Matching in case control studiesYvan Hutin

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

Attack rate per 1,000

> 4030-3920-29>0-100

Water pumping station

Leak

Drain overflow

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

3

Source of water HepatitisNo

hepatitisTotal

Leaking pipes /overflowing

drain144 8,694 8,838

No leakages / overflowing

drain89 12,436 12,525

Total 233 21,130 21,363

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

Ch

ipat

river

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

0 - 0.9 / 1000

1 - 9.9 / 1000

10 -19.9 / 1000

20+ / 1000

Attack rate

Underground water supply

Pump from river bed

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

Acute hepatitis

Control Total

Drunk pipeline water

493 134 627

Did not drink

pipeline water45 404 449

Total 538 538 1076

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

Consumption of pipeline water among acute hepatitis cases and controls,

Baripada, Orissa, India, 2004

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

Consequence....

• 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

Cases

Controls

Bag of cases Bag of controls

Matched control group

Cases

Controls

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

OR M-H=ai.di) / Ti]

bi.ci) / Ti]

Mantel-Haenszel adjusted odds ratio

Cases Controls Total

Exposed 1 1 2

Non exposed 0 0 0

Total 1 1 2

Cases Controls Total

Exposed 0 0 0

Non exposed 1 1 2

Total 1 1 2

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

No effect No effect

Cases Controls Total

Exposed 1 0 1

Non exposed 0 1 1

Total 1 1 2

Cases Controls Total

Exposed 0 1 1

Non exposed 1 0 1

Total 1 1 2

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

Positive association Negative association

OR M-H=ai.di) / Ti]

bi.ci) / Ti]

The Mantel-Haenszel odds ratio...

OR M-H=Discordant sets case exposed

Discordant sets control exposed

…becomes the matched odds ratio

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

Cases Controls Total

Exposed a b L1

Unexposed c d L0

Total C1 C0 T

Odds ratio: ad/bc

The old 2 x 2 table...

ControlsExposed Unexposed Total

Exposed e f a

Unexposed g h c

Total b d P (T/2)

Odds ratio: f/g

Case

s... is difficult to recognize!

Chi2 McN=(f - g) 2

(f+g)

The Mac Nemar chi-square

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