Share of deceased cases

In infection epidemiology , the case-deceased proportion or (colloquially) case mortality is often referred to as the case-related fatality rate or case fatality rate , less often as the case fatality ratio , case fatality risk (CFR) or case fatality proportion (CFP) (outside of the Infection epidemiology also known as mortality rate  ) the proportion of people with a particular disease (cases) who die from this disease. The denominator is the number of incidence cases ; the numerator is the number of cause-specific deaths among these cases. The choice of the denominator results in different concepts:

• A case-deceased percentage can indicate the percentage of people with a certain diagnosed illness who die from this illness. A high number of undiagnosed cases makes the proportion of deaths appear higher than the actual mortality of the disease.
• The proportion of deceased cases can also refer to the proportion of all symptomatic cases ( #Symptomatic proportion of deceased cases ), which must be estimated using epidemiological model calculations.

The proportion of those who have died is a common statistical measure for the short-term severity of an acute illness and enables a direct assessment of the effectiveness of intervention measures. A related measure is the proportion of infected and deceased , which also includes undiagnosed cases in the number of cases, which must be estimated using epidemiological model calculations. There is a lot of talk in the media of a “death rate”. Definition and reference value (e.g. CFR, IFR, lethality, etc.) are often not mentioned, mixed up and confused.

Introduction to the problem

The lethality of a disease describes the proportion of sick people who die from the disease at some point. Lethality thus describes the "fatality" of an illness without depicting the "speed" of dying. One can also interpret lethality as the probability of dying from the disease under the condition of being ill. Analogously, the proportion of those who died in cases generally describes the probability of dying from the disease under the condition of being diagnosed with the disease . The proportion of those who have died is usually shown as a percentage. The attempt to estimate a lethality in this way is fraught with sometimes considerable systematic errors . An unreported number of unrecognized sick people leads to an overestimation of lethality because the deaths are related to too small a number of sick people.

Especially in the monitoring of outbreaks of infection, however, these measures cannot be determined satisfactorily because the sick would have to be tracked for at least as long as the illness lasts, but due to the urgency of the pending decisions, the duration of the illness cannot be waited for. One often makes do with dividing the deaths from the disease recorded in a period by the cases of illness recorded in the same period. The problem here is that the deaths follow the cases of illness in time, so that the mortality or the proportion of deaths would be underestimated as long as the number of new cases rises and would be overestimated as long as the number of new cases falls. In order to communicate these possible distortions, an estimate obtained in this way is also referred to as the raw case / deceased proportion or crude case fatality ratio .

A further bias arises in diseases with long disease courses in which patients in the meantime die for other reasons and thus the number of those who have died from the disease cannot be determined with certainty. The deceased percentage is therefore mainly used for acute illnesses with a short illness duration and less for chronic illnesses.

Labeling problem

The frequently used expression case fatality rate is viewed by many authors as incorrect, since it is formally not a rate but a quotient (“share”) ( English case fatality proportion (CFP) ). Ratios, proportions and rates are precisely defined and cannot be used as synonyms.

As a ratio ( english ratio sets) two similar sizes into consideration, but not to a specific range of values is limited, the case-dead-share is limited to values between 0 and 1, if it were, strictly speaking, a measure of risk ( case fatility risk )

Some epidemiologists reject the word “rate” for incidence measures in which the denominator is the “number of individuals” (instead of person time at risk ) and prefer, for example, terms such as proportion of incidence or cumulative incidence :

"This portion has been referred to as case fatality, case fatality rate, case fatality ratio and case fatality risk [...] to emphasize that it is a proportion that can take values ​​between 0 and 1, we can call it case fatality proportion. "

Variants of the deceased percentage

The deceased percentage is generally defined as:

${\displaystyle {\text{Fall-Verstorbenen-Anteil}}={\frac {\text{Anzahl der an der Krankheit Verstorbenen unter den diagnostizierten Fällen}}{\text{Gesamtzahl der diagnostizierten Fälle}}}}$

The diagnosed cases also include those who have died. The measure is therefore truly a proportion . A period of time can be specified to which the deaths relate, which results in different values ​​in each case; z. B. the 5 and 10 year deaths rates for breast cancer among women in the United States are approximately 14% and 24%, respectively.

In contrast to mortality , in which the entire population is at risk of dying in the denominator, the denominator in the case-deceased proportion only represents the total number of individuals who already have the disease.

