradoxically, when applied to everyone in the population (e.g., when used for asymptomatic screening, rather than as a diagnostic tool), a positive result with this highly accurate test means that an individual has only a 50% chance of truly being infected. In other words, if they do not have any symptoms or reason to expect that they are infected, and if they receive a positive COVID test, they are just as likely to be disease free as they are to have the disease. To make this concrete, consider applying this test to 100 people who do not have symptoms. Because the prevalence of disease is 1%, you can expect 1 true positive. However, because the test has a 1% false positive rate, you can also expect 1 false positive. So, among the 2 positive tests, one is true and one is false (i.e., only a 50/50 chance of the disease for any person who tests positive).

The solution to this problem is quite simple. Test again. This does not mean that you take the same specimen and run it through the test machine a second time; the false positive might have occurred owing to contamination of the specimen or from mis-labeling of the specimen. Instead, what it means is that you bring the individual back and collect a new specimen for a second independent test. Because this second test is independent, the probability of two false positives is the multiplication (the “square’) of the false positive rate, i.e., 1 in 10,000 for a test with a 1% false positive rate. Performing two tests lowers the probability of a misdiagnosis considerably, even with a low prevalence of the disease. The WHO writes:

Where test results do not correspond with the clinical presentation, a new specimen should be taken and retested using the same or different NAT technology.

Of note, the asymptomatic testing program at the University of Massachusetts Amherst does not advise a second test currently. Instead, after a positive test result, the prescription is an immediate quarantine, which serves to block the individual from seeking a second test (and furthermore, many testing sites will not test an individual who has already received a positive test result). For the Spring 2021 semester, UMass undergraduates are expected to take 2 PCR tests every week during the 15 weeks of the semester. In recent weeks, as the new in-house UMass test has been introduced, the asymptomatic testing program at UMass has seen its positivity rate rise to around 1% and sometimes higher – it is unknown whether this recent increase reflects an increase in true positives or in false positives. If the test has a 1% false positive rate, the chances that all thirty tests deliver a negative result as applied to a disease-free individual are .9930 = .74. In other words, the chances of at least one positive test for this COVID-free individual are 1-.74 = .26; every COVID-free student would nevertheless suffer a 26% chance of receiving at least one false positive test result (a 26% chance of at least one needless quarantine)! This will produce a massive disruption to the community and entail serious consequences for mental health if 26% of the population can expect a false positive diagnosis at some point.

Considering that the goal of COVID-19 screening is to identify those who are infected before they spread the disease, there is in fact a third kind of error, which is a true positive result that comes too late. This can occur either if the test result is too slow in arriving or if the test is administered after the individual has already gone through their infectious stage of the disease, but still has enough virus to yield a low viral load positive test. For most diseases this third kind of error is unlikely to occur because individuals typically experience symptoms at the height of infectiousness (i.e., the disease is likely to be caught prior to this post-infectiousness stage). However, a sizable proportion of individual infected with COVID-19 never experience symptoms and may have progressed beyond the point of infectiousness before being screened for the disease.

This third kind of error is more likely with a highly sensitive test, such as PCR. A recent paper in The New England Journal of Medicine (Nov. 26, 2020) indicated that PCR tests applied to an individual with COVID-19 are just as likely to give a positive result after their period of infectiousness as compared to before or during their period of infectiousness. This is because the virus has a “long tail” and a low level of the virus remains for a long time after infectiousness, even though the individual has ostensibly recovered during this time. PCR tests use cycles (Ct) to amplify the signal to a set threshold and after many cycles even a very low viral load will be detected. This lowers the false negative rate, but it also raises the false positive rate and raises the rate for this third kind of error: a true positive that occurs after infectiousness. On the issue of viral load, the WHO writes:

“careful interpretation of weak positive results is needed (1). The cycle threshold (Ct) needed to detect virus is inversely proportional to the patient’s viral load…Action to be taken: Provide the Ct value in the report to the requesting health care provider.”

In conclusion, it is not always clear what a positive test result means, particularly when the test is used for mass screening of the population, and when the test is used repeatedly on the same individuals. If the prevalence in the community low, then the test may be a false positive even if the test is highly accurate, and the chances of this occurring grow with each additional test of the same individual. The WHO concludes their guidance by writing:

Most PCR assays are indicated as an aid for diagnosis, therefore, health care providers must consider any result in combination with timing of sampling, specimen type, assay specifics, clinical observations, patient history, confirmed status of any contacts, and epidemiological information.

Finally, I note that this discussion pertains to the use of tests for screening of asymptomatic individuals, rather than for patients experiencing symptoms, or for contact tracing where there is good reason to expect that an individual has been exposed to the virus. If there are other indicators of disease, then Bayes rule tells us that there is a much greater probability that a positive test accurately indicates the presence of disease. This occurs because the prevalence of the disease is higher among the population experiencing symptoms and higher for the population who have had a recent exposure to someone with the disease. In brief, this discussion concerns the ways in which things might go wrong when a test designed as a diagnostic tool is instead used for mass screening of the entire population.

David Huber:

Thanks to Adrian Staub, Carlo Dallapiccola, Rosemary Cowell, and William Cowell for helpful discussion and comments.

UPDATE 2/8/2021: The positivity rate for UMass asymptomatic screening has recently surged to above 2%. This seems to indicate an alarming increase in local infections. However, this positivity rate is approaching the positivity rate for symptomatic testing for the state of Massachusetts, but in general the positivity rate for symptomatic testing should be lower than the positivity rate for asymptomatic testing. UMass uses a mixture of two different PCR tests each day (an in-house version and the Broad institute’s PCR test). What’s needed is a breakdown by the two types of tests to ascertain whether they yield the same positivity rate. In any case, I still urge the asymptomatic testing program to follow WHO guidelines to obtain a second test following a positive test for asymptomatic individuals.

UPDATE 3/22/3021: William Cowell posted a comment in regard to asymptomatic screening in UK schools. In his comment he compares two different kinds of second tests that might be used after a positive first test. The graphic shown here provides some supporting information for his comment.

Delusions of Virus Control in a Free Society

One of the more confounding aspects of the SARS-CoV-2 pandemic is the degree to which changes in human activity and behavior (socialization between households, opening/closing of schools and/or universities, adoption of face coverings, restriction of travel between regions, opening/closing of various businesses, etc.) are responsible for the numerous waves of infections seen across geographical regions such as US states or European nations.  Conventional wisdom seems to be that the main driver of regional surges is either failure to appropriately implement mitigation/suppression efforts, or, in situations where they have been implemented, non-compliance by individuals.  In this scenario, regional epidemics are thought to be “controllable,” but only if the right combination of mitigation or suppression measures are implemented, at the optimal moment and for the appropriate amount of time, and only if the population were to fully comply.  On the mechanistic level, the logic is straightforward, as a respiratory virus cannot spread if hosts are kept as separated from each other as possible, either physically (aka social distancing) or effectively (face coverings and hygiene measures).  There is also an abundance of empirical evidence that at least the most draconian forms of suppression are very effective:  the 70-day and 111-day strict lockdowns in Hubei, China, and Victoria, Australia, respectively, are famous examples.  “Softer” forms of mitigation, of the variety that have become common in the US and Europe since April 2020, undoubtedly also shape the course of infections and the ensuing hospitalizations and deaths, but a closer look at the data that has been compiled over the last 10 months reveals a much more complicated and perplexing story than is commonly expressed in the media and communicated to the public by public health and government officials.

