Principles of case control studies Part III • Matching Many slides in this presentation are from the World Health Organization and ization and Many slides in this presentation are from the World Health Organ the European Programme Programme for Intervention Epidemiology Training for Intervention Epidemiology Training, , thank you thank you. . the European Piyanit Tharmaphornpilas MD, MPH The I nternational Field Epidemiology Training Program, Thailand
Confounding Hypothesis: Sunbathe is a risk factor for being diabetes mellitus Sunbathe Diabetes mellitus Age is confounding factor! Reality : need to be controlled Age Sunbathe Diabetes mellitus
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 is confounding factor! Reality : need to be controlled Age Sunbathe Diabetes mellitus
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 matching Small 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 Cases Controls Age 30 60 15-24 The distribution of cases and controls is similar for age, and 30 60 25-34 controls are no more 20 40 35-44 representative of the not-ill 10 20 45-54 population for age 10 20 >54 100 200 Total
Individual matching For each case one or more controls are selected with the matching characteristics No. Case Control1 Control2 age 30 ฑ 5 age 30 ฑ 5 1 age 30 age 20 ฑ 5 age 20 ฑ 5 2 age 20 age 10 ฑ 5 age 10 ฑ 5 3 age 10 The distribution of cases and controls is similar for age, and controls are no more representative of the not-ill population for age
Matching : analysis If…. control enrolment is done by matching Then…. analysis should be adjusted for it (by strata)
Adjustment by Mantel-Haenszel Using confounding (matching) variable as strata Σ [( a i .d i ) / Ti] OR M-H = Σ [( b i .c i ) / Ti]
Frequency matching : analysis • Stratified analysis on the frequency matching variable • Mantel Haenszel weigthed OR Exposure Cases Controls Total Strata 1 yes a i b i L1 i no c i d i L0 i Total C1 i C0 i T i Strata j .... Σ [( a i .d i ) / Ti] OR M-H = Σ [( b i .c i ) / Ti]
Individual matching analysis Controls Exposed Not Exposed Exposed C + / Ctr + C + / Ctr - Cases C - / Ctr + C - / Ctr - Not Exposed Pairs of cases and controls
Individual matching analysis Controls Exposed Not Exposed e f Exposed Cases g h Not Exposed Pairs of cases and controls
One control per case : 4 situations for the calculation of the OR MH 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 2 0 1/2 - 1 0 0 Total 1 1 2 _ Weighted OR MH = Σ [(a i x d i ) / T i ] = (1 / 2) * (C+/Ctr-) = C+ / Ctr - Σ [(b i x c i ) / T i ] (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
Controls Exposed Not exposed Total e f a C Exposed A g h c Not exposed S E b d T Total S Odds ratio: f/g
Atherosclerosis risk in Communities study Association between CMV infection and Carotid Atherosclerosis Controls CMV+ CMV- CMV+ 214 65 Atherosclerosis 42 19 CMV- Cases and controls individually match paired by Age group, sex, ethnicity, field center and date of exam 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 the calculation of the OR MH 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 OR MH = Σ [(a i x d i ) / T i ] = (1 / 2) . ( 65 ) = 65 = 1.55 Σ [(b i x c i ) / T i ] (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 study by 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 I I I
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