Raw case-deceased share

The proportion of those who have died can also be approximated via the ratio of the number of sick people in a period and the number of people who have died in the same period:

${\displaystyle {\text{Fall-Verstorbenen-Anteil}}={\frac {\text{Gesamtzahl der an der Krankheit Verstorbenen in einem Zeitraum}}{\text{Gesamtzahl der diagnostizierten Fälle im gleichen Zeitraum}}}}$

This definition assumes that the likelihood of recovery would remain the same at any point in time after diagnosis. For some diseases, however, the longer the disease lasts, the more likely it is to be fatal. In this case, the true deceased percentage would be underestimated. The diagnosed cases and those who died of the disease do not come from the same population.

In order to obtain the most up-to-date values ​​possible in the course of a newly spreading epidemic or pandemic , a case-deceased proportion can be estimated using the reported cumulative numbers of the total number of diagnosed cases of the disease and the total number of deaths. This is also referred to as crude CFR or raw CFR and is a special case of this definition, since the entire duration of the epidemic or pandemic is used for the period. However, this information is initially a “raw” estimate. A more precise estimate is obtained from the time- and age-adjusted proportions of the deceased cases (see also # Delay- adjusted proportion of the deceased cases ).

Alternative proportion of deceased cases

As an alternative, especially to the raw number of cases with a known outcome (recovered and deceased cases), dividing by the number of cases with a known outcome, here based on the cumulative numbers since the outbreak of the epidemic or pandemic:

${\displaystyle {\text{Alternativer Fall-Verstorbenen-Anteil}}={\frac {\text{Gesamtzahl der an der Krankheit Verstorbenen}}{\text{Gesamtzahl der an der Krankheit Verstorbenen + Genesene}}}}$.

The above formula represents an alternative way of calculating the proportion of deceased cases. Since the denominator only contains cases with a known outcome that are not included, this definition would overestimate the true proportion of deceased cases for some diseases.

Share of cases and deceased persons in different countries during the Covid 19 pandemic

example

On February 27, 2020, China reported a total of 78,514 infected people in the wake of the COVID-19 pandemic . Of these, 2,747 died as a result of their infection and 32,926 recovered. Accordingly, the raw case-deceased percentage would be estimated at, according to the alternative definition, at . As the pandemic spread to other regions of China and around the world, significantly lower values ​​were sometimes measured for the proportion of people who died. ${\textstyle {\frac {2.747}{78.514}}=3{,}5\,\%}$ ${\textstyle {\frac {2.747}{32.926+2.747}}=7{,}7\,\%}$

Delay-adjusted proportion of deceased cases

In the case of rapidly spreading epidemics or pandemics with strong growth in the number of cases, strong distortions arise in the raw and alternative case-deceased proportion, since the time between the occurrence of a case and possible death is not taken into account. This delay can be modeled by the adjustment for the delay time-dead case portion ( English delay-adjusted case fatality ratio , abbreviated ): ${\textstyle CFR_{\text{del}}}$

${\displaystyle CFR_{\text{del}}={\frac {\text{Gesamtzahl der an der Krankheit Verstorbenen}}{\text{Gesamtzahl der diagnostizierten Fälle vor X Tagen}}}}$.

Confirmed proportion of deceased cases

In order to take into account the lack of comparability across different countries, it is advisable to only use cases confirmed by laboratories (e.g. by PCR ) for the denominator. To delimit z. B. also cases diagnosed by clinical symptoms, the designation confirmed (raw) case-deceased proportion is used for this. (here often as English (crude) confirmed case fatality ratioand thus abbreviated to cCFR .)

However, this measure is not always suitable for international comparisons if different test strategies are used.

Symptomatic proportion of deceased cases

The symptomatic case fatality rate ( sCFR ) is the proportion of infected people who show symptoms who die in the course of their infection. It is thus defined as:

${\displaystyle {\text{symptomatische CFR}}={\frac {\text{Gesamtzahl der infizierten Personen die Symptome zeigen}}{\text{Gesamtzahl der Todesfälle unter den infizierten Personen die Symptome zeigen}}}}$.

This proportion is clinically relevant for assessing the prognosis of the requirements for the healthcare system.