In late Spring, 2020, there was widespread concern that a few US states were “opening up too early and too much” and would face an explosion of exponential growth of cases, as had been experienced in the Northeastern states in March and April.  Georgia, Florida and Texas are some of the larger states that were the focus of such attention.

“In an announcement last week, Kemp abruptly reversed course on the shutdown, ending many of his own restrictions on businesses and overruling those put in place by mayors throughout the state. On Friday, gyms, churches, hair and nail salons, and tattoo parlors were allowed to reopen, if the owners were willing. Yesterday, restaurants and movie theaters came back…Kemp’s order shocked people across the country…In the grips of a pandemic, the approach is a morbid experiment in just how far states can push their people. Georgians are now the largely unwilling canaries in an invisible coal mine, sent to find out just how many individuals need to lose their job or their life for a state to work through a plague.”, (“Georgia’s Experiment in Human Sacrifice:  The state is about to find out how many people need to lose their lives to shore up the economy,” Amanda Mull, 29 April 2020)

In reality, although the COVID epidemic has indeed taken a serious toll on these states, the outcome of reopening in early summer was not as catastrophic as predicted.  For purposes of comparison, Fig. 1 shows the daily COVID deaths, normalized by population, for Massachusetts (which did not “reopen early”), Georgia and Florida (which did).

Figure 1: Weekly average of COVID deaths per day, normalized to population (deaths per 100,000 persons), for Massachusetts, Florida and Georgia.

Even just a casual glance at the time evolution of the epidemic in these three states invites a number of questions.  On 18 May, 230 days ago (as of 2 Jan. 2021), restrictions on social distancing and business closures began to be lifted in Massachusetts, yet the daily number of cases, and deaths, continued to fall, leveling off and staying relatively low for the next several months.  Why?  In Georgia and Florida, similar restrictions were lifted even earlier (approximately 250 days ago), and, eventually, to an even greater extent (e.g. opening of bars, clubs and university campuses, and 100% in-person K-12 instruction).  Instead of a sharp, exponential growth of the epidemic, as experienced in Massachusetts and elsewhere in March, there was a more muted, drawn-out period of elevated cases and deaths, slowly falling off until about two months ago.  How can this be explained?   And why were these states castigated for reopening their economies and allowing people to socialize again?  Some experts are now expressing regrets for the messaging from this past Summer:

“University of Minnesota epidemiologist Michael Osterholm, a member of Biden’s advisory board, said one March mistake was closing businesses in places in the middle of the country that had seen almost no cases. ‘Was it appropriate to shut down so many things back then when there was so little, if any transmission? I think you can argue now that probably was not the best use of resources … it clearly alienated the very populations that we needed to have work with us,’ he says.

The time was squandered and so was public trust. He compares the situation to hurricane warnings. People take them seriously because they are usually right. In many Midwest states, people went into emergency mode at the wrong time.

Last spring’s approach left the public full of rancor and deeply divided, with some seeing the restrictions as tyrannical and others convinced, just as wrongly, that if people weren’t ‘selfish’ the control measures would have eradicated the virus. That’s never been feasible in a country where so many people live in crowded housing and can’t afford to stay home.”, (“Pandemic Regrets?  Experts Have a Few,” Faye Flam, 29 Dec. 2020)

Another common belief was that eight months of pent up “COVID fatigue,” combined with increased socialization and travel during the Thanksgiving holiday period, would lead to a pronounced, and especially deadly new surge of cases.[1]  Surprisingly, this does not seem to have had a marked effect on the trajectory of the epidemic in the US:

“More than three weeks after Thanksgiving, epidemiologists and local health officials across the country are picking apart the holiday, seeking signs of the pandemic’s latest riddle: the Thanksgiving effect… Still, experts said that, in general, parts of the country that were improving pre-Thanksgiving continue to improve post-Thanksgiving, while other regions experiencing surges before the holiday continue to worsen, suggesting that any nationwide Thanksgiving effect was muted.”, (“As Christmas Nears, Virus Experts Look for Lessons from Thanksgiving,” 20 Dec. 2020)

In fact, in a number of states in the Midwest and Northern Plains, cases peaked before Thanksgiving (38 days ago) and have since fallen sharply, without additional lockdown measures having been implemented (Fig. 2)!

Figure 2: Weekly average of COVID deaths per day, normalized to population (deaths per 100,000 persons), for selected Northern Plains states – North Dakota, South Dakota, Nebraska and Iowa.

What, then, are the conclusions we can draw from this confusing picture?  The dynamics of a pandemic are complex, with an enormous number of confounding factors contributing to the timing, duration and relative sizes of peaks and troughs in the spread of the virus across the landscape.  The gross effects displayed in the figures presented here and in the various COVID online dashboards are likely shaped dominantly by regional growth of community immunity[2], seasonal variation of the basic reproduction number[3] (in temperate climates, for instance, all respiratory diseases strongly surge in Fall and Winter, and almost completely disappear in the Summer) and other factors over which we exert limited control.  For regions with similar climatic conditions, population density, levels of economic activity and median age, the trajectories of the epidemic are strikingly alike (Figs. 3 and 4).

Figure 3: Weekly average of COVID deaths per day, normalized to population (deaths per 100,000 persons), for selected Northeastern states – Pennsylvania, Massachusetts, New Jersey, Connecticut and New York
Figure 4: Weekly average of COVID deaths per day, normalized to population (deaths per 100,000 persons), for Massachusetts, Italy and France.

We would do well to avoid the hyperbole[4], the shaming over behavior[5], the pitting of “red states” against “blue states,”[6] etc., that have characterized so much of our public discourse, and recognize that nobody is “winning” the pandemic, and reasonable, empathetic individuals will disagree on how to weigh the unavoidable tradeoffs associated with COVID mitigation and suppression efforts.  Many mainstream, influential epidemiologists and public health experts understood, at the very start, the enormous complexity of the problem, the difficult tradeoffs to consider and the necessity for a balanced, level-headed approach, as exemplified in the Op-Ed written on 21 March 2020 by Michael Osterholm, prominent member of President-Elect Biden’s coronavirus advisory group:

“China and Italy have imposed near-draconian lockdowns in an effort to halt the spread of covid-19. But how and when will these two ‘test’ nations return to normal life? And when they do, will there be a major second wave of cases? If that happens, should they simply ‘rinse and repeat’?… Consider the effect of shutting down offices, schools, transportation systems, restaurants, hotels, stores, theaters, concert halls, sporting events and other venues indefinitely and leaving all of their workers unemployed and on the public dole. The likely result would be not just a depression but a complete economic breakdown, with countless permanently lost jobs, long before a vaccine is ready or natural immunity takes hold… But the best alternative will probably entail letting those at low risk for serious disease continue to work, keep business and manufacturing operating, and ‘run’ society, while at the same time advising higher-risk individuals to protect themselves through physical distancing and ramping up our health-care capacity as aggressively as possible. With this battle plan, we could gradually build up immunity without destroying the financial structure on which our lives are based.”, “Facing covid-19 reality: A national lockdown is no cure,” Michael Osterholm and Mark Olshaker, 21 March 2020.

