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Measures of mortality and natality Deaths, births, and rates of changeOn this page: Proportions & rates Mortality Natality Life-tables
Proportions and rates
We have entitled the next section 'mortality' rather than 'mortality rate'. This is because several of the measures given below are proportions rather than true rates.
The better medical and veterinary journals now prefer that the term rate is only used to describe a change with time. Nevertheless, some of the proportions below are so often described as 'rates' that we have given the synonyms where appropriate. Moreover, ecologists use the terms finite (or multiplication) rates and instantaneous rates to distinguish between proportions and 'true' rates - for more discussion on finite and instantaneous rates see the related topic (above). Here we begin with a measure that is neither a proportion nor a rate - namely the number of deaths.
Number of deaths
The number of deaths in the population is the simplest measure of its mortality. For human populations, governments usually keep detailed records of the number and timing of deaths. But it can be more difficult to determine the number of deaths for a livestock population, and it may be difficult or impossible for wildlife or insect pest populations. The number of (recorded) deaths is analogous to the number of cases when considering measures of disease frequency.
Even though the total number of human deaths may be recorded fairly accurately (except in war situations), it is much more difficult to obtaining an accurate count of the number of deaths from a specific cause. This is because it is dependent on accurate diagnosis of the disease or condition the individual was suffering from - an issue discussed in the More Information page on measures of disease
If the population size is reasonably stable, the number of deaths is directly related to the mortality rate (defined under mortality rate below). This will usually be true for human populations, but again much less so for wildlife and (especially) insect pest populations.
Cumulative mortality and cumulative survival
The cumulative mortality (also termed mortality risk or finite mortality rate) is the proportion of individuals alive at the start of a period that die over that period. It is analogous to the cumulative incidence (the proportion of new cases of a disease), with deaths replacing cases as the numerator.
Cumulative mortality is sometimes qualified in relation to the cause of death. Hence all-cause cumulative mortality is the proportion of individuals dying from any cause over a given period and cause-specific cumulative mortality is the proportion of individuals dying from a specific disease over a given period.
As with cumulative incidence, the length of the period cannot be changed by simply dividing or multiplying the cumulative mortality by the length of the period required - hence a cumulative mortality of 20% over 1 month does not give a cumulative mortality of 120% over 6 months. Instead use the following formula:
The cumulative survival is the proportion of individuals alive at the start of a period that remain alive for a specified length of time. It is the complement of cumulative mortality - hence, if the cumulative mortality of piglets after 3 months is 11%, the cumulative survival is 89%.
Other proportional measures
These two terms are generally only used by medical and veterinary researchers.
Case fatality must be interpreted with caution. An episode of illness does not last for a fixed time interval - it varies depending on many factors. The time period used for estimating case fatality is usually the period of medical care. Hence the case fatality is dependent on the length of stay in hospital. Survival analysis, with follow up over a long period, provides a much better measure of mortality from a particular disease.
The proportional mortality is the proportion of deaths that are caused by a specific disease.
Be especially cautious with this measure. It is routinely misinterpreted by the media. A 10% proportional mortality from MSR in hospital wards (in other words 10% of all deaths result from MSR) is likely to be (wrongly) reported as a 10% (cumulative) mortality of all hospital patients.
The mortality rate (or death rate or mortality density) is the probability of an individual dying per unit time. A precise estimate is obtained by dividing the number of deaths in an interval by the (total) sum of time at risk over all individuals. It is analogous to the incidence rate, with deaths replacing cases as the numerator. Again we may refer to a cause-specific mortality rate, or the all-cause mortality rate.
The mortality rate as calculated above provides an estimate of the hazard function (also termed the instantaneous mortality rate) - which is the theoretical limit approached as the time interval approaches zero (see related topic
As with the incidence rate, we can use the average number at risk multiplied by the time period, to approximate sum of time at risk. When the exact time of death is unknown, the mortality rate has to be estimated in this way. This estimate of the mortality rate is sometimes called the crude mortality rate (or crude death rate).
Epidemiologists distinguish a number of different age-specific death rates for human populations:
Number of birthsThe same comments apply here as for the number of deaths. For human populations, detailed records are usually kept of the number of births and when they occurred, but this is less true for livestock populations - and not the case at all for natural populations.
Two terms are often used to describe reproductive capacity:
Natality rateA precise estimate of the natality rate (or birth rate) could be calculated by dividing the number of births by the sum of time at risk of giving birth over all individuals. But in practice an approximation is nearly always used, namely the number of births divided by the average size of the population multiplied by the time period. This gives the crude natality rate (or crude birth rate). For human populations it is commonly expressed per 1000 of the population.
The same method can be used to work out an age-specific birth rate, except that estimates are usually confined to the female part of the population. Hence the age-specific birth rate is obtained by dividing the number of female offspring by the average size of the population - of a specified age-group of females.
Life and fertility tables provide a standardized way of tabulating, summarizing and displaying mortality and natality data. Life tables were first used to describe mortality rates in human populations, but have since been widely used for many animal and plant populations. There are two general approaches to obtaining life table data:
The simplest method is to follow a
If we are recording time to death there are three possible outcomes for individuals in a study:
It may not be viable to follow cohorts of invertebrate populations, especially if the organisms are very mobile. For these the commonest approach is mark-release-recapture - as described in the related
The alternative is to take a cross-sectional sample to determine the numbers alive in each age group, and also determine the number of deaths in each age group during a given time period. This provides a static life table (or current life table, stationary life table or vertical life-table or time specific life table). For human populations information on the numbers of deaths in each age group is usually available from government records. For animal and plant populations such data can be obtained from age at death, providing individuals that have recently died can be aged, and are equally available to the sampling method.
Another approach to obtain a static life table is to estimate the mortality rates from the relative numbers in each age group. However, this method is only valid if a number of assumptions are made. The most important is that there is a stable age distribution - in other words the relative frequencies of each age class do not change over time. This will only be the case if birth and death rates are constant. For the simplest version of this method the population must also be stationary - in other words, the birth rate must equal the death rate, so that the population is neither increasing nor decreasing. These assumptions are very improbable for most populations including insect vectors of disease which is what this method is mainly used for.
Cohort and static life tables only give the same results for a given population if birth and death rates are constant. In practice they give different results because birth and death rates vary considerably over time in almost all populations whether human or animal.
The approach to life table analysis depends on whether we only use the number of events occurring within set intervals, or whether we utilise the precise timing of the event for each individual. The first of these termed standard life tables is the longer established method, but the newer Kaplan-Meier