Arranged marriage

1. Arranged marriage Matching in case control studies FETP India

2. Competency to be gained from this lecture Design and analyze a matched case control study

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

4. Controlling a confounding factor • Stratification • Restriction • Matching • Randomization • Multivariate analysis The concept of matching

5. 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

6. Why matching? • If cases and controls are similar for the matching variables, • Then, differences must be otherwise explained. The concept of matching

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

8. 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

9. Types of matching strategies • Frequency matching • Large strata • Set matching • Small strata • Sometimes very small (1/1: pairs) The concept of matching

10. 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

11. Matching: True statements • Matching can put you in trouble • Matching can be useful to quickly recruit controls The concept of matching

12. Matching criteria • Potential confounding factors • Associated with exposure • Associated with the outcome • Criteria • Unique • Multiple • Always justified The concept of matching

13. 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

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

15. 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

16. 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 Matched analysis

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

18. …becomes the matched odds ratio SDiscordant sets case exposed SDiscordant sets control exposed OR M-H= Matched analysis

19. …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

20. 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

21. 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

22. ... is difficult to recognize! ControlsExposed UnexposedTotal Exposed e f a Unexposed g h c Total b d P (T/2) Odds ratio: f/g Cases Matched analysis

23. The Mac Nemar chi-square (f - g) 2 (f+g) Chi2McN= Matched analysis

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

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