PAPP101 - S06: Mortality statistics and standardisation

Basic measures of mortality (cont.)

Age-specific mortality rates

Among other limitations, the crude death rate makes no allowance for the mortality pattern in a population by age. In most populations, mortality rates are very high in infancy, fall to a low-point in late childhood (around the age of 10), and increase with increasing age thereafter. It therefore makes sense to calculate mortality rates by single years of age (although often there will be a significant element of random variation in these) or for fairly narrow age groups. The high level of mortality in infancy means that conventional demographic practice is to mortality in the first year of life distinctly from mortality at other ages in early childhood, resulting in a usual classification of age-specific mortality measures covering ages 0-1; 1-4; and 5-year age groups thereafter up to some final open interval, perhaps beginning at age 80, or some higher age above which rather few deaths occur.

Therefore differences between populations in the Crude Death Rate may reflect differences in their age structures rather than accurately reflect differences in individuals’ propensity to die given their ages.

An age-specific death rate is defined similarly to that of a crude death rate:

Exercise

If the number of deaths of people aged 5-9 in a given year in a population is a 578, and the mid-year population aged 5-9 in that year is 74 934, what is the age-specific death rate for ages 5-9 in that population per 1000, to one decimal place?

The correct answer is: 7.7 per 1000

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Finally, it should be appreciated that the crude death rate is simply a weighted average of the age-specific death rates, where the weights are the proportions of the population at each age. Mathematically – and working with single ages for ease of exposition:

$$CDR=1000.\frac{D}{N}=\frac{1000}{N}\sum _{X=0}^{\infty }{D}_x=1000.\sum _{X=0}^{\infty }\frac{D_x}{N_x}.\frac{N_x}{N}=1000.\frac{\sum _{X=0}^{\infty }{m}_x.w_x}{\sum _{X=0}^{\infty }{w}_x}$$

Moving from the second to the third expression, we can express the total number of deaths in the population as the sum over all ages, x, of the deaths at each age, D_x.

In the fourth expression, the denominator, N, is independent of x, so can be brought inside the summation, and we can multiply the Dx/N in the summation by (Nx/Nx, =1). But Dx/Nx is the age specific mortality rate, m_x, and D_x/N_x is, by definition, w_x. In the final expression, we note that the sum of w_x is one, so the division is irrelevant except for the observation that the final expression is the analytical form for calculating a weighted average of the m_x, weighted by w_x.

This identity demonstrates that the relative sizes of the different age groups determine their influence on the crude death rate. Because mortality varies greatly with age, this implies that a population's age structure strongly influences its crude death rate. Therefore, the measure is of limited use for comparing mortality in different populations. The discussion of standardization that follows explains one way of overcoming this limitation of crude measures.