Standardisation and Reference Values

Overview

Medical values are often interpreted relative to a reference.

Examples include:

• a child’s height relative to children of the same age and sex;
• a laboratory result relative to a selected reference population;
• a clinic’s disease prevalence relative to a population with a common age structure; and
• a measurement expressed in standard-deviation units.

Standardisation changes values or summary measures to support a defined comparison. It does not make different populations or measurements inherently equivalent. The reference and method must always be stated.

This lecture covers:

• z-scores;
• percentiles;
• reference intervals;
• clinical decision limits; and
• direct age standardisation of prevalence or rates.

Why this matters

A raw value can have different meanings in different contexts.

A height of 88 cm may be expected for one child and low for another because age and sex differ.

A crude disease prevalence may be higher in one district because its population is older, even if every age-specific prevalence is lower.

A laboratory result outside a reference interval may occur in a healthy person, while a result within the interval may still require clinical action because decision limits and reference intervals answer different questions.

Standardisation is useful only when the target comparison and reference population are defined.

Reference values and reference populations

A reference value is a measurement obtained from a member of a defined reference population.

A reference population is selected using specified criteria relevant to the interpretation.

Reference values may depend on:

• age;
• sex;
• pregnancy;
• time of day;
• posture;
• analytical method;
• specimen type;
• ethnicity or geography where scientifically justified;
• instrument or assay; and
• other physiological conditions.

The reference population should not be described vaguely as “normal people”. Selection criteria and measurement methods determine what the resulting values mean.

Standard scores or z-scores

A z-score, also called a standard score, expresses how far a value lies from a reference mean in reference standard-deviation units.

Interpretation under this simple reference model:

• $z=0$: equal to the reference mean;
• $z=1$: one reference SD above the mean;
• $z=-2$: two reference SDs below the mean.

A z-score has no physical unit.

The simple formula assumes the reference mean and SD adequately describe the relevant distribution. For skewed age-dependent measurements, specialised methods may be used. WHO growth z-scores are calculated using age-, sex- and indicator-specific parameters rather than one universal mean and SD [1].

Percentiles

A percentile expresses the position of a value within a reference distribution.

The 10th percentile is the value below which 10% of the reference distribution lies.

Percentiles and z-scores are related when the reference distribution and transformation are specified. Under an exact normal distribution:

• z-score 0 corresponds to the 50th percentile;
• z-score approximately −1.645 corresponds to the 5th percentile;
• z-score approximately 1.645 corresponds to the 95th percentile.

Percentile position does not measure the clinical importance of the difference between two values. Percentile spacing is compressed in the tails.

Reference intervals

A reference interval is an interval derived from a defined reference population using a specified procedure.

A common two-sided interval contains the central 95% of reference values:

• lower reference limit near the 2.5th percentile;
• upper reference limit near the 97.5th percentile.

This construction means that approximately 5% of reference individuals are expected to fall outside the interval even when measurement and reference selection are appropriate.

Reference intervals are not universal. They may vary by:

• population;
• age or sex partition;
• specimen collection;
• analytical method;
• laboratory; and
• statistical method.

Clinical laboratories should establish or verify intervals appropriate to their method and population [2].

Reference interval versus clinical decision limit

A clinical decision limit is a threshold used to support diagnosis, treatment, risk classification or another clinical action. It may be based on:

• outcome risk;
• trial evidence;
• expert guidance;
• analytical performance;
• cost–benefit considerations; or
• a combination of evidence.

It need not equal a reference limit.

Examples include treatment thresholds for blood pressure or glucose. These are not simply the upper 97.5th percentile of a healthy population.

A value:

• outside a reference interval is not automatically diagnostic;
• inside a reference interval is not automatically safe; and
• near a decision limit should be interpreted with measurement uncertainty and clinical context.

Table 1. Reference interval and decision limit

Direct standardisation

Population rates or proportions can differ because populations have different compositions.

Direct standardisation applies each population’s stratum-specific rates or prevalences to the same standard-population weights.

The standardised result is a weighted summary for comparison. It is not the crude observed prevalence of either population.

WHO has published a standard population for age-standardised rates used in international comparison [3]. A study may instead use another justified standard, such as the combined study population.

