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

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

attack rate of acute hepatitis e by zone of residence baripada orissa india 2004
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
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
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
Key elements
  • The concept of matching
  • The matched analysis
  • Pro and cons of matching
controlling a confounding factor
Controlling a confounding factor
  • Stratification
  • Restriction
  • Matching
  • Randomization
  • Multivariate analysis
the concept of matching
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
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
Types of matching strategies
  • Frequency matching
    • Large strata
  • Set matching
    • Small strata
    • Sometimes very small (1/1: pairs)
unmatched control group
Unmatched control group



Bag of cases

Bag of controls

matched control group
Matched control group



Sets of cases and controls that cannot be dissociated

matching false pre conceived ideas
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: True statements
  • Matching can put you in trouble
  • Matching can be useful to quickly recruit controls
matching criteria
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
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
Mantel-Haenszel adjusted odds ratio

ai.di) / Ti]

 / Ti]


matched analysis by set pairs of 1 case 1 control
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 by set pairs of 1 case 1 control1
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

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

the mantel haenszel odds ratio
The Mantel-Haenszel odds ratio...

S [(ai.di) / Ti]

S [( / Ti]


becomes the matched odds ratio
…becomes the matched odds ratio

SDiscordant sets case exposed

SDiscordant sets control exposed


and the analysis can be done with paper clips
…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
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
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

is difficult to recognize
... is difficult to recognize!

Controls Exposed Unexposed Total

Exposed e f a

Unexposed g h c

Total b d P (T/2)

Odds ratio: f/g


the mac nemar chi square
The Mac Nemar chi-square

(f - g) 2



matching advantages
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
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
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
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
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
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
Take home messages
  • Matching is a difficult technique
  • Matching design means matched analysis
  • Matching can always be avoided