Matching

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Matching
EPIET Mahón, 2006
J Stuart F Simón, 2005T Grein, 2006
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Once again confounding
Exposure
Outcome
Third variable
Be associated with exposure - without
being consequence of exposure
Be associated with outcome -
independent of exposure
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Control of confounders

• In analysis
• Stratification
• Multivariable analysis
• In study design
• Randomization (experiment)
• Restriction
• Matching

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Matching

• Ensures that confounding factor is equally
  distributed among each of study groups
• Controls selected to match specific
  characteristics of cases
• Unexposed selected to match specific
  characteristics of exposed
• Achieves balanced data set that can
• Prevent confounding (if matched on confounder)
• Increase study precision

• Focus on case-control studies as implications
  more important

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Types of matching

• Individual matching
• Controls selected individually for each case by
  matching variable
• Pairs of individuals (11)
• Selection of more than one control per case (1n)
• Frequency matching
• Number of controls selected according to number
  of cases in categories of matching variable
• Matching done by groups of subjects
• In both cases, analysis must take matching design
  into account

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Individual matching

• Echovirus meningitis outbreak, Germany, 2001
• Is swimming in pond A risk factor?
• Case control study with each case matched to one
  control

Source A Hauri, RKI Berlin
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Individual matching

• Echovirus meningitis outbreak, Germany, 2001
• Is swimming in pond A risk factor?
• Case control study with each case matched to one
  control

Concordant pairs
Source A Hauri, RKI Berlin
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Individual matching
Matched 2x2 table
Unmatched 2x2 table
x
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Individual matching Analysis

• Treat each pair as one stratum
• Calculate Mantel-Haenszel odds ratio
• Nomenclature matched 2x2 table

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Individual matching Analysis
11
Individual matching Analysis
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Individual matching Analysis
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Individual matching Analysis
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Individual matching Analysis
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Individual matching Analysis
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Matching case to n controls

• Same principle as 11 matching
• Constitute pairs
• Pair (1 case, 1 control)
• Triplet (1 case, 2 controls) yields 2 pairs
• Quadruplet (1 case, 3 controls) yields 3 pairs
• Etc
• Stratified analysis by pairs

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Matching case to n controls

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Frequency matching Analysis

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Frequency matching Analysis

Stratum 3Stratum 4
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Frequency matching Analysis

• With many strata, stratification quickly leads to
  sparse data problem
• Matching for gt 1 confounder
• Numerous nominal categories
• Conditional logistic regression
• Logistic regression for matched data
• Conditional on using discordant pairs only
• Matching variable itself cannot be analysed
• Testing for interaction of matching variable
  possible

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Why stratified analysis?

• Matching eliminates the original confounding, but
  introduces another confounding factor
• Controls no longer representative of source
  population as selected according to matching
  criteria (selection bias)
• Cases and controls more alike. By breaking match,
  OR usually underestimated
• Matched design matched analysis

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Overmatching

• 20 cases of cryptosporidiosis
• ? associated with attendance at local swimming
  pool
• Two matched studies
• Controls from same general practice and nearest
  date of birth
• Cases nominated controls (friend controls)

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Overmatching
GP, age-matched OR f/g 15/1 15
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Advantages of matching

• Useful method in case-control studies to optimise
  resources
• Can control for complex environmental, genetic,
  other factors
• Siblings, neighbourhood, SES, utilization of
  health care
• Can increase study efficiency
• Overcomes sparse-data problem by balancing strata
• Maximises information when sample size small
• Sometimes easier to identify controls
• Random sample may not be possible

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Disadvantages of matching

• Cannot examine risks associated with matching
  variable
• If no controls identified, lose case data, and
  vice versa
• Overmatching on exposure will bias OR towards 1
• Complicates statistical analysis
• Residual confounding by poor definition of strata
  
• Sometimes difficult to identify appropriate
  controls

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Take-home messages

• Useful technique if employed wisely
• Balanced data sets, increased precision,
  prevention of confounding
• Can control for complex factors which would be
  difficult to measure otherwise
• Do not match because it is convenient
• Routine
• Tedious to obtain random sample from source
  population
• Want to avoid large sample size
• If you match, make sure you match on a confounder

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Thank you