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Matching in case control studies. Yvan Hutin. Cases of acute hepatitis (E) by residence, Girdharnagar, Gujarat, India, 2008. Attack rate per 1,000 > 40 30-39 20-29 >0-10 0. Water pumping station. Leak. Drain overflow.

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Matching in case control studies

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Matching in case control studies

Yvan Hutin

Cases of acute hepatitis (E) by residence, Girdharnagar, Gujarat, India, 2008

Attack rate per 1,000

> 4030-3920-29



Water pumping



Drain overflow

Risk of hepatitis by place of residence, Girdharnagar, Gujarat, India, 2008

RR = 2.3, Chi Square= 41.1 df= 1. P < 0.001

Underground water supply

Pump from river bed

Attack rate of acute hepatitis (E) by zone of residence, Baripada, Orissa, India, 2004

Attack rate

0 - 0.9 / 1000

1 - 9.9 / 1000

10 -19.9 / 1000

20+ / 1000

Chipat river

Case-control study methods, acute hepatitis outbreak, Baripada, Orissa, India, 2004

  • Cases

    • All cases identified through active case search

  • Control

    • Equal number of controls selected from affected wards but in households without cases

  • Data collection

    • Reported source of drinking water

    • Comment events

    • Restaurants

Consumption of pipeline water among acute hepatitis cases and controls, Baripada, Orissa, India, 2004

Adjusted odds ratio = 33, 95 % confidence interval: 23- 47

Key elements

  • The concept of matching

  • The matched analysis

  • Pro and cons of matching

Controlling a confounding factor

  • Stratification

  • Restriction

  • Matching

  • Randomization

  • Multivariate analysis

The concept of matching

  • Confounding is anticipated

    • Adjustment will be necessary

  • Preparation of the strata a priori

    • Recruitment of cases and controls

      • By strata

      • To insure sufficient strata size

  • If cases are made identical to controls for the matching variable, the difference must be explained by the exposure investigated


  • The problem:

    • Confounding

  • Is solved with another problem:

    • Introduction of more confounding,

    • so that stratified analysis can eliminate it.

Definition of matching

  • Creation of a link between cases and controls

  • This link is:

    • Based upon common characteristics

    • Created when the study is designed

    • Kept through the analysis

Types of matching strategies

  • Frequency matching

    • Large strata

  • Set matching

    • Small strata

    • Sometimes very small (1/1: pairs)

Unmatched control group



Bag of cases

Bag of controls

Matched control group



Sets of cases and controls that cannot be dissociated

Matching: False pre-conceived ideas

  • Matching is necessary for all case-control studies

  • Matching needs to be done on age and sex

  • Matching is a way to adjust the number of controls on the number of cases

Matching: True statements

  • Matching can put you in trouble

  • Matching can be useful to quickly recruit controls

Matching criteria

  • Potential confounding factors

    • Associated with exposure

    • Associated with the outcome

  • Criteria

    • Unique

    • Multiple

    • Always justified

Risk factors for microsporidiosis among HIV infected patients

  • Case control study

  • Exposure

    • Food preferences

  • Potential confounder

    • CD4 / mm3

  • Matching by CD4 category

  • Analysis by CD4 categories

Mantel-Haenszel adjusted odds ratio

ai.di) / Ti]

 / Ti]


Matched analysis by set (Pairs of 1 case / 1 control)

  • Concordant pairs

    • Cases and controls have the same exposure

    • No ad and bc: no input to the calculation



Non exposed000




Non exposed 112


No effect

No effect

Matched analysis by set (Pairs of 1 case / 1 control)

  • Discordant pairs

    • Cases and controls have different exposures

    • ad’s and bc’s: input to the calculation



Non exposed011




Non exposed 101


Positive association

Negative association

The Mantel-Haenszel odds ratio...

S [(ai.di) / Ti]

S [( / Ti]


…becomes the matched odds ratio

SDiscordant sets case exposed

SDiscordant sets control exposed


…and the analysis can be done with paper clips!

  • Concordant questionnaire : Trash

  • Discordant questionnaires : On the scale

    • The "exposed case" pairs weigh for a positive association

    • The "exposed control" pairs weigh for a negative association

Analysis of matched case control studies with more than one control per case

  • Sort out the sets according to the exposure status of the cases and controls

  • Count reconstituted case-control pairs for each type of set

  • Multiply the number of discordant pairs in each type of set by the number of sets

  • Calculate odds ratio using the f/g formula

Example for 1 case / 2 controls

Sets with case exposed:+/++, +/+-, +/--Sets with case unexposed: -/++, -/+-, -/--

The old 2 x 2 table...





Odds ratio: ad/bc

... is difficult to recognize!



Unexposed ghc

TotalbdP (T/2)

Odds ratio: f/g


The Mac Nemar chi-square

(f - g) 2



Matching: Advantages

  • Easy to communicate

  • Useful for strong confounding factors

  • May increase power of small studies

  • May ease control recruitment

  • Suits studies where only one factor is studied

  • Allows looking for interaction with matching criteria

Matching: Disadvantages

  • Must be understood by the author

  • Is deleterious in the absence of confounding

  • Can decrease power

  • Can complicate control recruitment

  • Is limiting if more than one factor

  • Does not allow examining the matching criteria

Matching with a variable associated with exposure, but not with illness(Overmatching)

  • Reduces variability

  • Increases the number of concordant pairs

  • Has deleterious consequences:

    • If matched analysis: reduction of power

    • If match broken: Odds ratio biased towards one

Hidden matching (“Crypto-matching”)

  • Some control recruitment strategies consist de facto in matching

    • Neighbourhood controls

    • Friends controls

  • Matching must be identified and taken into account in the analysis

Matching for operational reasons

  • Outbreak investigation setting

  • Friends or neighbours controls are a common choice

  • Advantages:

    • Allows identifying controls fast

    • Will take care of gross confounding factors

    • May results in some overmatching, which places the investigator on “the safe side”

Breaking the match

  • Rationale

    • Matching may limit the analysis

    • Matching may have been decided for operational purposes

  • Procedure

    • Conduct matched analysis

    • Conduct unmatched analysis

    • Break the match if the results are unchanged

Take home messages

  • Matching is a difficult technique

  • Matching design means matched analysis

  • Matching can always be avoided

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