It is curious that, back in March 2020, Osterholm was so willing to acknowledge the damage caused by the long-term implementation of strict virus suppression measures, but, like many experts, seems so much less willing to do so now. After 10 months, the available data provide very little evidence that the “soft lockdown” measures implemented by Western countries have actually suppressed the virus – they have largely shifted the waves to slightly later points in time. The notion that we should be able to control the virus with sheer willpower and abstention at this point seems based on wishful thinking rather than data. It is true that we are far from “out of the woods” with this pandemic, and in some regions of the world (like the UK), a more transmissible variant threatening to overwhelm hospitals may be justification for the short-term implementation of extreme measures, locally. But in regions not currently on the brink of crisis, we must be careful not to use the delusion of control to justify black-and-white moral judgements of others’ behavior that only add to the strife of this exceptionally challenging era.

Carlo Dallapiccola and Rosie Cowell (

Thanks to Dave Huber and Adrian Staub for helpful discussion and comments.

[1], “Thanksgiving Will Soon Empty Campuses. Will Students Bring Coronavirus Home?  Experts worry that some of the hundreds of thousands of departing students will be ‘little ticking time bombs,’” Shawn Hubler, 9 Nov. 2020.

[2], “Modeling suggests lower COVID-19 cases in Lombardy’s second wave,” Lakshmi Supriya, 12 Nov. 2020., “Report 9 – Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand,” Neil Ferguson et al, 16 Mar. 2020: “The more successful a strategy is at temporary suppression, the larger the later epidemic is predicted to be in the absence of vaccination, due to lesser build-up of herd immunity.”

[3], “Global Seasonality of Human Seasonal Coronaviruses: A Clue for Postpandemic Circulating Season of Severe Acute Respiratory Syndrome Coronavirus 2?” You Li et al, 21 July 2020.

[4], “Wearing masks could save more than 100,000 US lives through February, new study suggests,” Jacqueline Howard, 23 Oct. 2020., “It’s Time to Scare People About Covid,” Elisabeth Rosenthal, 7 Dec. 2020.

[5], “Maskless Parties And Crowded Beaches Across U.S. As Coronavirus Spikes Over Holiday Weekend,” Nicholas Riemann, 5 July 2020.

[6], “As Covid Has Become a Red-State Problem, Too, Have Attitudes Changed?” Robert Gebeloff, 30 July 2020.

COVID-19 Facts (with focus on Massachusetts)

last updated 01/02/2021


  • Average age of COVID-19 death in Massachusetts: 81yrs[1]
  • Proportion of COVID-19 deaths in Massachusetts associated with an underlying condition: 98.2%[2]
  • Proportion of COVID-19 deaths in Massachusetts in Long Term Care facilities: 58.7% (see here)


  • Massachusetts has suffered more COVID-19 deaths/million than all European countries and all US States except New Jersey and New York:
    • COVID-19 cumulative deaths/million in hardest-hit European country of Belgium: 1,737 (1/2/2021)
    • Massachusetts’ rank among States, by deaths/million: 3rd (after New Jersey and New York)
  • As of 1/2/20, Hampshire County has suffered more COVID-19 deaths/million than the US National average and most European countries including Italy, the UK, Spain (and many more than Sweden)
    • COVID-19 cumulative deaths/million in Hampshire County: 1,250 (calculated from here and here, 1/2/2020)
    • Italy 1,241; UK 1,096; Spain 1,087; Sweden 861 (worldometers, 1/2/2021)


  • The large majority of Massachusetts’ COVID-19 deaths occurred before July 2020 (e.g., see here, scroll down to plot of Daily Reported Deaths, observe area under curve)
  • From early April to early June 2020, Massachusetts saw thousands of excess deaths, compared to recent prior years (see here – scroll down to the plot and select Massachusetts as the jurisdiction).
  • Since July 2020, Massachusetts has recorded:
    • ~3,800 COVID-19 deaths (calculated by subtracting deaths here from deaths here)
    • fewer than 100 excess deaths in total from any cause, compared to recent prior years (see here, true of data reported up to 1/2/2021).
    • The above two facts clearly do not square with each other. See here for a discussion of whether we have been over-attributing deaths to COVID-19 in Massachusetts in recent months.

[1] In the two weeks leading up to Dec 26, 2020. This figure has hovered at 80-82 yrs for the entire pandemic.

[2] Cumulative up to and including 12/29/2020. See page 45 of this report.

Why is Sweden a Bogeyman?

Though Sweden is a small country of about 10 million people, its response to the Covid-19 pandemic has captured the world’s attention.  As almost everyone knows at this point, Sweden followed a different path than its neighbors.  Schools have stayed open, businesses have (for the most part) stayed open, and mask-wearing was never mandated.  

It is difficult to overstate the level of media interest in how Sweden is faring during the pandemic.  The New York Times alone has devoted at least 14 articles (listed below, in reverse chronological order) to this topic.  There may be more – this list includes only those whose title explicitly mentions Sweden!  The language of these titles seems to reflect a newsroom reaching an increasingly clear and confident verdict on the success of the ‘Swedish experiment’.

  • “In Sweden, Infections and Calls for a Lockdown are Rising” (12/17/2020)
  • “As cases surge and criticism swells, Sweden rethinks its response” (12/16/2020)
  • “Abandoning its loose approach to virus controls, Sweden clamps down” (11/18/2020)
  • “Pandemic Exposes Holes in Sweden’s Generous Social Welfare State” (10/08/2020)
  • “How cuts to Sweden’s social welfare state led to a wave of death in nursing homes” (10/8/2020)
  • “Vilified Early Over Lax Virus Strategy, Sweden Seems to Have Scourge Controlled” (9/29/2020)
  • “Sweden Tries Out a New Status:  Pariah State” (6/22/2020)
  • “Sweden Stays Open. A Deadly Month Shows the Risks.” (5/15/2020)
  • “I Live in Sweden.  I’m Not Panicking” (Opinion, 5/15/2020)
  • “Coronavirus and the Sweden Myth” (Opinion, 5/4/2020)
  • “ ‘Life Has to Go On’:  How Sweden Has Faced the Virus Without a Lockdown” (4/28/2020)
  • “Is Sweden Doing it Right?” (Opinion, 4/28/2020)
  • “In the Coronavirus Fight in Scandinavia, Sweden Stands Apart” (3/28/2020)

Closer to home, a recent guest column in the Daily Hampshire Gazette  (COVID Wars, Thérèse Soukar Chehade, 12/22/2020) discussed the question of why “the media went on the attack” against Sweden, which seemed, in the author’s view “driven by a strange and mean-spirited wish to see the country fail.”

