[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Study designs](https://durgical.com/en/epidemiology/areas/designs/) › Matching

# Matching

- Concept

Choosing controls who resemble the cases in age, sex or another factor, so that factor cannot confound the comparison.

Updated Nov 13, 2026

## Key points

- Individual: each case with one or more similar controls; frequency: the same distribution of the variable in both groups.
- Matched OR = pairs (case exposed, control not) / pairs (case not, control exposed); concordant pairs add nothing.
- You cannot study the effect of a variable you matched on.
- Overmatching: matching on something linked to the exposure (or on the causal pathway) pulls the OR towards 1.
- More than one control per case adds power, but beyond about 4 controls the gain is small.

On this page

- The basics Key points
- What it is
- Key facts
- Worked example
- Individual and frequency matching
- Markers
- In practice
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

Matching selects controls so that they resemble the cases on variables that could confound the association, such as age or sex. It can be individual (each case gets its own control or controls) or frequency matching (the groups share the same overall distribution). A matched design needs a matched analysis: with pairs, the odds ratio (OR) is computed from the discordant pairs only.

## Key facts

- With c controls per case, relative efficiency versus unlimited controls is c/(c + 1): 1 control 50 %, 2 controls 67 %, 4 controls 80 %.
- The significance test for pairs is McNemar's; with several controls per case, conditional logistic regression is used.

## Worked example

- Case-control study of pneumonia in people over 65: 150 pairs, each case with a neighbour of the same sex and age ± 3 years.
- Exposure: cooking with firewood. Both exposed: 60 pairs; neither exposed: 34 pairs.
- Only the case exposed: 42 pairs; only the control exposed: 14 pairs. Check: 60 + 34 + 42 + 14 = 150.
- The 94 concordant pairs carry no information on the association and are set aside.
- Matched OR = 42 / 14 = 3.0.
- Reading: the odds of having cooked with firewood are 3 times higher in cases than in their controls matched on age, sex and neighbourhood.

## Individual and frequency matching

| Aspect | Individual | Frequency |
| --- | --- | --- |
| Unit | Each case with its control (pairs or triplets) | The control group as a whole |
| Example | Control of the same sex, age ± 2 years and neighbourhood | Same percentage of women and of people over 60 |
| Analysis | Matched (discordant pairs, conditional logistic) | Stratified by the matched variable |
| Advantage | Controls factors that are hard to measure (neighbourhood, family) | Easier to recruit |
| Risk | Cases with no suitable control are lost | Coarser control of confounding |

## Markers

- Matched OR
- Discordant pairs
- McNemar
- Conditional logistic

## In practice

- Used mostly in case-control studies, when a strong confounder (age, sex) would make the groups very unequal.
- Matching on neighbourhood or sibling controls environmental or family factors that are hard to measure.
- In case-crossover designs each person is matched with themselves at another time.

## Common pitfalls

- Analysing matched data as if the groups were independent: the OR is biased towards 1.
- Matching on too many variables: controls become hard to find and cases are lost.
- Matching on a variable that is a consequence of the exposure (overmatching).

## Memory aid

In pairs, only the ones who disagree get a vote: concordant pairs stay silent in the OR.

## Test yourself

Think of the answer, then tap the question to see it.

## In 200 pairs, 30 have only the case exposed and 10 only the control exposed. What is the matched OR?

OR = 30 / 10 = 3.0. Concordant pairs do not enter the calculation.

## What is overmatching?

Matching on a variable linked to the exposure or on the causal pathway; it makes cases and controls alike in exposure and pulls the OR towards 1.

## If you matched on sex, can you estimate the effect of sex on the disease?

No: cases and controls have the same sex distribution by design, so its effect cannot be studied.

## Why are more than 4 controls per case rarely used?

Relative efficiency is c/(c + 1): it goes from 80 % with 4 controls to only 83 % with 5; cost rises faster than power.

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## Connections

## Related 6

- [Case-control study](https://durgical.com/en/epidemiology/case-control-study/)
- [Confounding](https://durgical.com/en/epidemiology/confounding/)
- [Controlling confounding](https://durgical.com/en/epidemiology/controlling-confounding/)
- [McNemar test](https://durgical.com/en/epidemiology/mcnemar-test/)
- [Odds ratio](https://durgical.com/en/epidemiology/odds-ratio/)
- [Case-crossover design](https://durgical.com/en/epidemiology/case-crossover-design/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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: [Principles of Epidemiology | Lesson 1 - Section 7](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson1/section7.html) (Centers for Disease Control and Prevention, 2012); [Confounding | Catalog of Bias](https://catalogofbias.org/biases/confounding/) (Catalogue of Bias Collaboration, 2018); [Chapter 25: Assessing risk of bias in a non-randomized study](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-25) (Cochrane, 2024).

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Representative model, for educational purposes only.

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