PAPP101 - S06: Mortality statistics and standardisation

Basic measures of mortality

The crude death rate (CDR)

The crude death rate (CDR) is the simplest and one of the more common indicators of mortality in a population. It is the ratio of the numbers of deaths (D) observed in a population in a year to the population at risk of dying in that year (N), usually multiplied by 1 000:

$$CDR=\frac{D}{N}.1000$$

Demographers tend to use a period of a year – typically a calendar year running from 1 January to 31 December – to derive a CDR so as to eliminate possible seasonal fluctuations in mortality (deaths of the elderly, for example, tend to occur disproportionately in winter) while still retaining a degree of precision in the estimate by not smoothing out trends in mortality over a number of years.

The numerator comes directly from a tabulation of the number of deaths observed. The denominator, however, is more problematic. To accurately reflect the level of mortality, the denominator should reflect the person-years of exposure to the risk of dying in the population over the course of the year, as discussed in PAPP101_S02 . In most applications, this information is not readily available

Exercise

What might be a good approximation to the population exposed to risk in the calculation of a crude death rate?

a) Population at the start of the year b) Population at the middle of the year c) Population at the end of the year Check your answer Please select an answer Incorrect. This would not produce a rate, but a probability since the population at the start of the year would represent the universe of people alive at the start of the year, without allowing for the fact that some of that population would die; and that births and deaths occurring in the same year would be missed entirely in the denominator but represented in the numerator. Correct. This represents a reasonable approximation to the population exposed-to-risk. The reason is clear from the diagram: In the diagram, the population exposed to risk is represented by the area under the line connecting the population size Pt at time t and Pt+1 at time t+1. If one assumes that population change between two points in time, t and t+1, is linear, differential calculus tells us that the area under the sloped line will be equal to the area defined by the rectangle defined by the population size at time t+ ½ , P t+½. In other words, the mid-period population is a reasonable approximation to the exposed to risk for the period. Incorrect. Think about the question and try again.