SADC Course in Statistics Preparing & presenting demographic information: 2 (Session 06)

SADC Course in Statistics

Preparing & presenting demographic information: 2

(Session 06)

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Learning Objectives

At the end of this session, you will be able to

• appreciate the general issue of correcting for differences in age structure when comparing demographic rates

• use basic standardisation methods to compare death rates between populations

• correctly interpret directly and indirectly standardised rates


Comparison of populations

As before we focus for simplicity on death rates, but following applies more generally.

Suppose we have crude death rates for two towns, Reading and Bournemouth, in UK, say the death rate for Reading is only 70% of that for Bournemouth. Does that mean Reading has a healthier climate, is a better place to live, or much richer place? NO! Reading has a young working popn. People retire to sunny seaside Bournemouth: and death rates are higher for older people.


Composition of Crude Death Rate

Artificial data “Alpha” for teaching purposes

The Crude Death Rate

in this population is

Total deaths

Total population

i.e. 5200/130,000

.04 or 4%, a weighted

average of the age-groups’ separate ASDRs:-

50000 40000 30000 10000 130000 130000 130000 130000

Age range

ASDR Mid YrPopn

TotalDeaths

0-<15 .01 50000 500

15-<40 .03 40000 1200

40-<70 .05 30000 1500

70 + .20 10000 2000

x.01 + X .20 = .04x.03 + x.01 +

CDR =


Comparison of CDRs

If two (or more) populations have different age-compositions, the crude death rates (CDRs) will reflect this, because the ASDRs are each weighted by population fractions e.g. above.

If we want to compare the ASDRs in two different populations EITHER compare the rates one-by-one e.g. by graphing each set vs. age OR produce a compromise summary by using (artificial) common age structure.

50000130000


Population Alpha () as above Population “Beta” () for comparison

Age range

AS DR

Mid YrPopn

TotalDeaths

0-<15 .01 50000 500

15-<40 .03 40000 1200

40-<70 .05 30000 1500

70 + .20 10000 2000

Age range

AS DR

Mid YrPopn

TotalDeaths

0-<15 .02 500000 10000

15-<40 .05 350000 17500

40-<70 .06 200000 12000

70 + .09 50000 4500

-CDR = 0.04 -CDR = 0.04

Example for comparison of CDRs


Basic interpretation of Example

Population Beta has higher death rates in the age groups below age 70, a lower death rate in the top age group.

The two age-structures are different: we can show this better by expressing them in % terms. Which is generally older?

Age range 0-<15 15-<40 40-<70 70 +

Alpha % 38.46 30.77 23.08 7.69

Beta % 45.45 31.82 18.18 4.55


A “standard” population

There is no right way to do this! One option is to use the total popn as “standard” and combine that with each set of death rates. Then the directly-standardised death rates are:-

-ASDR = .0331; -ASDR = .0404

Confirm the calculations yourself!

Ages -ASDR -ASDR Tot. Popn -Deaths -Deaths

0-<15 .01 .02 550000 5500 11000

15-<40 .03 .05 390000 11700 19500

40-<70 .05 .06 230000 11500 13800

70 + .20 .09 60000 12000 5400


Interpretation

IF both populations had had their own (real) ASDRs, but had had same age structure (imaginary “standard”) their equivalents of Crude Death Rates would have been the above directly standardised death rates.

Because Beta has larger numbers, it contributed most of that “standard” population, so the resulting standardised

death rate was affected less for than :

[: 0.04 0.0331; 0.04 .0404]


A different “standard” population

Another standard would be to use a 50:50 average of the popn percentages by age:-

This yields -ASDR = .0361; -ASDR = .0419

Check for yourself!

Age range 0-<15 15-<40 40-<70 70 +

Alpha % 38.46 30.77 23.08 7.69

Beta % 45.45 31.82 18.18 4.55

Average % 41.96 31.29 20.630 6.12


Interpretation

IF both populations had had their own (real) ASDRs, but had had same age structure (imaginary “standard”) their equivalents of Crude Death Rates would have been the above DSDRs.

