1. Matching in case control studies
Lecture notes
Matching in case control studies
Yvan Hutin

2. Cases of acute hepatitis (E) by residence, Girdharnagar, Gujarat, India, 2008
Attack rate per 1,000
>
>0-10
Water pumping
station
Leak
Drain overflow

3. RR = 2.3, Chi Square= 41.1 df= 1. P < 0.001
Risk of hepatitis by place of residence, Girdharnagar, Gujarat, India, 2008
Source of water
Hepatitis
No hepatitis
Total
Leaking pipes /overflowing drain
144
8,694
8,838
No leakages / overflowing drain 89
12,436
12,525
233
21,130
21,363
RR = 2.3, Chi Square= 41.1 df= 1. P < 0.001

4. Attack rate of acute hepatitis (E) by zone of residence, Baripada, Orissa, India, 2004
Underground water supply
Pump from river bed
/ 1000
/ 1000
/ 1000
20+ / 1000
Chipat river

5. 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

6. Adjusted odds ratio = 33, 95 % confidence interval: 23- 47
Consumption of pipeline water among acute hepatitis cases and controls, Baripada, Orissa, India, 2004
Acute hepatitis
Control
Total
Drunk pipeline water
493
134
627
Did not drink
pipeline water 45
404
449
538
1076
Adjusted odds ratio = 33, 95 % confidence interval:

7. Key elements The concept of matching The matched analysis
Pro and cons of matching

8. Controlling a confounding factor
Stratification
Restriction
Matching
Randomization
Multivariate analysis

9. 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

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

11. 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

12. Types of matching strategies
Frequency matching
Large strata
Set matching
Small strata
Sometimes very small (1/1: pairs)

13. Unmatched control group
Cases
Controls
Bag of cases
Bag of controls

14. Sets of cases and controls that cannot be dissociated
Matched control group
Cases
Controls
Sets of cases and controls that cannot be dissociated

15. 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

16. Matching: True statements
Matching can put you in trouble
Matching can be useful to quickly recruit controls

17. Matching criteria Potential confounding factors Criteria
Associated with exposure
Associated with the outcome
Criteria
Unique
Multiple
Always justified

18. 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

19. Mantel-Haenszel adjusted odds ratio
ai.di) / Ti]
bi.ci) / Ti]
OR M-H=

20. 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
Total 1 1 2
No effect
No effect

21. 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
Total 1 1 2
Positive association
Negative association

22. The Mantel-Haenszel odds ratio...
S [(ai.di) / Ti]
S [(bi.ci) / Ti]
OR M-H=

23. …becomes the matched odds ratio
S Discordant sets case exposed
S Discordant sets control exposed
OR M-H=

24. …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

25. 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: -/++, -/+-, -/--

26. 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

27. ... 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
Cases

28. The Mac Nemar chi-square
(f - g) 2
(f+g)
Chi2 McN=

29. 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

30. 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

31. 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

32. 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

33. 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”

34. Breaking the match Rationale Procedure 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

35. Take home messages Matching is a difficult technique
Matching design means matched analysis
Matching can always be avoided