# Lethality

The mortality rate (of Latin letum 'death' or lethal , deadly ') of a disease refers to the proportion of patients who will eventually die from the disease. 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. When calculating the lethality of an illness, the number of illness-related deaths is set in relation to the number of sick people; in the case of mortality, on the other hand, the deaths occurring during a certain period of time are considered in relation to the population. The mortality rate is understood to mean the ratio of the number of people who have died from a certain disease to the number of new cases of disease in a certain period of time; it is only sensible to calculate it in acute cases.

In medical parlance, lethal means something like "fatal" (see lethal dose ); with exitus letalis the "fatal outcome (of an illness)" is designated. In the case of genetic defects that lead to the death of the embryo or the newborn in humans or animals, one also speaks of lethal factors .

## Mortality rate

To determine the mortality rate, the ratio of people from a selected population who died of a certain disease in a selected period (e.g. one year) to the number of those who died from the disease within the same population and the same period is calculated and are acutely ill.

Most of the time, this ratio is given as a percentage or in parts per thousand , more rarely as a value between 0 and 1. In both cases, “zero” means that nobody dies of this disease.

${\ displaystyle {\ text {Lethality rate}} = {\ frac {\ text {Number of deaths from a specific illness within a certain period of time}} {\ text {Number of specific illnesses}}}}$

However, the mortality rate is less suitable for determining the individual risk of death of an affected person, since it B. can be strongly dependent on the selection of the population or the period. An alternative name for the mortality rate for the same concept, but almost exclusively in the epidemiology of infectious diseases is used is case fatality rate ( German  case-dead-share ).

Furthermore, the contagion index (probability of infection after contact with a specific pathogen) must be observed. In the case of polio e.g. B. the lethality is given as 0.0002 to 0.002 (0.02-0.2%). This number refers to the number of people infected, not the number of those who have come into contact with the virus. The contagion index is 0.001-0.003. This means that only 0.1–0.3% of (non-vaccinated) people become ill after contact with the virus. The lethality due to contact is therefore max. 0.002 x 0.003 = 0.000006 (= 0.0006% or 6 out of 1,000,000 or 480 out of 80 million).

 Number of diagnosed cases: 79200 Number of deaths: 65700 It follows ${\ displaystyle L = {\ frac {65700} {79200}} = 83 \, \%}$

The statement of lethality is particularly suitable for acute illnesses, because in principle all diagnosed cases must be followed up until the death or the definitive healing of the individual patient.

New diagnostic options and healing methods can lead to a dramatic change in mortality for a certain disease over a very short or very long period. Conversely, a drastic deterioration in the health care system can significantly increase the mortality of an illness - even if it may take years.

The stage at which a disease is diagnosed is often of decisive importance in determining lethality.

## Problems of interpretation

### "Age" weak point

When giving information on lethality, the age of the sick person must be taken into account. While the mortality rate at a pneumococcal - bacteremia is over 65 years at 30-50%, this combined is only 16-36% for all ages. The mortality rate of a disease in the population group of over 65-year-olds is significantly higher than in younger comparison groups (with the exception of infants ) , especially if there are comorbidities .

Example: The prostate cancer is a disease with high mortality, however, occurs usually in the higher manhood. Since the length of time that elapses from the onset of an illness to the death of precisely this illness is not recorded with the statement of the lethality , most patients do not experience death from this illness at all, but die with it from other causes of death .

The determined values ​​for lethality are therefore relative frequencies . They relate to a defined population and a defined period.

### Weak point dynamics

The lethality of an illness is only a statement on the probability of death in the event of illness if the recorded period is significantly greater than the changes in the illness over time and knowledge about the illness is large enough to keep the statistical errors small. In particular, the following points must be taken into account when interpreting the lethality of a dynamic disease ( epidemic , epidemic ), as they differ significantly from a stable disease ( endemic ):

1. Unknown infection rate or unknown disease rate after infection: Not every infected person gets sick, not every sick person is recognized as such.
2. Unknown deaths: Not everyone who died of an illness is recorded in the statistics.
3. Changes in the pathogen, the hygienic conditions, the treatment: The epidemiological indicators can change significantly.
4. Fluctuating case numbers within the recorded period: A base reproduction number greater or less than 1 results in statistical distortions.
5. The recorded period is not significantly longer than the incubation period or the average time to death.

Example : If a new epidemic epidemic occurs, it can mean that sick people are initially identified, but hardly any deaths, because the cause of death was not determined or was wrongly determined or both figures show a high number of unreported cases. The number of those who are infected and also become ill may also be unknown, but so weak that no diagnosis or the wrong diagnosis is made. In addition, the number of sick people is growing, while the number of those who have died of the disease lags behind the average time between illness and death.

• At the beginning, a cumulative 10 sick and 2 dead are registered, whereby only every 10th case is recorded.
• After 30 days, 90 sick and 22 dead were registered, 40% of which were recorded during this period.
• After 60 days, 370 sick and 92 dead were registered, 70% of which were recorded during this period.
• After 90 days, a total of 1090 sick and 272 dead were registered and the coverage rate in the last period has risen to 90%.

In this example the mortality would be 20% at the beginning, 24.4% after 30 days, 24.8% after 60 days and 24.9% after 90 days. However, these figures only apply if the number of unreported cases is negligible or the number of unreported cases of the sick and the dead almost cancel each other out, as in this example: without the unreported number, the mortality rate in this calculation example would be a constant 25%.

However, since the average time between illness and death in this calculation example is 30 days, the mortality after illness is actually 50%.