As if on cue, today (1/1/2021) the Gazette published a reply from Shelly Berkowitz, MD, entitled “Columnist pushes ‘pseudo-scientific’ fraud.”  Dr. Berkowitz writes:

Advocating for people in the U.S. to value the Swedish approach to the pandemic is a little like selling hydrogen for dirigibles the day after the Hindenburg crashed and burned in 1937.

Soukar Chehade seems to be unaware that the Swedish “experiment” has been universally recognized as a crushing failure and that the Swedish government has abandoned this disastrous policy of seeking “herd immunity,” and has issued COVID restrictions that are in line with most European COVID responses.

Sweden’s immediate Scandinavian neighbors — Norway and Finland — have COVID death rates that are 8-10 times lower than Sweden’s catastrophic pandemic carnage.

Is it true that the Swedish ‘experiment’ is a ‘crushing failure,’ let alone that it is universally recognized as one?  

Let’s start by comparing Sweden to other European countries, as Dr. Berkowitz has done.   Dr. Berkowitz is correct that in Sweden, Covid-related mortality has been 8-10 times greater than in its neighbors Norway and Finland:  According to the latest data from Johns Hopkins, Sweden has had 85.70 deaths per 100,000 population, while Finland has had 10.17 and Norway 8.20. 

Many other European countries, however, have had substantially higher Covid-related mortality than Sweden; to take just a few examples from various parts of the continent, Belgium is at 170.97 deaths per 100,000 population, Slovenia at 130.46, Spain at 108.80, and Switzerland at 89.77.  After approximately 9 months of this pandemic, Sweden’s death toll is entirely unremarkable in this broader European context; it is near the middle of the pack.  Norway and Finland are the outliers in Europe, at the extreme low end of Covid-19 impact.

The same picture emerges if, instead of focusing on recorded deaths from Covid-19 itself, we focus on the total number of excess deaths in each country, from all causes, as compiled by Euromomo.  In these z-score plots, the number of deaths is substantially above the seasonally-adjusted, predicted number of deaths when the solid blue line is above the dashed red line; see the Euromomo site for technical details.  Note that these plots allow direct comparison of the relative numbers of excess deaths in countries of different sizes; in any country, a solid blue line that reaches a z-score of 5 means that a country’s death count is five standard deviations above the expected count for that country, in that time of the year.

In the three plots below, we see that Sweden did indeed have a ‘wave’ of excess deaths in the spring of 2020, which was not present in Finland or Norway.

But now compare Sweden to Belgium, Slovenia, Spain, and Switzerland.  

Here we see, again, that the Covid-19 pandemic has had a less severe impact in Sweden than in these other countries; we also see that these countries differ substantially in when the toll of the pandemic was felt.  In Spain, like in Sweden, the death toll was mostly in the spring; in Slovenia and Switzerland the toll was mostly in the fall, though Switzerland also had a smaller wave in the Spring; in Belgium there have been two clear waves, with another small wave in between.

Is there a justification for focusing specifically on Norway and Finland as the appropriate comparisons for Sweden, as Dr. Berkowitz does, and as many other media outlets have done?  The implicit assumption seems to be that because the three are all Scandanavian countries, in close geographical proximity, Sweden would have done as well as Norway and Finland if only they had adopted more stringent lockdown measures.  

But does geographical location actually predict the severity of a country’s Covid impact? There is little indication that it does.  Covid mortality per 100,000 population is much higher in Spain (108.80; again, all data from Johns Hopkins) than in Portugal (67.17); it is much higher in Belgium (170.97) than in the Netherlands (66.89); much higher in the UK (110.73) than in Ireland (46.09).  In a statistical model predicting the severity of a country’s Covid impact, it is not clear that geography, or even the severity of the impact in adjacent countries, would play much role at all. Thus, there is no clear reason to judge Sweden in comparison to Finland and Norway, as opposed to judging Sweden in comparison to, say, Belgium or Slovenia.

Finally, let’s consider the impact of Covid in Sweden compared to the U.S., rather than to European countries, as well as the impact compared to Massachusetts and Hampshire County specifically, where the debate in the pages of the Daily Hampshire Gazette is taking place.  The U.S. has experienced 105.68 Covid deaths per 100,000 people – higher than Sweden, at 85.70.  Massachusetts has experienced 180 deaths per 100,000 people – more than double that of Sweden!  Even Hampshire County has experienced 123 deaths per 100,000 people, more than Sweden.  (These last two values are computed based on the latest state and county-level death counts from the NY Times.) 

We are left, then, with no evidence that the Swedish experiment has been a “crushing failure,” as Dr. Berkowitz puts it.  Nine months in, Sweden’s choice not to ‘lock down’ has left it in the middle of the European pack, in terms of Covid impact, and with fewer Covid deaths per 100,000 population than the U.S., Massachusetts, or Hampshire County.  At the same time, Sweden has managed to continue to educate its children, and has avoided many of the other health costs and economic costs of lockdowns.  This bears repeating: Sweden has a lower Covid death count, per 100,000 population, than Hampshire County, despite the fact that we in Hampshire County have closed our schools and colleges, shuttered businesses, and enforced social isolation.

Ms. Chehade is right:  It is an interesting question why the media and expert opinion have been so eager to condemn Sweden’s response. It is, perhaps, as interesting as the question of whether Sweden’s response is the right one.

Adrian Staub (

Thanks, as usual, to Rosie Cowell, Carlo Dallapiccola, and David Huber.

Addendum: For added visual impact, I attach a plot of the number of daily COVID deaths (weekly average, to smooth over fluctuations in daily reporting of data) for Sweden and Massachusetts, normalized by population (i.e. deaths per 100,000 people). As can be seen, except for a span of about 7 days at the very beginning, at no point during the pandemic has the death rate in MA been lower than that in Sweden, and much of the time it was more than a factor of two higher.

Carlo Dallapiccola

The End of the Pandemic: A Case for Optimism

As we reach the end of a year in which the world has suffered through the worst respiratory-disease pandemic in a century, it is natural that we look ahead and wonder what we should expect for the coming year.  Speculation about the timeline for a “return to normal” began as early as April, when the pandemic had just begun to unfold in Europe and North America.  Nine months later, it is increasingly a topic of discussion both in the public sphere and in casual conversations amongst friends and neighbors.  One of the more striking aspects of this discourse is how persistently gloomy it remains in many corners, despite the mounting evidence that augurs a relatively quick return to the vibrant, healthy society that existed before the pandemic.  Much of this pessimism can be attributed to the ever-present reminders of the most frightening aspects of the pandemic – the COVID dashboards and graphics, the steady drumbeat of reporting of death milestones, the comparisons of the death toll to that of terrorist attacks – and the sensationalist reporting of outcomes that are exceedingly rare and, often, only very tenuously attributable to COVID (Kawasaki-like disease in children[1], teeth falling out[2], erectile disfunction[3], psychoses[4]).  All the while, positive signs are typically shrouded in a cloud of caveats and qualifying statements that cast doubt on the reliability of the information.  Over time, this has solidified into a standard narrative that has proved remarkably difficult to counter.  The end result is a populace increasingly pushed to the limits of COVID fatigue, left wondering if society will ever regain its footing.

