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: dehuber@umass.edu

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.”

https://www.theatlantic.com/health/archive/2020/04/why-georgia-reopening-coronavirus-pandemic/610882/, (“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.”

https://money.yahoo.com/pandemic-regrets-experts-few-133019805.html, (“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.”

https://www.nytimes.com/interactive/2020/12/20/us/covid-thanksgiving-effect.html, (“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.”

https://www.washingtonpost.com/opinions/2020/03/21/facing-covid-19-reality-national-lockdown-is-no-cure/, “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 (carlo.dallapiccola@gmail.comrcowell@umass.edu)

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

[1] https://www.nytimes.com/2020/11/09/us/colleges-coronavirus-thanksgiving.html, “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] https://www.news-medical.net/news/20201112/Modeling-suggests-lower-COVID-19-cases-in-Lombardys-second-wave.aspx, “Modeling suggests lower COVID-19 cases in Lombardy’s second wave,” Lakshmi Supriya, 12 Nov. 2020.  https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-9-impact-of-npis-on-covid-19/, “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] https://academic.oup.com/jid/article/222/7/1090/5874220, “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] https://www.cnn.com/2020/10/23/health/masks-ihme-model-study-wellness/index.html, “Wearing masks could save more than 100,000 US lives through February, new study suggests,” Jacqueline Howard, 23 Oct. 2020.

https://www.nytimes.com/2020/12/07/opinion/covid-public-health-messaging.html, “It’s Time to Scare People About Covid,” Elisabeth Rosenthal, 7 Dec. 2020.

[5] https://www.forbes.com/sites/nicholasreimann/2020/07/05/maskless-parties-and-crowded-beaches-across-us-as-coronavirus-spikes-over-holiday-weekend/?sh=50e43ddc4699, “Maskless Parties And Crowded Beaches Across U.S. As Coronavirus Spikes Over Holiday Weekend,” Nicholas Riemann, 5 July 2020.

[6] https://www.nytimes.com/2020/07/30/upshot/coronavirus-republican-voting.html, “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 (astaub@umass.edu)

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