Data structure

Simulated district child-growth data

simulated data

Table 2. Age-specific stunting prevalence

District	Age group	Children surveyed	Children classified as stunted	Age-specific prevalence
A	0–23 months	700	70	10.0%
A	24–59 months	300	60	20.0%
B	0–23 months	300	24	8.0%
B	24–59 months	700	126	18.0%

Note: Classification uses the prespecified height-for-age z-score threshold. Counts are simulated.

Table 3. Crude district prevalence

District	Stunted	Total	Crude prevalence
A	130	1,000	13.0%
B	150	1,000	15.0%

Note: District age structures differ substantially.

Within both age groups, District A has higher stunting prevalence than District B:

• 10.0% versus 8.0% among children aged 0–23 months;
• 20.0% versus 18.0% among children aged 24–59 months.

Yet District B has the higher crude prevalence because it contains more children in the older, higher-prevalence group.

Worked example

Choosing the standard population

Possible standards include:

• a national census population;
• a WHO standard population;
• the combined populations being compared;
• a clinically relevant target population; or
• a trial or registry population.

The choice affects the numerical standardised result when stratum-specific differences vary. Therefore, reports must state the standard and weights.

Standardised rates from studies using different standards should not be compared without recalculation or careful qualification.

Indirect standardisation

Indirect standardisation applies reference stratum-specific rates to the study population’s stratum distribution to calculate an expected number of events.

A standardised mortality ratio is:

$$SMR = \frac{\text{observed deaths}}{\text{expected deaths}}$$

An SMR of 1 indicates observed and expected counts are equal under the reference rates.

Indirectly standardised ratios from different study populations are not always directly comparable because each uses its own composition.

Standardisation does not estimate one universal truth MMed extension

The crude and standardised measures answer different questions.

• Crude prevalence describes the actual observed population composition.
• Directly standardised prevalence compares populations under a common composition.
• A model-adjusted estimate may standardise over several variables and target another population.

None should be labelled simply “the true rate”.

The target population, standard weights and estimand determine which measure is appropriate.

Reference values in individual interpretation

When using a reference value:

1. verify the measurement method and unit;
2. identify the correct age, sex or physiological partition;
3. use the intended reference or standard;
4. consider analytical and biological variation;
5. distinguish percentile position from disease probability;
6. consider clinical decision limits; and
7. interpret with symptoms, history and other findings.

Reference values support interpretation but do not replace clinical judgement.

Suggested reporting

Common mistakes

Knowledge check

What does a z-score of −2 mean?

Answer and reasoning

Under the stated reference method, the observed value lies two reference standard-deviation units below the reference centre. Interpretation requires the variable, reference population and algorithm.

Does a result outside a central 95% reference interval prove disease?

Answer and reasoning

No. About 5% of reference individuals are expected outside a central 95% interval, and disease diagnosis depends on the test purpose, clinical context, decision limits and measurement quality.

Why did the crude and age-standardised district rankings reverse?

Answer and reasoning

District B had more children in the older age group, which had higher prevalence in both districts. Direct standardisation applied the same age weights, revealing the age-specific pattern.

Is an age-standardised prevalence the actual observed prevalence?

Answer and reasoning

No. It is a weighted comparison summary under a specified standard age distribution. The crude prevalence describes the actual observed composition.

Why must the standard population be reported?

Answer and reasoning

Different standard weights can produce different summary values when age-specific rates differ. Readers need the standard to reproduce and interpret the comparison.

Key take-home messages

References

1. World Health Organization. WHO child growth standards: length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age—methods and development. Geneva: World Health Organization; 2006. https://www.who.int/publications/i/item/924154693X
2. Ozarda Y. Reference intervals: current status, recent developments and future considerations. Biochem Med (Zagreb). 2016;26(1):5–16. https://doi.org/10.11613/BM.2016.001
3. Ahmad OB, Boschi-Pinto C, Lopez AD, Murray CJL, Lozano R, Inoue M. Age standardization of rates: a new WHO standard. GPE Discussion Paper Series No. 31. Geneva: World Health Organization; 2001. https://cdn.who.int/media/docs/default-source/gho-documents/global-health-estimates/gpe_discussion_paper_series_paper31_2001_age_standardization_rates.pdf