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# Standardisation of rates

- Measure

It lets you compare mortality between populations with different ages, as if they all had the same age structure.

Updated Nov 5, 2026

## Key points

- Age is a confounder when comparing crude rates; standardising is one way to control it.
- Direct: each population's age-specific rates × standard population = expected deaths in the standard; divide by its total.
- Indirect: reference rates × study population = expected deaths; SMR = observed / expected.
- SMR of 1 = as expected; above 1 = excess; below 1 = fewer deaths than expected.
- The indirect method suits groups whose age-specific rates are unstable because of small numbers (for example, a cohort of workers).
- A standardised rate is an index for comparison, not the real risk of the population.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- Direct versus indirect method
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Direct: my rates, someone else's population. Indirect: someone else's rates, my population.

## 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.

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## Connections

## Related 5

- [Mortality rates: crude and specific](https://durgical.com/en/epidemiology/mortality-rates-crude-and-specific/)
- [Confounding](https://durgical.com/en/epidemiology/confounding/)
- [Controlling confounding](https://durgical.com/en/epidemiology/controlling-confounding/)
- [Life expectancy](https://durgical.com/en/epidemiology/life-expectancy/)
- [Infant, neonatal and perinatal mortality](https://durgical.com/en/epidemiology/infant-neonatal-and-perinatal-mortality/)

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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](https://www.cdc.gov/nchs/hus/sources-definitions/age-adjustment.htm) (National Center for Health Statistics, Centers for Disease Control and Prevention, 2026); [Principles of Epidemiology | Lesson 3 - Section 3](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section3.html) (Centers for Disease Control and Prevention, 2012).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/standardisation-of-rates/