Arranged marriage

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Arranged marriage

• Matching in case control studies
• FETP India

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Competency to be gained from this lecture

• Design and analyze a matched case control study

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Key elements

• The concept of matching
• The matched analysis
• Pro and cons of matching

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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

The concept of matching
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Matching concept

• Confounding is anticipated
• Adjustment will be necessary
• Preparation of the strata a priori
• Recruitment of cases and controls
• By strata
• To ensure sufficient strata size

The concept of matching
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Why matching?

• If cases and controls are similar for the
  matching variables,
• Then, differences must be otherwise explained.

The concept of matching
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Consequences....

• The problem
• Confounding
• Is solved with another problem
• Introduction of more confounding,
• so that stratified analysis can eliminate it.

The concept of matching
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Matching Definition

• 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

The concept of matching
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Types of matching strategies

• Frequency matching
• Large strata
• Set matching
• Small strata
• Sometimes very small (1/1 pairs)

The concept of matching
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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

The concept of matching
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Matching True statements

• Matching can put you in trouble
• Matching can be useful to quickly recruit
  controls

The concept of matching
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Matching criteria

• Potential confounding factors
• Associated with exposure
• Associated with the outcome
• Criteria
• Unique
• Multiple
• Always justified

The concept of matching
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Example 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

The concept of matching
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Mantel-Haenszel adjusted odds ratio
????ai.di) / Ti ????bi.ci) / Ti
OR M-H
Matched analysis
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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

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
No effect
No effect
Matched analysis
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Matched analysis by set (Pairs of 1 case / 1
control)

• Discordant pairs
• Cases and controls have different exposures
• ads and bcs input to the calculation

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
Positive association
Negative association
Matched analysis
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The Mantel-Haenszel odds ratio...
S (ai.di) / Ti S (bi.ci) / Ti
OR M-H
Matched analysis
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becomes the matched odds ratio
S Discordant sets case exposed S Discordant
sets control exposed
OR M-H
Matched analysis
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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

Matched analysis
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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 -/, -/-, -/--
Matched analysis
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The old 2 x 2 table...
Cases Controls Total Exposed a b L1 Unexposed c
d L0 Total C1 C0 T Odds ratio ad/bc
Matched analysis
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... is difficult to recognize!
Controls Exposed Unexposed To
tal Exposed e f a Unexposed g h c Total b d P
(T/2) Odds ratio f/g
Cases
Matched analysis
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The Mac Nemar chi-square
(f - g) 2 (fg)
Chi2 McN
Matched analysis
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Matching Advantages

• Is easy to communicate
• Is useful for strong confounding factors
• Can increase the power of small studies
• Can ease control recruitment
• Is useful if only one factor is studied
• Allows looking for effect modification with
  matching criteria

Pro and cons
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Matching Inconvenience

• 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 association with the
  matching criteria

Pro and cons
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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

Pro and cons
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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

Pro and cons
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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 result in some overmatching, which places the
  investigator on the safe side

Pro and cons
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Breaking the match

• Rationale
• Matching may limit the analysis
• Matching may have been decided for operational
  purposes only
• Procedure
• Conduct matched analysis
• Conduct unmatched analysis
• Break the match if the results are unchanged

Pro and cons
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Take-home messages

• Matching is a difficult technique
• Matching design means matched analysis
• Matching can always be avoided