Equation 1. Calculation of mortality rate
Mortality rate = Number of deaths
Number of cases
New data and an intriguing case example suggest the mortality rate may be decreasing. What does this mean for the days ahead?
This column is the third in a series1,2 written to help psychiatrists and other health care providers better understand the range of severity of illness that the coronavirus disease 2019 (COVID-19) virus can cause so that they can better explain the facts (as we know them today) to their patients and their families.
Calculating the mortality rate
The mortality rate reported for COVID-19 has declined since the earliest days of the pandemic. This is partly due to better knowledge about the infection and better protocols that have been developed to treat the more serious forms of the illness. However, arguably the greatest decline in mortality rates is the result of being better able to identify who has been infected with the virus. This increase in identification of infections has increased the size of the denominator, while the numerator has remained relatively unchanged.
Equation 1. Calculation of mortality rate
Mortality rate = Number of deaths
Number of cases
“Cases” refers to individuals who have been infected with the Sudden Acute Respiratory Syndrome Coronavirus 2 (SARS CoV-2).
The calculation of the mortality rate is illustrated in Equation 1. As explained in the first column, cases of COVID-19 initially were determined by the number of individuals who sought medical attention because of fever, cough, respiratory distress, or other flu-like symptoms and had no other potential causes for these symptoms including not having the seasonal influenza.1 Thus, it was a symptomatic diagnosis, just as it the case with most psychiatric diagnoses. Using this definition of a case, the denominator was smaller than the actual number infected, with the degree of underestimation being a function of how many individuals were infected but either were asymptomatic, did not have sufficient symptoms to seek medical attention, or for some other reason did not seek out care. The degree of underestimation would result in proportional overestimation of the mortality rate based on the Equation.
Case example: A floating, unintentional laboratory experiment
Cruise ships can function as naturalistic research experiments with more controls than is true in clinical practice. The following summary, based on the original report published by Ing and colleagues3, details such an example. In May 2020, a trio of Australian physicians and health researchers who traveled on an expeditionary cruise to the Antarctic Peninsula published a report about their experiences in the medical journal Thorax. Two of the authors, Alvin J. Ing, MBBS (Hons 1 Syd), MD FRACP, and Christine Cocks, were passengers on the cruise, and Jeffrey Green, MD, was a ship physician for this expedition.
Of the individuals who tested positive, 104 individuals (81%) were asymptomatic at the time of testing. The other individuals who tested positive (about 1 out of 5) were symptomatic at the time of testing. Of those 24 symptomatic individuals, 16 (two-thirds of the group) had only fever and mild symptoms, while 8 (one-third of the group) had to be medically evacuated. Four of those individuals required intubation and ventilation, and 1 of them died (mortality rate = 0.8% based on 1/128). He was a 50-year-old crew member with no known comorbid medical illness (personal communication, Ing 2020).
Note: When a population is small (as was true for this cruise ship with about 100 positive individuals), the confidence interval for a rare adverse event (ie, death, which was < 1 out of 100) is large. In such instances, a general rule for estimating the 95% confidence interval is that the upper and lower boundaries would be 3 times higher and 3 times lower, respectively, compared to what was observed. Hence, the estimate of the 95% confidence interval for the mortality rate in this case would be between 2.4% and 0.27% (ie, 0.8% multiplied by and divided by 3, respectively).
Difference in mortality rates based on symptoms versus on the total infected
In the example of the cruise ship, the mortality rate would have been calculated as 4% when the presence of symptoms was required to define a case (ie, 1 death among 24 symptomatic individuals) versus 0.8% when laboratory evidence of infection was sufficient to define a case (1 death among 128 infected cases). The result is a 5-fold difference in the calculated mortality rate depending on whether it was calculated based on symptomatic cases versus all infected cases.
The difference in practice would likely be even greater because mildly symptomatic cases may be missed in clinical practice because asymptomatic patients may not present for medical attention or because their symptoms might be attributed to a common cold or a mild flu-like syndrome. The number of infected individuals on the ship may also have been underestimated, since all 89 individuals who tested negative for actively shedding virus did not have antibody testing. It is possible that some of those who tested negative for actively shedding the virus may have been infected but the virus had already been cleared via an immune response before testing.
While the availability of reliable and valid laboratory tests is a great advance over the early symptomatic-based diagnosis (readers may want to think about the implications for symptomatic diagnosis in psychiatry), the tests can only determine if an individual is actively shedding virus. Obviously, a negative test does not tell us whether the individual will become infected in the future (even within an hour of having the test done) nor does it tell us if the individual has already been infected and has mounted a sufficient immune response to have eradicated the virus. (The first column in this series1 discussed this issue in more detail, along with the need for other reliable and valid tests to identify a history of an eradicated infection that will hopefully convey immunity against the virus—perhaps lifelong as with measles or perhaps much shorter as with seasonal influenza.)
