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

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

To put your footer here go to View > Header and Footer 2 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

To put your footer here go to View > Header and Footer 3 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 pop n. People retire to sunny seaside Bournemouth: and death rates are higher for older people.

To put your footer here go to View > Header and Footer 4 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 ASDRMid Yr Pop n Total Deaths 0-<15.0150000500 15-<40.03400001200 40-<70.05300001500 70 +.20100002000 x.01 + X.20 =.04 x.03 + x.01 + CDR =

To put your footer here go to View > Header and Footer 5 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. 50000 130000

To put your footer here go to View > Header and Footer 6 Population Alpha ( ) as above Population Beta ( ) for comparison Age range AS DR Mid Yr Pop n Total Deaths 0-<15.0150000500 15-<40.03400001200 40-<70.05300001500 70 +.20100002000 Age range AS DR Mid Yr Pop n Total Deaths 0-<15.0250000010000 15-<40.0535000017500 40-<70.0620000012000 70 +.09 50000 4500 - CDR = 0.04 Example for comparison of CDRs

To put your footer here go to View > Header and Footer 7 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 range0-<1515-<4040-<70 70 + Alpha %38.4630.7723.087.69 Beta %45.4531.8218.184.55

To put your footer here go to View > Header and Footer 8 A standard population There is no right way to do this! One option is to use the total pop n 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 Tot. Pop n -Deaths 0-<15.01.02550000550011000 15-<40.03.053900001170019500 40-<70.05.062300001150013800 70 +.20.09 6000012000 5400

To put your footer here go to View > Header and Footer 9 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]

To put your footer here go to View > Header and Footer 10 A different standard population Another standard would be to use a 50:50 average of the pop n percentages by age:- This yields -ASDR =.0361; -ASDR =.0419 Check for yourself! Age range0-<1515-<4040-<70 70 + Alpha %38.4630.7723.087.69 Beta %45.4531.8218.184.55 Average %41.9631.2920.6306.12

To put your footer here go to View > Header and Footer 11 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]

To put your footer here go to View > Header and Footer 12 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 pop n could give one corrected overall comparison.

To put your footer here go to View > Header and Footer 13 The method in reality For 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 pop n where younger age ASDRs were lower, old-age ASDR was higher than in pop n. 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.

To put your footer here go to View > Header and Footer 14 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).

To put your footer here go to View > Header and Footer 15 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.

To put your footer here go to View > Header and Footer 16 Example The general population in Betastan has known age composition and ASDRs as opposite There is a sub-population of Gamma people about whom we know the pop. n size for each age group, and total no. of deaths = How do they compare With general population? Age range AS DR Mid Yr Pop n Total Deaths 0-<15.0250000010000 15-<40.0535000017500 40-<70.0620000012000 70 +.09 50000 4500 Age range AS DR Mid Yr Pop n Total Deaths 0-<15?5000 15-<40?3000 40-<70?1000 70 +? 100 766

To put your footer here go to View > Header and Footer 17 Example arithmetic: 1 Age range ASDRMid Yr Pop n Total Deaths Gamma Pop.n Expected Deaths 0-<15.02500000100005000100 15-<40.05350000175003000150 40-<70.0620000012000100060 70 +.09 50000 4500 1009 Total-1,100,00044,0009100319 The expected deaths are what we would expect in the gamma population if they had the same ASDRs as the general Betastan pop n

To put your footer here go to View > Header and Footer 18 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 =

To put your footer here go to View > Header and Footer 19 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 pop n 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.

To put your footer here go to View > Header and Footer 20 And now … ? These few sessions have introduced simple examples of some key demographic ideas. They illustrated 2 (of many) possible choices of standard pop n, 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.

To put your footer here go to View > Header and Footer 21 Practical work follows to ensure learning objectives are achieved…