When comparing populations (either between or within countries) we have to be careful as populations can differ in a number of important characteristics.
These include:
These may act as confounding factors when comparing populations.
EXAMPLE
New Zealand
The following graphs of the total New Zealand and New Zealand Māori populations show that they have different age structures. The total population has a higher proportion of elderly and a smaller proportion of young people and children than the Maori population.
New Zealand - with higher elderly population
Māori - with higher young population
If we compared the proportion of each population with some characteristics (e.g. receiving a superannuation benefit) this would be confounded by the difference in the age structures (proportions of elderly) of each population. A similar confounding would occur if we compared the proportions of each population in tertiary education.
Many social and economic variables need to be standardised by age (that is adjusted for the proportion in each age group in the population) before we can make valid comparisons between groups.
END COMPARING POPULATIONS EXPLANATION
When populations differ in some important variable we can standardise on this variable in the following way:
The most common form of standardisation is age standardisation.
Age Standardisation
EXAMPLE 1
Age standardisation of Population 1 with a Comparison Population (made up data).
| Age | Population 1 | Number of deaths | Age-specific rate / 1000= C 4 | Comparison population = C5 | C4xC5 |
|---|---|---|---|---|---|
| 15 | 2000 | 30 | 15 | 30000 | 450 |
| 15 - 64 | 3000 | 150 | 50 | 150000 | 7500 |
| 65 + | 100 | 20 | 200 | 10000 | 2000 |
| Total | 5100 | 200 | 190000 | 9950 |
The crude death rate for population 1 is:
This could be expressed as 39 per 1000.
The standardised death rate for population 1 compared to the comparison population is just the average of the age-specific rates weighted by the comparison population (i.e. a weighted average).
This could be expressed as 52 per 1000.
That is, if the death rate of Population 1 had NOT been age standardised it would have looked as if it was less than that of the comparison population when, once it was adjusted for having more elderly than the comparison population the death rate was higher.
EXAMPLE 2
The following example uses World Health Organisation data.
| Age | Cases | Population | Age-specific (Crude) rate | WHO population | ASR |
|---|---|---|---|---|---|
| 0 | 2 | 153750 | 1.3E-05 | 8.86 | 1.5252E-06 |
| 5 | 0 | 147350 | 0 | 8.69 | 0 |
| 10 | 0 | 150190 | 0 | 8.6 | 0 |
| 15 | 0 | 164660 | 0 | 8.47 | 0 |
| 20 | 0 | 150190 | 0 | 8.22 | 0 |
| 25 | 0 | 134390 | 0 | 7.93 | 0 |
| 30 | 2 | 129740 | 1.54E-05 | 7.61 | 1.17312E-06 |
| 35 | 7 | 148660 | 4.71E-05 | 7.15 | 3.36674E-06 |
| 40 | 7 | 151510 | 4.62E-05 | 6.59 | 3.04468E-06 |
| 45 | 9 | 155120 | 5.8E-05 | 6.04 | 3.50438E-06 |
| 50 | 11 | 135830 | 8.1E-05 | 5.37 | 4.34882E-06 |
| 55 | 18 | 120530 | 0.000149 | 4.55 | 6.79499E-06 |
| 60 | 28 | 103880 | 0.00027 | 3.72 | 1.0027E-06 |
| 65 | 39 | 81000 | 0.000481 | 2.96 | 1.42519E-05 |
| 70 | 40 | 60360 | 0.000663 | 2.21 | 1.46455E-05 |
| 75 | 41 | 48180 | 0.000851 | 1.52 | 1.29348E-05 |
| 80 | 20 | 32720 | 0.000611 | 0.91 | 5.56235E-06 |
| 85 | 19 | 20740 | 0.000916 | 0.63 | 5.77146E-06 |
| TOTAL | 243 | 2093250 | 0.000116 | 100 | 8.65782E-05 |
| Population Crude Rate |
| Reference Population Proportion |
| Strata Age Standardised Rate |
| Population Age Standardised Rate |
Some calculations are as follows:
The Population Age Standardised Rate is the addition of the values in column 6 (ASR) of the table. It is the addition of Age-specific crude rates weighted by the reference (WHO) population figures.
For Population Age Standardised Rate the Age-specific death rates are weighted by the reference population. For example, for age class 85:
| = |
19
20,740
|
x |
0.63
100
|
| = | 0.000916 | x |
0.63
100
|
This produces a Age Standardised Rate for 85 of 5.77146E-06.
EXERCISE 1
Calculate the crude death rate, the age-specific death rates and the standardised death rate for Region A below using the Whole Country population distribution as the standard population.
| Age Group | REGION A | Age specific rate / 1000 | WHOLE COUNTRY Age distribution per 1000 | WHOLE COUNTRY Death Rate /1000 | |
|---|---|---|---|---|---|
| Population | No. of deaths | ||||
| 0-(10) | 21 000 | 350 | ... | 221 | ... |
| 10-(25) | 30 000 | 102 | ... | 298 | ... |
| 25-(45) | 37 000 | 229 | ... | 285 | ... |
| 45-(65) | 17 000 | 354 | ... | 149 | ... |
| 65 + | 5000 | 415 | ... | 47 | ... |
| TOTAL | 110 000 | 1450 | ... | 1000 | .... |
If you have spreadsheet software, you can work on this exercise using this Excel Spreadsheet linked below. The final answers are to two decimal places.
EXERCISE 2
Two industry sectors with male employees produced the following information on numbers of accidents and the age distribution of their male employees. Compare the incidence of accidents in the two industries.
| Age | INDUSTRY 1 | INDUSTRY 2 | |||
|---|---|---|---|---|---|
| No. of employees | No. of accidents | No. of employees | No. of accidents | ||
| <21 | 330 | 28 | 400 | 38 | |
| 21-29 | 570 | 40 | 720 | 67 | |
| 30-39 | 710 | 45 | 810 | 60 | |
| 40-49 | 780 | 55 | 390 | 34 | |
| 50-59 | 690 | 54 | 250 | 25 | |
| >60 | 250 | 25 | 80 | 11 | |
| TOTAL | 3330 | 247 | 2650 | 235 | |
a. Crude rate industry 1 =
Crude rate industry 2 =
b. Standardised rate industry 1 =
Standardised rate industry 2 =
| (Standard) Accident Rates Reference | ||
|---|---|---|
| Population (Industry 1) | Industry 2 Accident Rates | |
| 11.34 | 9.50 | |
| 16.19 | 9.31 | |
| 18.22 | 7.41 | |
| 22.27 | 8.72 | |
| 21.86 | 10.00 | |
| 10.12 | 13.75 | |
| 100.00 | ||
e.g. for industry 1:
e.g. for industry 2:
Standardised Rate for industry 2 with industry 1 weights is:
11.34 x 9.50 + 16.19 x 9.31 + 18.22 x 7.41 + 22.27 x 8.72 + 21.86 x 10.00 + 10.12 x 13.75
= 107.73 + 150.73 + 135.01 + 194.19 + 218.60 + 139.15
= 945.41
c. Conclusion regarding the safety standards?
END