The number of participants in this naturalistic experiment was small, which means that the 95% confidence interval for a mortality rate of 0.8% would be large as previously discussed. However, this caveat does not change the basic observation that the initial mortality rate, by virtue of being based on symptomatic cases, would be several times higher than the true mortality rate with a virus such as SARS CoV-2 because it can produce many mild and even asymptomatic cases.
Figure 1. Cumulative COVID-19 Hospitalization Rate per 100,000 Population in the United States Through July 4, 2020 This graph shows the hospitalization rate of SARS CoV-2 positive individuals as expressed per 100,000 individuals in the US population in each specific age bracket without regard to whether they have been infected or not. This latter point is a critical distinction between this graph and the one shown in Figure 2. The X-axis is the age groups and the Y-axis is the number of hospitalizations. Above each bar is the observed rate for each age bracket. The curve shows the line of best fit which fits an exponential function. Source: COVID-NET: COVID-19-Associated Hospitalization Surveillance Network, Centers for Disease Control and Prevention. https://gis.cdc.gov/grasp/COVIDNet/COVID19_3.html
The mortality rate observed on this ship is consistent with rates observed in the low-risk population discussed in the second article in this series.2 This population has a low risk of developing an illness that requires hospitalization (Figure 1) and a low risk of death (below 1% but nevertheless not zero; Figure 2) from infection with the SARS CoV-2 virus. In contrast, nearly 35% of those who die will be 85 years of age or older. The individuals younger than 85 who die will most likely have comorbid medical illnesses (Figure 2).
For these reasons, it is extremely important to protect high-risk populations via social distancing, the use of masks, and limited contact with anyone nonessential to the health and well-being of these individuals. The experience from this cruise ship also illustrates 2 important factors to consider when endeavoring to protect the vulnerable population. First, there is long incubation period between infection and the development of symptoms (8 days or more). Second, a high number of individuals who are infected are not symptomatic (more than 80% in the case of the experience on this ship).
Figure 2. Cumulative Deaths from COVID-19 in the United States Through July 4, 2020 This graph shows the data on 112, 226 deaths in the United States as a function of age. The X-axis is the age groups and the Y-axis is the percentage of all deaths that occurred in individuals within each specific age bracket. Above each bar is the observed percentage for each age bracket. Note that the percentages for the youngest age groups look to be 0 because they are so low that they cannot be distinguished from 0 on the graph. Note: Approximately 33% (1 out of 3) of all deaths occurred in individuals who were 85 years of age or older. Source: Centers for Disease Control and Prevention. https://data.cdc.gov/NCHS/Provisional-COVID-19-Death-Counts-by-Sex-Age-and-S/9bhg-hcku
The role of the media
The media can inform the population, but they can also hype topics to increase audience ratings to drive their revenue as has clearly been the case with COVID-19 reporting (in the author’s opinion). The most recent, egregious example is the focus on increasing numbers of cases, which is directly relevant to the discussion in this series of columns. What the media has not adequately explained (in the author’s opinion) is the nuanced understanding that a rising number of cases may not necessarily be bad but rather could be a positive development—if the cases occur in the low-risk and not the high-risk population and morbidity and mortality remain low. As explained in the second column in this series2 a higher number of low-risk cases could bring us closer to the number needed to achieve community (ie, “herd”) immunity.
Achieving such immunity is an important consideration because a reliable, safe, and effective vaccine has not been developed.While there is hope that a safe and effective vaccine may be available by late this year or early next year, the historical track record suggests it may be years before one is successfully produced for the world population. The reasons for caution relative to vaccines involve many facets, and a full discussion of this issue is beyond the scope of this column. One reason for caution is that vaccines may promote an antibody response that may alone be sufficient to prevent the illness, but it may be that a T cell (lymphocyte) response is also necessary to prevent the illness and that such a response may not occur with some vaccines. In addition, people have to be willing to receive the vaccine. Meanwhile, a recent survey found that 49% of Americans reported that they would be agreeable to vaccination against COVID-19 if such a vaccine becomes available, but 31% were not sure and 20% said they would not be vaccinated.4 Of course, these responses may change as the public becomes more familiar with the illness and more is known about the efficacy and safety of any vaccine.
With that said, there are several important concerns about a strategy of letting the virus propagate through the low-risk population while protecting the vulnerable population. First is the question of how feasible it will be to accomplish this dual goal. For example, grandparents want to see their grandchildren, but the grandchildren may be asymptomatic even though they are shedding the virus. Protecting the vulnerable populations will also be difficult if the current problem of compliance with wearing masks to decrease the spread of the virus in the United States continues.