Early in 2020, experts spoke of an effective end of the pandemic and return to a “new normal” in late 2021, at the earliest, with the arrival of an effective vaccine coming too late to make a significant difference in the overall timeline.

“we must be prepared for at least another 18 to 24 months of significant Covid-19 activity, with hot spots popping up periodically in diverse geographic areas…So, lacking a vaccine, our pandemic state of mind may persist well into 2021 or 2022…” (“This Is the Future of the Pandemic,” Siohban Roberts, 8 May, 2020)

This set the baseline for expectations:  a pandemic, with its concomitant non-pharmaceutical interventions (NPI), consisting of lockdowns, social distancing and other suppression efforts, that will span a miserably long period of 18 to 24 months.

As we entered the Fall, however, the first glimmers of hope for a more rapid escape from the nightmare were emerging:  early results from several vaccine trials were promising, and timelines indicated that millions of doses could be ready for distribution to the population as early as the end of the year.  Not to be deterred, the reflexive posture of the media was to temper expectations and frustrate any nascent effort to begin seeing the light at the end of the tunnel!

“Americans are also overestimating what a vaccine might do. Many are focusing on whether approval is being rushed as a campaign ploy, but that’s almost beside the point. It seems likely that a vaccine will be approved this fall and that it will be ‘effective.’ But it’s very unlikely that this vaccine will be a game changerWe don’t know yet where a coronavirus vaccine will fall, although something along the lines of a flu shot seems more probable. We don’t know how long whatever immunity it provides will last. We don’t know whether there will be populations that derive more or less benefit…Even this assumes, of course, that we can distribute the vaccine widely and quickly (which is doubtful), that most people will get it (many won’t) and that we will succeed in prioritizing distribution so that those most at risk will get it first (flying in the face of decades of disparities in the way health care is distributed).” (“Stop Expecting Life to Go Back to Normal Next Year,” Aaron Carroll, 15 Sep., 2020)

In November, many of these unknowns evaporated, when efficacy and safety results for the Pfizer and Moderna vaccines were finally released:  efficacies of around 95%, far surpassing expectations, and no reported serious adverse effects in the more than 20,000 individuals who participated in the vaccinated arm of each of the trials.

“’This is really a spectacular number,’ said Akiko Iwasaki, an immunologist at Yale University. ‘I wasn’t expecting it to be this high. I was preparing myself for something like 55 percent.’” (“Pfizer’s Early Data Shows Its Vaccine is More Than 90% Effective,” Katie Thomas, David Gelles, Carl Zimmer, 9 Nov., 2020)

“The drug maker Pfizer said on Wednesday that its coronavirus vaccine was 95 percent effective and had no serious side effects…The data showed that the vaccine prevented mild and severe forms of COVID-19, the company said. And it was 94 percent effective in older adults, who are more vulnerable to developing severe Covid-19 and who do not respond strongly to some types of vaccines.” (“New Pfizer Results:  Coronavirus Vaccine is Safe and 95% Effective,” Katie Thomas, 18 Nov., 2020)

Surely with a vaccine of spectacularly high efficacy presently in deployment, Americans could now begin to entertain some degree of hope that life would return to normal on an appreciably shorter timeline than previously imagined?  Not so fast, we are told.  While a “minority” of the experts believe this possible, the consensus is, strangely, as pessimistic as ever – no change in the baseline!

“A minority of the epidemiologists said that if highly effective vaccines were widely distributed, it would be safe for Americans to begin living more freely this summer: ‘I am optimistic that the encouraging vaccine results mean we’ll be back on track by or during summer 2021,’ said Kelly Strutz, an assistant professor at Michigan State University…But epidemiologists are a very cautious group. Most said that even with vaccines, it would probably take a year or more for many activities to safely restart, and that some parts of their lives may never return to the way they were.  Karin Michels, professor of epidemiology at U.C.L.A., said it would probably be many years until it was safe enough to ‘return to approximately the lifestyle we had.’ She said, ‘We have to settle to live with the virus.’” (“How 700 Epidemiologists are Living Now, and What They Think is Next,” 4 Dec., 2020)

This mostly-unidentified panel of 700 experts are indeed some of the most cautious members of the population. According to the article, 74% had yet to send their children on an outdoor playdate, 38% had not yet “hiked or gathered outdoors with friends,” 28% still were not “bringing in mail without precautions,” and 10% had not even “gone on errands, such as to the grocery store or the pharmacy.”  Little wonder, then, that they foresee such a long, possibly never-ending road to the pre-COVID life many of us are already forgetting had ever existed.

Even Dr. Anthony Fauci, America’s most respected expert in infectious diseases, is apt to keep us off balance – grateful for the unprecedented speed in which highly-effective vaccines have been developed and brought to market, while all the same quietly ‘moving the goal posts.’

“Recently, a figure to whom millions of Americans look for guidance — Dr. Anthony S. Fauci, an adviser to both the Trump administration and the incoming Biden administration — has begun incrementally raising his herd-immunity estimate…In a telephone interview the next day, Dr. Fauci acknowledged that he had slowly but deliberately been moving the goal posts. He is doing so, he said, partly based on new science, and partly on his gut feeling that the country is finally ready to hear what he really thinks…” (“How Much Herd Immunity is Enough?” Donald McNeil, 24 Dec., 2020)

Does any of this make sense?  The myriad deleterious effects from NPIs being just as serious as COVID itself, should we not strive to end them on as hasty a timeline as reasonably possible?

If we make a reasonable appraisal of the situation in the US, and put aside any biases we may have due to ‘gut feelings,’ the forecast for 2021 is decidedly more positive than most seem to realize.  The distinguishing feature of the pandemic is the relatively high rate of hospitalizations and deaths attributable to COVID in the elderly population, and it is in this population that a successful vaccination campaign will be paramount.  Nursing home residents make up a dramatically disproportionate share of COVID deaths.  They represent less than 1% of the US population (about 2.5 million, in all), but so far account for more than 38% of all COVID deaths ( – and in some states, the figure is much higher (in Massachusetts, it stands at 60%).  More than one million Americans have already received the first dose of the vaccine, and by the middle or end of January we can expect that all residents and workers in nursing homes will have been vaccinated; in the Massachusetts schedule (, this group is second highest in priority amongst the six groups covered by Phase 1 of the campaign, where the projected timeline is December 2020 – February 2021.  The next-most at-risk demographic is elderly Americans living in the community (outside of care homes):  persons over 70 years old, about 15% of the population, account for 80% of COVID deaths (  A credible estimate for when this group will have been fully vaccinated is the end of March or April (Phase 2 in the Massachusetts plan).  The Pfizer and Moderna vaccines have been shown to work nearly equally well in the elderly population as they do in in the younger population, and they reduce Sars-Cov-2 infections that present as mild to moderate symptoms by a factor of twenty.  There were zero cases of severe symptoms and zero deaths in the vaccinated groups, signifying protection against severe forms of COVID very close to 100%.  It follows that hospitalizations and deaths due to COVID will steadily fall through the Winter, as the most at-risk members of the population become inoculated.  As an example, the daily rate of COVID deaths in the population over 70 would be reduced, via vaccination, from its current value of about 1,800 (nearly its highest value since the pandemic began) to less than 90! 

