sadc course in statistics preparing & presenting demographic information: 2 (session 06)
TRANSCRIPT
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
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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.
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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 =
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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
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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
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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
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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
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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]
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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
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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]
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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.
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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.
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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).
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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.
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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
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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
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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 =
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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.
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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.
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Practical work follows to ensure learning objectives
are achieved…