Second, a small percentage of the low-risk population may be at risk for serious infections, and even death, for reasons that have not yet been identified, or at least not in the public domain. The mortality rate in what should be low-risk individuals is perhaps between 0.01% and 0.1% (Figure 2). However, the problem is that those numbers are so small that the 95% confidence intervals will be large, as previously discussed, so that it is difficult to calculate the rate with certainty.
While a difference between 0.01% and 0.1% may seem small, the issue is what such numbers mean in large populations. For example, a major issue is how to re-open schools. There are 72.7 million children 0 to 17 years of age in the United States (www.childstats.gov/americaschilrden/tables/tables/pop1/asp). If the mortality rate in this population is within the noted range, that would translate to between 7270 and 72,700 deaths of children 0 to 17 years of age (ie, the difference between a risk of 0.01% versus 0.1%).
Given these estimates, one must ask: What risk is acceptable (and to whom) to achieve community immunity and save more individuals in the higher risk groups? Or, should that even be a consideration? How does one balance risk when it comes to lives of young healthy individuals versus older and/or unhealthy individuals? These are the type of calculated decisions that Americans have not faced since perhaps World War II. Parenthetically, this discussion illustrates how important it is to know the mortality rate and provides a quite crude example of the type of mathematical modelling of a pandemic that is driving governmental decisions. Currently, it appears that every citizen is free to make these decisions (eg, to wear a mask or not) based on their understanding of the illness and their sense of community responsibility (because wearing a mask protects others more than the life of the person wearing the mask).
Third, little is known about whether and how long immunity lasts after a person has been infected and recovered (again highlighting the problems posed by a novel human pathogenic virus). The assumption is that immunity has occurred with recovery but even that remains to be proven. Beyond that, there is the potential problem that the virus may be able to mutate to overcome immunity. It should be kept in mind that all these caveats also apply to the development of a vaccine. Life is not always straightforward.
Finally, there is little known about whether there are after-effects of viral infection, such as shingles with herpes zoster. What has been established is that the virus can cause damage to other organs beyond the lungs in some (probably small) fraction of those infected. The virus attacks the circulatory system and, hence, can affect any organ in the body even though it probably does so relatively rarely.5
The ship’s experience illustrates how difficult it is to stop the spread of the SARS CoV-2 virus unless social distancing and masks are used, especially since people can be are infectious long before they become symptomatic. In the case of the Antarctica cruise ship, SARS CoV-2 spread to the majority of the passengers and crew, even though the passengers were sheltering in their cabins and wearing masks as soon as the first individual developed symptoms.
This article was originally published in the Journal of Psychiatric Practice and has been adapted here with permission from Lippincott Williams & Wilkins. The original version can be found online at www.psychiatricpractice.com.
Dr Preskorn is professor in the department of Psychiatry and Behavioral Sciences. The author notes that he has received grants/research support from or has served as a consultant, on the advisory board, or on the speaker’s bureau for Alkermes, BioXcel, Eisai, Janssen, National Institute of Mental Health, Sunovion, and Usona Institute. All clinical trial and study contracts were with and payments made to The University of Kansas Medical Center Research Institute, a research institute affiliated with The University of Kansas School of Medicine-Wichita.
1. Preskorn SH. Coronavirus disease 2019: The first wave and beyond. Psychiatric Times. April 28, 2020. Accessed August 3, 2020. https://www.psychiatrictimes.com/view/coronavirus-disease-2019-first-wave-and-beyond
2. Preskorn SH. COVID-19: Protecting the Vulnerable and Opening the Economy. Psychiatric Times. 2020;37(5):22-25.
3. Ing AJ, Cocks C, Green JP. COVID-19: in the footsteps of Ernest Shackleton. Thorax. 2020;75:693-694. May 27, 2020. Accessed August 3, 2020. https://thorax.bmj.com/content/thoraxjnl/75/8/693.full.pdf
4. Neergaard L, Fingerhut H. AP-NORC poll: Half of Americans would get a COVID-19 vaccine. ABC News. May 27, 2020. Accessed August 3, 2020.https://abcnews.go.com/Health/wireStory/ap-norc-poll-half-americans-covid-19-vaccine-70897024
5. Gupta A. Madhavan MV, Sehgal K, et al. Extrapulmonary manifestations of COVID-19. Nat Med. 2020;26:1017-1032. Accessed August 3, 2020. https://www.nature.com/articles/s41591-020-0968-3.pd