But the fraction of the population that is vaccinated does not tell the whole story – there are also the tens of millions of Americans who have acquired durable immunity through infection by the virus itself.  Many seem to believe, having been influenced by early, misleading media reports regarding waning antibody levels, that immunity is either very fleeting or even on-existent.  The truth of the matter is that reports of reinfection remain vanishingly small and all evidence points to long-lasting immunity – likely a year or two, possibly even longer.

“Within the last couple of months, several scientific studies have come out — some peer-reviewedothers not — indicating that the antibody response of people infected with SARS-CoV-2 dropped significantly within two months. The news has sparked fears that the very immunity of patients with Covid-19 may be waning fast — dampening hopes for the development of an effective and durable vaccine.

But these concerns are confused and mistaken…”

(“Scared That COVID-19 Immunity Won’t Last?  Don’t Be,” Akiko Iwasaki and Rusian Medzhitov, 31 July, 2020)

“How long might immunity to the coronavirus last? Years, maybe even decades, according to a new study.” (“Immunity to the Coronavirus May Last Years, New Data Hint,” Apoorva Mandavilli, 17 Nov., 2020)

The CDC estimates that by the end of November 2020 about 91 million Americans had already been infected (,  Using the same model parameters, it is conceivable that around 120 million, more than a third of the US population, will have been infected by the end of December.  Unlike in the earliest phase of the epidemic, younger Americans (< 50 years of age) are now the majority of those being infected.  Combining this large population of younger Americans who have acquired immunity naturally with the vaccinated population, which will initially skew towards older Americans, the full population-wide, or herd, immunity will already be very substantial by mid-Spring 2021, when the vaccine becomes available to the general population (Phase 3 in the MA plan).  The growth of herd immunity through the Winter and Spring will drive hospitalizations and deaths in the under 70 segment of the population to progressively lower levels, even before accounting for the effects of vaccination in this same group.

A likely scenario is that by Summer 2021 COVID will have ceased to be a serious public health threat and Americans of all ages will be leading normal lives, unburdened by the demands of social distancing.  The restaurant, hospitality, tourism and cultural event sectors of the economy will finally emerge from the devastation wrought by the pandemic and we will be on the road to full economic recovery.  Such is the story of every pandemic of the last 100 years (Fig. 1), and there is absolutely no reason to believe that this one is any different.

“According to historians, pandemics typically have two types of endings: the medical, which occurs when the incidence and death rates plummet, and the social, when the epidemic of fear about the disease wanes.” (“When Will the Pandemic End?  And How?” 10 May, 2020)

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Figure 1: Number of deaths (all-cause) per month, per million inhabitants, Jan. 1900 – 1 Sep. 2020, as recorded by the US CDC.  Notable respiratory-disease pandemics are indicated (most other peaks are seasonal, non-pandemic influenza deaths).  N.B. The graph includes data through the end of Aug. 2020, when Covid-19 deaths tallied 188,000 – there is a second peak of an additional 140,000 total deaths in the final four months of the year (106 deaths per month, per million).  Credit: @VoidSurf1 (Twitter Handle), from public CDC data (

Carlo Dallapiccola (

Thanks to Rosie Cowell, Dave Huber and Adrian Staub for helpful discussion and comments.

[1] “15 children in New York City have developed a puzzling and serious inflammatory syndrome possibly linked to covid-19,” 5 May, 2020.

[2] “Their Teeth Fell Out. Was It Another Covid-19 Consequence?” 28 Nov., 2020.

[3] “The Pandemic Is Stressing Your Body In New Ways,” 4 June, 2020.

[4] “Small Number of Covid Patients Develop Severe Psychotic Symptoms,” 28 Dec., 2020.

Measuring the Toll of a Pandemic

Setting policy in a pandemic is about trading off between alternative bad outcomes: coronavirus deaths, chronic virus-related illness, postponed medical procedures, economic devastation, missed education, increased mental illness, and on and on. There is no way out of a pandemic without incurring costs on some, or all, of these dimensions. But to chart the best course, we need, at a minimum, a good way of counting the toll for each.

Locally, most public schools remain closed and two recent Gazette reports highlighted one way of measuring the impact of this. As feared, children from low-income and racial/ethnic minority demographics have experienced a disproportionate rise in absenteeism under remote education. Doubtless, this will widen the already unacceptable gap between the most and least fortunate children in our society. Other negative effects of non-pharmaceutical interventions (NPIs) have impacted millions of adults: devastating social isolation in people who live alone, economic ruin for small business owners, financial and mental health crises in the unemployed, increased domestic violence against women, and more. These negative impacts of pandemic-mitigation measures will take years to measure; counting their toll as the pandemic unfolds is almost impossible.

What is certain is that both the virus itself and the NPIs it has invited have caused public health crises of unprecedented magnitude; both COVID and the lockdowns will lead to significantly reduced life expectancy in the worst afflicted groups. In deciding how to balance them, it is critical that we have an accurate estimate of the current and likely future impact of this devastating viral disease. How many people is COVID killing, now, in Massachusetts, and how many more virus-caused deaths can we expect to see under different policies?

The most straightforward way to do this is to look at COVID-related deaths in the comprehensive daily data summaries provided by the Massachusetts DPH (published on, the New York Times, and These data show COVID-related deaths at a steady level of 12-15 per day during the summer, followed by an increase, albeit not yet an exponential one, since October.

COVID deaths in Massachusetts this Fall have therefore been lower than in many states, but certainly not at zero. In our attempts to minimize the harsh effects of lockdowns, how should we set a threshold for determining the virus to be sufficiently “under control” to allow businesses and, most importantly, schools to open? A related question: are we sure that our measures of COVID-caused deaths are accurate? Are they too conservative (missing many cases) or too lax (chalking up deaths to COVID inappropriately)?

A hint that the counting of deaths is a difficult business comes from large variability in Case Fatality Rates in different regions ‒ that is, the number of deaths divided by the number of detected infections. (This is always an over-estimate of the Infection Fatality Rate, the number of deaths per number of infections, because we will always miss a greater proportion of COVID infections than of COVID deaths). However, if we examine two regions in which the per capita testing rate is similar, and hospital care can be assumed similarly effective, we’d expect the CFR to be about the same. In mid-September, Massachusetts was recording about 14 daily deaths against a backdrop of 355 daily detected cases 2-3 weeks earlier (assuming a 2-3 week mortality lag). This equates to a CFR of 3.9%. These data should be interpreted in the context of the daily testing rate of 638 per 100,000 people, keeping in mind that as the testing rate goes up, we catch more cases, and so the CFR should go down. In New York state on the same dates, the CFR was 1.3%, despite a testing rate of 443 tests per 100,000. That is, even though the testing rate was almost 1.5 times higher in Massachusetts than New York, the CFR in Massachusetts was 3 times greater. In Connecticut, the CFR was 1.3%, and the testing rate was 438 per 100,000: again, MA was reporting a death rate 3x higher despite a testing rate 1.5x greater. It seems implausible that Massachusetts, with some of the best hospitals in the world, was delivering significantly poorer clinical care than these other states. Therefore, either NY and CT were undercounting their COVID deaths (perhaps not testing enough), or Massachusetts was over-counting them (perhaps ascribing COVID as the cause of death in individuals who had multiple acute or chronic health problems at the time of their passing, of which COVID was not the most problematic). How can we determine which was true?

