FINAL TERM COURSE

Measures of Mortality (v) Standardized Death Rates

by Direct Method

Standardized Mortality Rate It is a weighted average of the

age-sex specific mortality rates of a particular population under observation, the weights being the proportions in each age-sex group of a standard population (not the particular population under observation)

Explanation The crude death rates of two localities or

in two occupations cannot be compared because mortality rates differ with age, sex, climate, occupation etc. Aged people even though well housed and well fed, die comparatively at a higher rate than the young people. Good climate is conductive to long life whereas bad climate is injurious to health. Moreover, mortality is highest at the extreme of age. To eliminate such effects, we compute “Standardized death rates”

Methods of calculating SDRStandardized death rates can be

computed either by ◦ Direct method: SDR by direct method can

be calculated by applying different age-specific death rates of the population being studied (or given population), to a standard population (which may be any population selected to be on the basis of the comparison)

◦ Indirect method: SDR by indirect method can be calculated by applying different age specific death rates of a standard population to the population being studied.

Direct method The direct method for computing

the SDR consists in calculating the number of deaths that would be expected to occur in a standard population if the age specific death rates of the given population were to apply; and dividing the sum of the expected deaths by standard population.

That is the age adjusted or standardized death rate is computed by the formula

Where denotes the number of deaths

occurring in the given population in the ith age group during a calendar year

denotes the mid year population figures in the given population in ith age-group during the same year.

denotes the mid year population figure in the standard population in the ith age group in the same year.

If the death rates are adjusted both for age and sex, the expected deaths are calculated as follows:

The standardized death rate or age sex-adjusted death rate is then given by the formula:

This sort of SDR is easy to compute and to explain. The choice of standard population being subjective, may influence the comparison of standardized death rates.

Example 1

Given the following data for the two districts:

Compute Crude Death Rates for district A and B and interpret by pointing out the fallacies.

Considering district A as a standard population, calculate standardized death rate for district B using direct method.

Data TableAge group (years)

District A District B

Population Deaths Population Deaths

0-14 500 2 400 1

15-29 2000 8 300 1

30-44 2000 12 1000 5

45-59 1000 10 2000 18

60-74 500 20 2000 70

75 & over 100 15 400 50

Solution The computation of crude death

rates and age-specific death rates in both the districts to point out the fallacies, if any, are given below:

Age-group (years)

District A District B

Population

Deaths A.S.D.R Population

Deaths A.S.D.R

0-14 500 2 (2/500)x1000=4.0

400 1 2.5

15-29 2000 8 4.0 300 1 3.3

30-44 2000 12 6.0 1000 5 5.0

45-59 1000 10 10.0 2000 18 9.0

60-74 500 20 40.0 2000 70 35.0

75 & over

100 15 150.0 400 50 125.0

Total 6100 67 11.0 6100 145 23.8

Calculation of CDR

Calculation of SDRTo compute the SDR for district B

by the direct method, we first calculate the expected deaths in district A (standard population) as experienced in district B by the formula

The deaths are given in the next table

Expected death calculation Age group (years) Expected deaths in standard

population as experienced in district A

0-14 (1/400)x500 = 1

15-29 (1/300)x2000 = 7

30-44 10

45-59 9

60-74 18

75 & over 12

Total 57

Hence standardized death rate is:

Interpretation The CDR for district B, which

contains a very large proportion of older people. i.e. 72% of district B’s population is over the age 45 years, comes to 23.8 unusually high, whereas the CDR for district A, which contains a smaller proportion of older people i.e. only 26% population is over age 45 years, is 11.0, unusually low.

Interpretation The death rate at all age groups

in district B are lower than those in district A but the CDR of B is more than double the CDR of A. The fallacy this sort of unusual behavior lies in the fact that the like is not being compared with the like. For such situation SDR are calculated. Standardizing has lowered the death rate for district B, which turn out to be 9.3

Mathematical formula of SDRRef. Benjamin B. & Pollard J.H. (1980), “The Analysis of Mortality and Other Actuarial Statistics”, William Heinemann Ltd

The Direct Standardized Death Rate can be calculated as:

where is the standard population.

ExampleRef. Benjamin B. & Pollard J.H. (1980)

The data are available for males in two areas A & B and for the whole country Ca. Calculate the death rate by age for

each area.b. Also calculate CRDc. Standardize the all ages death

rates for area A and B directly by reference to the population of C

d. Interpret all the findings.

Data Table Population (000s) Annual deaths (all

causes)

Age A B C A B C

0-14 150 100 1450 600 400 3190

15-44 300 350 2700 600 520 4050

45-64 150 100 1600 3000 1500 24000

65-84 120 75 1200 10200 5550 88000

85+ 10 5 60 300 1280 15360

730 730 7010 17400 9250 134600

Solution (a)Values of

Age Area A Area B

0-14 600/150000=0.0040

0.0020

15-44 0.0020 0.0015

45-64 0.0200 0.0150

65-84 0.0850 0.0740

85+ 0.0300 0.2560

(b) Calculation of CDR (?)

Solution (c), AnswersStandardized death rate for area

A=0.0233Standardized death rate for area

B=0.0193

(d) Interpretation (?)