Because Alpha & Beta contributed equally to that “standard” population, the resulting standardised death rates were both

affected more nearly equally : [: 0.04 0.0361; 0.04 .0419]


Further interpretation

The directly standardised death rates used two different examples of a standard population structure to produce “synthetic” death rates (that did not actually arise in real populations), in each case to provide 2 figures that were more or less comparable

i.e. that more or less “corrected” for different age-structures so that the set of age-specific death rates for each popn could give one “corrected” overall comparison.


The method in realityFor classroom purposes this demonstration used

a very simplified artificial example. The summarisation benefit is much greater

where there are 100+ ASDRs for single years of age, and where many (sub-) populations are to be compared.

The example showed popn where younger age ASDRs were lower, old-age ASDR was higher than in popn . Like a CDR, the standardised DRs do not show that age pattern.

The Directly-Standardised Death Rate only provides a comparative summary combining across age groups.


Indirect standardisation: 1

This is a substitute method ~ easy to carry out but a bit harder to explain to non-experts. Sometimes Direct Standardisation is not possible; it uses the age-specific death rates from both/all populations & these may not be known.

Indirect standardisation can be used if for each population the total number of deaths (but not by age) is known ~ and the age distribution is known e.g. from a census (or proportions by age from a survey).


Indirect standardisation: 2

The method takes the (real) age-distribution for each population and combines it with a “standard” set of ASDRs to compute “expected deaths” then compares the number expected with the real number observed.

One quite plausible example is where one population IS the standard and the other to be compared is a “special” population, often a sub-population.


ExampleThe general population in Betastan has knownage composition andASDRs as opposite

There is a sub-populationof Gamma people about whom we knowthe pop.n size for eachage group, and total no.of deaths = How do they compare With general population?

Age range

AS DR

Mid YrPopn

TotalDeaths

0-<15 .02 500000 10000

15-<40 .05 350000 17500

40-<70 .06 200000 12000

70 + .09 50000 4500

Age range

AS DR

Mid YrPopn

TotalDeaths

0-<15 ? 5000

15-<40 ? 3000

40-<70 ? 1000

70 + ? 100

766


Example arithmetic: 1Age

rangeASDR Mid Yr

Popn

TotalDeaths

Gamma Pop.n

Expected Deaths

0-<15 .02 500000 10000 5000 100

15-<40 .05 350000 17500 3000 150

40-<70 .06 200000 12000 1000 60

70 + .09 50000 4500 100 9

Total - 1,100,000 44,000 9100 319

The “expected deaths” are what we would expect in the gamma population if they had the same ASDRs as the general Betastan popn


Example Arithmetic: 2

“standardised mortality ratio” (SMR) for the Actual Deaths

Expected Deaths

i.e. SMR = 766/319 = 2.40

Having regard to their age distribution the Gamma people are suffering deaths at 2.4 times the rate in the general population

Gamma people is SMR =


Example: the ISDR

By definition the Indirectly Standardised Death Rate is SMR for the Gamma population, multiplied by the Crude Death Rate for the standard population & from slide 6 above:- -CDR = 0.04, so the Gamma popn ISDR is 2.4 X 0.04 = 0.096.

As with DSDR, this provides an overall idea how much worse the Gammas are doing, but no information on the ages where they are particularly vulnerable.


And now … ?

These few sessions have introduced simple examples of some key demographic ideas.

They illustrated 2 (of many) possible choices of standard popn, mixing & , for DSDRs, and a third choice for ISDRs where one of the 2 populations was itself the standard.

Many demographic methods depend on similar arithmetic to this. The subject also includes many social scientific ideas and some highly mathematical approaches.


Practical work follows to ensure learning objectives

are achieved…

Documents

SADC Course in Statistics Preparing & presenting demographic information: 2 (Session 06)