A reliable way to assess the accuracy of the recorded death toll is to look at excess mortality from all causes, by comparing deaths in 2020 to deaths in recent years. The CDC provide these data in week-by-week plots. Excess deaths tell us indirectly about the number of deaths attributable to this extraordinary disease by allowing us to factor out the number of deaths we should expect from other “ordinary” causes ‒ a number which is seasonal, increasing reliably every Fall. The plot below shows weekly deaths in Massachusetts, from 2017 to 2020, with the orange line representing the threshold for excess deaths (relative to the same week in years 2013 – 2019, see technical notes here). The devastating impact of the first COVID wave in MA is evident in the 11 weeks marked with a red cross (+ means deaths exceeded the threshold). But since early June, only a single week in October reported excess deaths, with a total of 4 deaths above the excess death threshold (the plot includes data reported up to the week ending Nov 21).

The same plots for New York and Connecticut (find them here by selecting the relevant jurisdiction) show a similarly devastating Spring wave, followed by a very modest second wave, but one that does include some excess deaths in recent weeks (although in NY this “second wave” resembles the 2018 seasonal flu in terms of excess mortality). The overall picture ‒ with CFR higher in MA than in NY and CT, but excess deaths lower ‒ suggests that, rather than NY and CT under-counting deaths to produce a falsely low CFR, Massachusetts may be over-attributing deaths to COVID, resulting in an over-estimated CFR. In line with this, the cumulative number of COVID deaths had reached ~10,600 in Massachusetts by the end of November, but this number does not square with the cumulative excess mortality in MA from February to the end of November, which stands at around 7,500 (calculated from data here).

To be clear, I am far from suggesting fraud or scientific malpractice in the counting of deaths in Massachusetts. The attributing of deaths to COVID is tricky. The discrepancy of around 3,000 deaths (between excess mortality and COVID mortality) can perhaps be explained by the fact that the average age of COVID deaths is 81 years in Massachusetts, with 98% of deaths occurring in individuals with underlying conditions. In other words, many deaths are occurring in frail individuals with multiple co-morbidities, and it must often be impossible to distinguish between people who die of COVID (the virus is unambiguously the cause of death) and people who die with COVID (having had a positive test, but with the cause of death being a complex mixture).

In view of these analyses, it is clear that excess mortality is the best measure of the impact of COVID on society (even though it may even overestimate the true count, if the extraordinary circumstances of 2020 have increased other kinds of deaths, e.g., from dementia, untreated heart disease or unscreened cancer).

At the present time, we have no good measure of the long-term impact of school closures on children’s health and cognitive development, or of the economic ruin delivered by lockdowns on adults’ life expectancy. We know that the impact is likely, at least for some, to be devastating. As measured by excess mortality, the current impact of COVID on the Massachusetts population seems insufficient to justify the complete or even partial closure of elementary schools. It’s time to count the impact of COVID accurately and weigh it more carefully against the impact of our mitigation measures.

Rosie Cowell (

Thanks to Carlo Dallapiccola, Dave Huber and Adrian Staub for helpful discussion and comments.

How to measure COVID risk: Lives or life-years?

The implicit aim of government and state policies regarding COVID and the explicit focus of news media coverage of the pandemic is on lost lives. This is understandable. Every life is precious, and every lost life is a tragedy. However, everyone would agree that a life cut short is more tragic than a life well-lived to old age. One measure of the tragedy is in terms of lost life-years; a life cut short is a greater loss of life-years. It is the current focus on lives rather than life-years that leads to policies designed to protect the elderly from COVID more than younger people (e.g., special shopping hours), since the lives of the elderly are more likely to be lost. Paradoxically, however, many young people are unduly fearful of COVID and many older people are somewhat cavalier regarding COVID. But maybe both attitudes are rational when considering the potential risk of lost life-years rather than lost lives.

A remarkable feature of COVID deaths is their age dependency, with nearly a 1,000-fold difference between the probability of death from COVID for the elderly as compared to children. In fact, it has been pointed out that the age distribution of COVID deaths is similar to the age distribution of all deaths (see graph below, noting the huge spike for 85+, which is nearly identical for COVID versus death by any other cause). In other words, regardless of one’s age, the probability of dying in the next year is directly proportional to the probability of dying from COVID, once infected. As a direct result of this, the average age of COVID deaths is nearly the same as life expectancy (life expectancy is the mathematical average of all lifespans in the population).

US COVID-19 Reported Deaths by Age 2/1 – 11/28

Roughly speaking, around 1% of people in the U.S. die each year from any cause (i.e., around 3 million). Early in the pandemic, it was believed that the infection fatality rate for COVID was approximately 1% (note that infected is not the same as confirmed COVID cases considering that many infections are never confirmed). Because the infection fatality rate and death by any cause are both 1%, and in light of the age distribution of COVID deaths, this implies that the risk of dying from COVID, if one were infected, is equivalent to the probability that one would die in the next year from any cause. A 20-year old does not expect to die in the next year whereas an 80-year old knows there is a non-negligible chance that their next year might be their last. Putting this differently, one might say that the risk of death from living a normal year of life is about the same, for any given age group, as the risk of dying from a COVID infection.

Subsequent work established that the infection fatality rate is lower than 1%, and is approximately .5% in the United States (i.e. 5 deaths for every 1,000 persons infected). This number is heavily dependent on the age distribution in the population, with values ranging from .1% (Kenya) to 1% (Japan) across different countries (CDC report release November 24, 2020). So, if 1% of the population dies from any cause each year in the U.S., and if .5% of infected individuals die from COVID in the U.S., this implies that the risk of dying from COVID, if infected, is approximately equivalent to the risk of dying from living for 6 months, regardless of one’s age.

This life-years perspective on COVID risk can be used to determine which COVID mitigation strategies are sensible, weighing the costs against the benefits, and which are too extreme. For instance, an extreme form of lock-down in which no one was allowed to leave their home (i.e., shelter in place) for an entire year might be sensible to protect society from the bubonic plague, given its 50% infection fatality rate. However, such a policy would not be sensible for COVID – it would not make sense for everyone to suffer through 12 months of utter misery simply to save themselves from 6 months worth of life-risk from COVID. During 12 months of shelter in place, the probability that one would die from something other than COVID would be greater than the probability of dying from COVID, if infected.

