Mortality Rates

Mortality rates (synonym: death rates) are used to quantify the tendency to die in a population during a given time period. Since death can be considered as the utmost form of “unhealthiness” or “disease,” mortality rates are major (inverse) health indicators. Because measuring morbidity is often difficult, mortality rates or mortality-based indicators like life expectancy remain the major indicators used to ascertain the level of health in a society or social group.

Mortality rates always refer to a time period, usually 1 year, though monthly or even daily mortality rates are sometimes calculated for particular situations or processes—a war, epidemics, and so on. The annual crude death rate (m) can be thought as the proportion of the population dying during 1 year—presently not much above or below 1% throughout the world—and is computed by dividing the count of deaths during the year, d, by the total population or “population at risk,” p, generally approximated by the population at mid year, and expressing the result per thousand or, more generally, per some power of 10. Therefore, m = (d/p) × 10k, and k = 3, if the rate is expressed per 1,000.

Mortality rates can be conceptualized as an approximate measure of the probability of death during a given period of time in members of the group for which the rate is calculated, or as a special type of incidence rate, where the “disease” is death. If we know that 48,700 deaths occurred over 2 years in a population of 2.1 million people, we can estimate the annual mortality rate during that period as approximately 11.6 per 1,000, since (48,700/2)/2,100,000 =0.011595. However, when computing death rates for small groups, for instance, in a longitudinal study or a clinical trial, it is usually needed to consider properly the exact period of observation, expressing the rate per person-time units, and taking into account that those who die are no longer “at risk” for death. If 100 persons at the start of the observation period were followed for 3 years, during which 5 persons died, 2 at the end of the first year, and other 3 when 1.3, 2.2, and 2.6 years had passed, we have exactly

1:0 × 2 + 1:3 × 1 + 2:2 × 1 + 2:6 × 1 + 3 × 95

=293:1 person-years of observation.

[Page 691]1 × 2 = 2 + 1:3 = 3:3 × 1 = 3:3 × 1 = 3:3 + 2:2

=5:5 × 1 = 5:5 + 2:6 = 8:1 × 1 = 8:1 + 3 = 11:1 × 95 = 1054:5:

Since 5/293.1 = 0.0171, the mortality rate can be expressed as 0.0171 deaths per person-year, or 17.1 deaths per 1,000 person-years, or as an annual death rate of 17.1 per 1,000.

An age-specific mortality rate is a death rate in a given age stratum. If the subindex i refers to the particular age stratum, the age-specific mortality rate will be mi = 10k × di=pi, where mi is age-specific mortality in the age stratum i, di are total deaths in the age stratum i, and pi is the population in that age.

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