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Principles of case control studies
Part III
• Matching
Piyanit Tharmaphornpilas MD, MPH
Many slides in this presentation are from the World Health Organizatio Many slides in this presentation are from the World Health Organizatio n and n and
the European Programme for Intervention Epidemiology Training, than the European Programme for Intervention Epidemiology Training, than k you. k you.
The International Field Epidemiology Training Program, Thailand
Confounding
Hypothesis:
Sunbathe is a risk factor for being diabetes mellitus
Sunbathe Diabetes mellitus
Age
Sunbathe Diabetes mellitus
Reality :Age is confounding factor! need to be controlled
How to control confounding factors
Randomisation Restriction
Matching Adjustment Mutivariate analysis
Because age is confounding factor, so
(In cohort study) Age of exposed and unexposed population should be comparable!
Then, effect of age on the study association will be taken off.
(In case-control) age of cases and controls should be comparable!
If a case ages 30, his control should age 30 too.
Age
Sunbathe Diabetes mellitus
Reality :Age is confounding factor! need to be controlled
Types of matching Frequency matching
Large strata:Controls are selected in proportion to the number of
cases in each strata of the matching variable
Individual matchingSmall strata :For each case one or more controls are selected with
the matching characteristics
Frequency matching
Controls are selected in proportion (%) to the number of cases in each strata of the matching variable
Age15-2425-3435-4445-54>54
Total
Cases3030201010
100
Controls6060402020
200
The distribution of cases and controls is similar for age, and
controls are no more representative of the not-ill
population for age
Individual matching
For each case one or more controls are selected with the matching characteristics
The distribution of cases and controls is similar for age, and controls are no more representative of the not-ill population for age
No. Case Control1 Control2
1 age 30 age 30ฑ5 age 30 ฑ5
2 age 20 age 20 ฑ5 age 20 ฑ5
3 age 10 age 10 ฑ5 age 10 ฑ5
Matching : analysis
If….
control enrolment is done by matching
Then….analysis should be adjusted for it (by strata)
OR M-H=ai.di) / Ti]
bi.ci) / Ti]
Adjustment by Mantel-Haenszel
Using confounding (matching) variable as strata
Frequency matching : analysis
• Stratified analysis on the frequency matching variable
• Mantel Haenszel weigthed OR
Exposure Cases Controls TotalStrata 1 yes ai bi L1i
no ci di L0i
Total C1i C0i Ti
Strata j .... ai.di) / Ti]
bi.ci) / Ti]OR M-H =
Controls
Cases
Exposed
Exposed
Not Exposed
Not Exposed
Pairs of cases and controls
C+/Ctr + C+/Ctr -
C-/Ctr + C-/Ctr -
Individual matching analysis
Controls
Cases
Exposed
Exposed
Not Exposed
Not Exposed
e f
g h
Pairs of cases and controls
Individual matching analysis
One control per case : 4 situations for thecalculation of the ORMH
Situation Exp cases controls Total ad bc T ad/T bc/T C+ / Ctr+ + 1 1 2 0 0 2 0 0 - 0 0 0 Total 1 1 2 _C- / Ctr- + 0 0 0 0 0 2 0 0 - 1 1 2 Total 1 1 2 _ C+ /Ctr- + 1 0 1 1 0 2 1/2 0 - 0 1 1 Total 1 1 2 _C - / Ctr+ + 0 1 1 0 1 0 0 1/2 - 1 0 0 Total 1 1 2 _
Weighted ORMH = [(ai x di ) / Ti ] = (1 / 2) . ( C+/Ctr-) = C+ / Ctr - [(bi x ci) / Ti ] (1 / 2) . ( C+/Ctr-) C- / Ctr +Numerator : discordant pairs case exp+ / control exp-Denominator : discordant pairs case exp- / control exp+ Concordant pairs are not used
ControlsExposed Not exposedTotal
Exposed e f a
Not exposed g h c
Total b d T
Odds ratio: f/g
CASES
Controls
Atherosclerosis
CMV+
CMV+
CMV-
CMV-
Cases and controls individually match paired byAge group, sex, ethnicity, field center and date of exam
214 65
42 19
Atherosclerosis risk in Communities studyAssociation between CMV infection and Carotid Atherosclerosis
From: PD Sorlie et al, cytomegalovirus and carotid Atherosclerosis, Journal of Medical Virology, Vo 42, pp 33-37,1994
One control per case : 4 situations for thecalculation of the ORMH
Situation Exp cases controls Total ad/T bc/T C+ / Ctr+ + 1 1 2 e = 214 0 0 - 0 0 0 Total 1 1 2 _C- / Ctr- + 0 0 0 h = 19 0 0 - 1 1 2 Total 1 1 2 _ C+ /Ctr- + 1 0 1 f = 65 1/2 0 - 0 1 1 Total 1 1 2 _C - / Ctr+ + 0 1 1 g = 42 0 1/2 - 1 0 0 Total 1 1 2 _
Weighted ORMH = [(a i x di ) / Ti ] = (1 / 2) . ( 65 ) = 65 = 1.55 [(bi x c i) / Ti ] (1 / 2) . ( 42 ) 42
Numerator : discordant pairs case exp+ / control-Denominator : discordant pairs case exp- / control+Concordant pairs are not used for calculation
We cannot analyze a matched case-control studyby unmatched method
Why? ?
Because matching process introduce selection bias
This selection bias is controllable by stratified analysis
Matching : advantages
When there is a potentially strong confounding variable
Tends to increase the statistical power
Logistically straightforward way to obtain a comparable control group
Matching: disadvantages
Difficult to find a matched control Cannot assess the association between matching
variables and outcome Implies some tailoring of the selection of study groups
to make them comparable (less representativeness) Once is done cannot undone, risk of overmatching No statistical power is gained if the matched variables
are weak confounders
Don’t match (too much)
End of part III