The proportion can be estimated using conditional probabilities . It is believed that the deceased received prior medical care and admitted to hospital. This is also known as the servity pyramid (in German severity pyramid ) that patients go through. Thus the probabilities regarding

• to receive medical care under the service, to be symptomatic,
• Hospitalization provided that they have received medical care, and
• Death on condition of hospitalization,

can be estimated as a single probability. A natural estimator would then be a product of the estimated individual probabilities. This is particularly practical in the case of mild illnesses, where the probability of death is low and therefore large sample sizes would be required to estimate the proportion directly. The individual probabilities, however, can be better determined in such cases.

Infected / deceased proportion

The infected-dead-share ( english infection fatality rate or infection fatality ratio , actually infection fatality proportion : in short, IFR ; colloquially " infection mortality ") is a derived from the case-dead-share level. In contrast to the proportion of deceased cases, which is based on the number of clinically ill patients, the proportion of infected and deceased includes asymptomatic cases. It thus indicates the proportion of deaths among all infected people for an infectious disease:

${\displaystyle {\text{Infizierten-Verstorbenen-Anteil}}={\frac {\text{Anzahl der an der Infektion Verstorbenen in einem Zeitraum}}{\text{Gesamtzahl der Infektionen im gleichen Zeitraum}}}}$.

The IFR differs from the case-deceased proportion in that it aims to estimate the risk of death in all infected persons: the cases with a diagnosed disease and the cases with an undiagnosed disease (asymptomatic and untested group). People who are infected but always remain asymptomatic are said to have "silent infections". The IFR is always lower than the CFR as long as all deaths can be accurately attributed to either infected or non-infected. The infected / deceased proportion estimates the risk of an infected person dying from their disease. The total number of cases is, of course, unknown, so that the true proportion of infected and deceased cannot be precisely calculated. In order to calculate the proportion of infected and deceased people, one must therefore estimate the total number of infections. Contrary to some media reports, the proportion of deceased cases is not identical to the proportion of infected and deceased and can even differ significantly from it.

Robert Verity, an epidemiologist at Imperial College London , stated, "IFR is one of the most important metrics alongside the herd immunity threshold and has an impact on the size of an epidemic and how seriously we should take a new disease."

Example: In the Covid-19 pandemic of 2020, an IFR of 0.36 percent was determined in a COVID-19 case cluster study for the former hotspot Heinsberg. The proportion of confirmed deceased was much higher at 1.98 percent.

Example: In a comparative analysis of 50 publications with 77 case-death numbers for influenza A (H1N1) (pandemic 2009), significant deviations and heterogeneities were found. The CFR found that it was mostly in the range of 100 to 5,000 deaths per 100,000 laboratory-confirmed cases, 5 to 50 deaths per 100,000 symptomatic cases, and 1 to 10 deaths per 100,000 in studies that refer to it based on the estimated number of infected people (according to the IFR).

Web links

• Rebecca A. Harrington: Case fatality rate in the Encyclopædia Britannica
• Pay please! 3.4% coronavirus case mortality, a "false number"? Some pandemic statistics. heise online , accessed on May 3, 2020.

Remarks

1. ↑ ^{a b} To indicate problems see section name issue .

Individual evidence

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17. ^ Peter Cummings: Analysis of Incidence Rates
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23. ↑ ^{a b} numbers, please! 3.4% coronavirus case mortality, a "false number"? Some pandemic statistics. heise online, accessed on May 3, 2020 . 
24. ↑ M. Famulare: 2019-nCoV: preliminary estimates of the confirmed-case-fatality-ratio and infection-fatality-ratio, and initial pandemic risk assessment. Institute for Disease Modeling 19 (2020).
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27. ↑ Camille Pelat, et al: Optimizing the Precision of Case Fatality Ratio Estimates Under the Surveillance Pyramid Approach. In: American journal of epidemiology (2014)
28. ↑ Thomas Czypionka et al .: Assessment of the economic consequences of the outbreak of the novel coronavirus (SARS-CoV-2) - April 21, 2020. (2020), p. 8.
29. ↑ Numbers, please! 3.4% coronavirus case mortality, a "false number"? Some pandemic statistics. heise online, accessed on May 3, 2020.
30. ↑ Hannah Ritchie, Max Roser: What do we know about the risk of dying from COVID-19? March 25, 2020, accessed May 3, 2020.
31. ↑ Smriti Mallapaty: How deadly is the coronavirus? Scientists are close to an answer June 16, 2020, accessed August 21, 2020.
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