Standardisation of rates
- Measure
It lets you compare mortality between populations with different ages, as if they all had the same age structure.
What it is
Crude rates mix risk with age structure: an old population has more deaths even when every age group is healthy. The direct method applies each population's age-specific rates to one common standard population. The indirect method applies reference rates to the study population and compares observed with expected deaths: the standardised mortality ratio (SMR).
Formula and reading
- Standardised rate (direct) = Σ (rate at age i × standard population at age i) / total standard population.
- SMR = observed deaths / Σ (reference rate at age i × study population at age i).
- Two populations can only be compared if they were standardised to the same standard.
- WHO and countries publish standard populations; changing the standard changes the value, not usually the ranking.
Worked example
- Two made-up towns of 50,000. A is young (30,000, 15,000 and 5,000 aged 0–39, 40–64 and 65+); B is old (15,000, 15,000 and 20,000).
- Age-specific rates per 1,000: A = 1; 5; 40. B = 0.8; 4; 35. B has lower risk in every group.
- Crude: A = (30 + 75 + 200) / 50,000 = 6.1 per 1,000; B = (12 + 60 + 700) / 50,000 = 15.4 per 1,000 (rounded).
- Standard: both towns added together, 45,000, 30,000 and 25,000 (100,000 in all).
- Direct A: 45 + 150 + 1,000 = 1,195 expected deaths / 100,000 = 12.0 per 1,000 (rounded).
- Direct B: 36 + 120 + 875 = 1,031 expected deaths / 100,000 = 10.3 per 1,000 (rounded).
- Indirect for B with reference rates 1; 5; 40: expected = 15 + 75 + 800 = 890; SMR = 772 / 890 = 0.87.
- Reading: B seemed to die 2.5 times as much, but adjusted for age it dies less than A and 13% less than expected.
Direct versus indirect method
| Feature | Direct | Indirect |
|---|---|---|
| What you need | Age-specific rates of each population and a standard population | Reference age-specific rates and the study group's population by age, plus its total deaths |
| Result | Age-standardised rate | Standardised mortality ratio (SMR) |
| When it suits | Large populations with stable age-specific rates | Small groups or unreliable age-specific rates |
| How to read it | Compare rates with each other | Observed versus expected: 1 = the same |
Markers
- Adjusted rate
- Direct method
- Indirect method
- SMR
How to read it
- Mortality reports by department use age-adjusted rates so that young and ageing regions can be compared.
- The SMR is used in occupational health to see whether a group of workers dies more than expected for their age.
Common pitfalls
- Comparing a standardised rate with a crude one, or two standardised rates built on different standards.
- Reading the adjusted rate as the real risk of that population.
- Comparing the SMRs of two different groups with each other: each is compared only with its reference.
Test yourself
Think of the answer, then tap the question to see it.
Why are rates standardised by age before comparing two populations?
Because age strongly affects mortality and the populations have different age structures; without adjustment, age confounds the comparison.
What is multiplied in the direct method?
Each population's age-specific rates by the standard population of each age group; these are summed and divided by the standard total.
A factory has 30 deaths where 20 were expected from national rates. What is the SMR and what does it mean?
SMR = 30 / 20 = 1.5: there were 50% more deaths than expected for the age of those workers.
When is the indirect method preferred?
When the study group is small and its age-specific rates are unstable, or when its deaths by age are not known.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Age adjustment (National Center for Health Statistics, Centers for Disease Control and Prevention, 2026); Principles of Epidemiology | Lesson 3 - Section 3 (Centers for Disease Control and Prevention, 2012).
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Representative model, for educational purposes only.