1. Matching (in case control studies) James Stuart, Fernando Simón EPIET Dublin, 2006

2. Remember confounding… Confounding factor is variable independently associated with exposure of interest outcome that distorts measurement of association

3. Control of confounders In the study design Restriction Matching In the analysis Stratification Multivariate analysis

4. Control of confounders In the study design Restriction Matching In the analysis Stratification Multivariate analysis

5. Matching Selection of controls to match specific characteristics of cases a)Frequency matching Select controls to get same distribution of variable as cases (e.g. age group) b)Individual matching Select a specific control per case by matching variable (e.g. date of birth)

6. … but matching introduces bias because controls are no longer representative of source population

7. to remove this selection bias Stratify analysis by matching criteria matched designmatched analysis Can not study the effect of matching variables on the outcome

8. a) Frequency matching useful if distribution of cases for a confounding variable differs markedly from distribution of that variable in source population

9. a) Frequency matching Age Cases (years) 0-14 50 15-29 30 30-44 15 45+ 5 TOTAL 100

10. a) Frequency matching Age Cases Controls (years) unmatched 0-14 50 20 15-29 30 20 30-44 15 20 45+ 5 40 TOTAL 100100

11. a) Frequency matching Age Cases Controls (years) unmatched matched 0-14 50 10 50 15-29 30 25 30 30-44 15 25 15 45+ 5 40 5 TOTAL 100 100 100

12. a) Frequency matching: analysis Mantel-Haenszel Odds Ratio (weighted) Conditional logistic regression for multiple variables

13. a) Frequency matching: analysis keep stratification by age group 0-14 years Exposed CasesControlsTotal Yes45(a)30(b) 75 No 5(c)20(d) 25 Total 5050100(n i )

14. a) Frequency matching: analysis 15-29 years Exposed CasesControlsTotal Yes 15(a) 4(b) 19 No 15(c)26(d) 41 Total 3030 60(n i ) same process for each age group

15. b) individual matching Each pair could be considered one stratum 4 possible outcomes per pair Exposure + - Case1 0 Control1 0

16. b) individual matching Each pair could be considered one stratum 4 possible outcomes per pair Exposure+ - Case1 01 0 Control1 00 1

17. b) individual matching Each pair could be considered one stratum 4 possible outcomes per pair Exposure + -+ -+ - Case1 01 00 1 Control1 00 10 1

18. b) individual matching Each pair can be considered as one stratum 4 possible outcomes per pair Exposure + -+ -+ -+ - Case1 01 00 10 1 Control1 00 10 11 0 ad = zero unless case exposed, control not exposed bc = zero unless control exposed, case not exposed

19. b) individual matching The only pairs that contribute to OR are discordant OR MH = sum of discordant pairs where case exposed sum of discordant pairs where control exposed

20. b) individual matching If change way of presenting case and control data to show in pairs Controls ExposedUnexposed Exposed e f (ad=1) Cases Unexposed g (bc = 1) h OR MH = sum of discordant pairs where case exposed sum of discordant pairs where control exposed = f/g

21. b) individual matching: for n controls each set analysed in pairs case used in as many pairs as number of controls Case Control1 Control2 Control3 Control4 C+/Ctr- C-/Ctr+ + - + - - 3 0 + + - + + 1 0 - - - - - 0 0 + - - - + 3 0 - - + - - 0 1 + - + + + 1 0 + + + + + 0 0 Total......................................................................... 8 1 pairs case exp/control not 8 pairs case not/control exp 1 OR=== 8

22. Matched study: example 20 cases of cryptosporidiosis Hypothesis: associated with attendance at local swimming pool 2 matched studies conducted (i) controls from same general practice and nearest date of birth (ii) case nominated (friend) controls

23. Analysis: GP and age matched controls swimming pool exposure Controls + - +1 15 Cases -13 OR = f/g = 15/1 = 15.0

24. Analysis: friend controls swimming pool exposure Controls + - +133 Cases - 13 OR = 3/1 = 3.0

25. Why do matched studies? Random sample may not be possible Quick and easy way to get controls Improves efficiency of study (smaller sample size) Can control for confounding due to factors that are difficult to measure or even for unknown confounders.

26. Disadvantages of matching Cannot examine risks associated with matching variable If no controls identified, more likely if too many matching variables, lose case data and vice versa Overmatching on exposure of interest will bias OR towards 1 May be residual confounding in frequency matching

27. Over-matching exposure to the risk factor of interest under-estimates true association may fail to find true association

28. Key points Matching controls for confounding factors in study design Matched design matched analysis Matching for variables that are not confounders complicates design Frequency matching simpler than individual Multivariable analysis reduces need to match