If society is not in extreme lock-down, this ‘6-month benchmark’ can be applied to guide recommended activities. Wearing a mask does not entail much misery and it doesn’t have any lasting negative consequences. The same is true for avoiding hugs with people outside your home. But how about losing one’s job? By how much does that shorten one’s life expectancy? If it does so by more than 6 months, then it is better to risk COVID than to lose your job. How about missed education, which is known to shorten life expectancy? Gaining weight because of lack of access to a gym? Letting a small business collapse? Many of the COVID restrictions could result in the loss of personal endowments (e.g., weight gain, education loss) and the loss of brick-and-mortar institutions (e.g., businesses, universities, libraries, athletics clubs) that will cause the loss of more than 6 months’ worth of life expectancy for many of the people affected, or, if not lost life expectancy, then a severe reduction in the quality of life for a time period substantially greater than 6 months.

This life-years risk assessment highlights why there is an urgent need for government relief. Only with payroll relief and other grants (e.g., to help schools reopen) can we keep people employed, keep children in school, and keep our businesses and institutions in existence. This relief can help keep the life-years cost of COVID mitigation measures under the 6-month threshold.

David Huber (

Constructive comments welcome. Thanks to Rosie Cowell, Carlo Dallapiccola, and Adrian Staub for very helpful discussion.

So many new cases in Massachusetts, but relatively few deaths. Why?

For a first post on this blog, I’ll address a question of immediate local concern:  How worried should we be about the local and statewide increase in Covid-19 cases that we’ve seen in the last couple of months?  Are we heading back to the levels of hospitalizations and deaths that we saw in the spring?  A number of local sources have been sounding the alarm in the last few weeks, including here and here.  To anticipate the take-home message:  No, we are not heading back to springtime levels of hospitalization and death, because what predicts hospitalizations and deaths is not the number of cases, but the number of cases among older people…and we don’t have very many in Massachusetts.

Let’s start by looking at some data.  Below are the Massachusetts data from today’s (12/2/2020) New York Times Covid-19 dashboard.

On the upper left, we see the striking increase in the number of documented Covid-19 cases in Massachusetts in the last two months or so.  But the two graphs on the right indicate that there has been only a very slight increase in the number of Covid-19 deaths, and only a slightly steeper rise in the number of hospitalizations.  While the number of daily cases in recent weeks has actually exceeded the number during the ‘first wave’ in the spring, deaths and hospitalizations are a small fraction of their numbers in the spring.  

The dissociation between cases and deaths is even more striking when we zoom in on Hampshire County.  The New York Times now presents county-level data; a screenshot from today is below.

In Hampshire County, there has been a ‘wave’ of cases this fall, like at the state level, but simply no detectable increase in deaths.  (The Times does not provide county-level hospitalization data.) 

What should we make of this dissociation, whereby cases have increased dramatically, but deaths only slightly, or not at all?  Two simple positions could be labeled ‘alarmist’ and ‘denialist’.  The alarmist position would hold that the deaths are coming; an increase in Covid-related deaths will take a few weeks to appear after an increase in reported cases.  But a delay of a few weeks would not be enough to account for this pattern, as cases began their steep rise in October, at both the state and county level.  The denialist position would emphasize that we are identifying more cases only because of expanded testing; we are finding asymptomatic and mild cases that will not lead to hospitalization or death, which we would not have identified in the spring, when testing was quite restricted.  But this can’t account for all of the increase in cases; the left two panels of the first figure show that while the number of daily tests has gone up by perhaps 50% since early October, the number of cases has gone up by perhaps 300%. 

So, neither the alarmist explanation (the deaths are coming, just wait) nor the denialist position (there’s no real increase in cases, only an increase in testing) can fully explain why we have seen such a steep rise in cases, but without much (or any, in Hampshire County) rise in deaths.  This blog is called Covid Balance, after all!  Fortunately, this puzzle has a clear solution, though it does not seem to have been much discussed in the media.

Below are two sets of graphs from the Massachusetts Department of Public Health.  The left panel of the first figure shows the age distribution for cases reported as of May 29.  The left panel of the second figure shows the age distribution for cases reported in the midst of the ‘second wave,’ in the two weeks prior to November 27. 

We see a rather remarkable shift.  In the first wave in the spring, the average age of individuals diagnosed with Covid-19 was 52, while in November, the average age was 39.  But much more important is what is going on at the right edge of the age distribution.  In the spring, 14.6% (13882/95271) of all individuals who were diagnosed with Covid-19 were over 80 years old, and 23.6% were over 70.  In the two-week period in November, only 3.2% (1149/36194) were over 80 years old, and 7.6% were over 70.  It is difficult to overstate the importance of this shift:  In the Spring, almost 1 out of 7 Covid-19 cases occurred in people over the age of 80, and almost 1 out of 4 over age 70; in November, it was about 1 out of 31 over age 80, and 1 out of 13 over age 70.  

Below are two more figures from the Massachusetts DPH, this time showing the age distribution of Covid-19 deaths in the pre-May 29 period, and in the two weeks prior to November 27.  

We see that in both time periods, the majority of individuals who died from Covid-19 were in the 80+ age group.  In fact, the percentages of deaths that were among individuals in the 80+ group are remarkably similar:  62.6% in the first period, and 62.7% in the second.  People over 70 accounted for 84.9% of all deaths in the first period, and 82.6% in the second.  The average age of death was 82 in the first period, and 81 in the second.  

How can older adults account for a similar majority of deaths in November and in the spring, while accounting for a much smaller proportion of cases in November?  The answer is simple.  The risk of hospitalization or death from Covid-19 is so much greater for the elderly that most deaths will be among older people even when the vast majority of cases are among younger people.  Below is a graphic from the CDC that illustrates just how extreme are the age-related changes in Covid-19 hospitalization and death rates.

The risk of death from Covid-19 is, according to the CDC, 630 times higher in a person over the age of 85 as in a person in the 18-29 year-old comparison group.  This difference in mortality risk is so extreme that the number of cases in younger people is almost irrelevant to the overall number of deaths.  If you want to know how many deaths from Covid-19 will occur in a particular area, don’t ask how many cases there are; ask how many cases there are among elderly people.  

The simple answer to the question of why there has been little increase in deaths and hospitalizations in Massachusetts during this second wave of cases is that this wave is occurring mostly among younger people.  It is certainly an interesting question why this is so, and there are probably multiple contributing factors.  One factor might be increased awareness of what I’ve highlighted here, i.e., how the severity of Covid-19 depends on age.  This has probably made many older people quite cautious, while at the same time it has allowed younger people to take some risks, as they are aware that getting Covid-19 is not likely to result in serious health consequences, for them personally.

The impressive rise in cases, in Massachusetts and in Hampshire County more specifically, does not indicate that we are heading back toward springtime levels of death and hospitalization.  To the contrary, with the current age distribution of cases, where only 3.2% of cases are in people over the age of 80, it would be essentially impossible for the state of Massachusetts to return to the levels of hospitalization and death that we saw in the spring.  The age distribution could change, of course, but at present we should be reassured that we are keeping the health impact of Covid-19 low, in relative terms, by doing a fairly good job at preventing the most vulnerable among us from getting it. 

Adrian Staub (

Constructive comments welcome. Thanks to Rosie Cowell, Carlo Dallapiccola, and Dave Huber for very helpful discussion.