There is frequently a need to compare proportions or rates between populations. This applies whether we are comparing cases of a disease or, for that matter, cases of injury, deaths or births - all of which can be referred to as events.

We might, for example, wish to assess the effect of pollution by comparing the mortality rate of a population in a low pollution area, with that of a population in a high pollution area. *But what if the two populations differ considerably in their age distributions?* Given that elderly people usually have a higher mortality rate, whichever population has a higher proportion of old people will have a higher overall mortality rate - irrespective of any effect of pollution. Age would therefore be a confounding factor for the effect of pollution - in other words it would obscure the effect of the factor of interest.

This problem can be avoided by adjusting, or standardizing, the event proportion or rate to the age structure of a standard population. The standard population may be the overall population of the area, the country, or even the World Standard Population of the United Nations. There are two ways in which this adjustment can be done. We will consider them in relation to rates, but the adjustment is done in exactly the same way for proportions:

### Direct adjustment

The direct standardized event rate is the number of events that would be expected in the standard population if we had the age-specific event rates present in the study population. We must know the age-specific event rates in the study population, and the number of people in each age category in the standard population. The procedure is as follows.

To obtain the study population age specific event rates (column 4, below):

divide the number of events in the study population (column 2) by the population size (column 3) in each age category.

To determine the number of events that would occur in the standard population (column 6):

Multiply those rates by the numbers in each category of the standard population (column 5).

To obtain the standardized event rate (see table bottom row):

Add up the standard number of events and divide by the total standard population size.

**Direct standardization** |
1. Age range | Study population | Standard population |
2. No. of events | 3. Population size
| 4. Age specific event rate | 5. Population size
| 6. Standardized no. of events |
0-4 | 3 | 5200 | 0.000577 | 215000 | 124.1 |
5-14 | 2 | 8800 | 0.000227 | 520000 | 118.0 |
15-29 | 5 | 12500 | 0.000400 | 656250 | 262.5 |
30-44 | 7 | 10700 | 0.000654 | 505000 | 330.3 |
45-59 | 14 | 6800 | 0.002059 | 320935 | 660.8 |
60-74 | 20 | 3700 | 0.005405 | 203959 | 1102.4 |
>74 | 90 | 2500 (5%) | 0.046666 | 62019 (2.5%) | 2894.2 |
Total | 141 | 50200 | 0.00281 | 2483163 | 5616.4 |
Standardized event rate = 5616.4/2483163 = **0.00226** |
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In this example the study population has a higher percentage (5%) of people over 74 years of age than the standard population (2.5%). Since most of the events occur in this group, the effect of standardization is to reduce the event rate from 2.81 per thousand to 2.26 per thousand.

### Indirect adjustment

There are two potential difficulties in using direct adjustment. Firstly if the numbers of deaths in some age categories in the study population are very small, the resulting age specific rates are not very reliable. Secondly we may not know the age specific event rates in the study population, but only have data on the total number of deaths in the study population. Providing we know the age distribution of the study population, and the age specific event rates of the standard population, we can the indirect standardized event rate . The procedure is as follows:

To obtain the standard population age specific event rates (column 4, below):

Divide the number of events in the standard population (column 2) by the population size (column 3) in each age category.

To give the expected number of events in the study population (column 6):

Apply the standard population age specific event rates to each age category of the study population (column 5).

To give the standardized event ratio or SER (see 2nd to bottom row of table):

Divide the total observed number of events (column 7) by the total expected number of events.

To give the indirect standardized event rate (see bottom row):

Multiply the study population's overall event rate by the SER.

**Indirect standardization** |
1. Age range | Standard population | Study population |
2. No. of events | 3. Population size
| 4. Age specific event rate | 5. Population size
| 6. Expected no.of events | 7. Observed no.of events |
0-4 | 120 | 215000 | 0.000558 | 5200 | 2.9 | ? |
5-14 | 100 | 520000 | 0.000192 | 8800 | 1.7 | ? |
15-29 | 252 | 656250 | 0.000384 | 12500 | 4.8 | ? |
30-44 | 320 | 505000 | 0.000634 | 10700 | 6.78 | ? |
45-59 | 650 | 320935 | 0.002025 | 6800 | 13.8 | ? |
60-74 | 1150 | 203959 | 0.005638 | 3700 | 20.9 | ? |
>74 | 2900 | 62019 | 0.046760 | 2500 | 116.9 | ? |
Total | | | | 50200 | 167.8 | 141 |
Standardized event ratio = 141/167.8 = 0.8403 |
Standardized event rate = 0.00281×0.8403 = **0.00236** |
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### Assumptions

Both methods of standardization assume that the effect of age upon the event rate is common across all groups.