Principles of case control studies Part III Matching Many slides - - PowerPoint PPT Presentation

Principles of case control studies

Part III

• Matching

Piyanit Tharmaphornpilas MD, MPH

Many slides in this presentation are from the World Health Organ Many slides in this presentation are from the World Health Organization and ization and the European the European Programme Programme for Intervention Epidemiology Training for Intervention Epidemiology Training, , thank you thank you. . The I nternational 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 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 Age 15-24 25-34 35-44 45-54 >54 Total Cases 30 30 20 10 10 100 Controls 60 60 40 20 20 200

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 30 ฑ 5 age 30 ฑ 5 2 age 20 age 20 ฑ 5 age 20 ฑ 5 3 age 10 age 10 ฑ 5 age 10 ฑ 5

Matching : analysis

If….

control enrolment is done by matching

Then….

analysis should be adjusted for it (by strata)

OR M-H=

Σ [(ai.di) / Ti] Σ [(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 Total Strata 1 yes ai bi L1i no ci di L0i Total C1i C0i Ti Strata j ....

Σ [(ai.di) / Ti] Σ [(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 the calculation 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 2 0 1/2

• 1 0 0

Total 1 1 2 _ Weighted ORMH = Σ[(ai x di ) / Ti ] = (1 / 2) * (C+/Ctr-) = C+ / Ctr - Σ[(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

Controls

Exposed Not exposed Total Exposed

e f a

Not exposed

g h c

Total

b d T

Odds ratio: f/g

C A S E S

Controls Atherosclerosis

CMV+ CMV+ CMV- CMV- Cases and controls individually match paired by Age group, sex, ethnicity, field center and date of exam 214 65 42 19 Atherosclerosis risk in Communities study Association 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 the calculation 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 = Σ[(ai x di ) / Ti ] = (1 / 2) . ( 65 ) = 65 = 1.55 Σ[(bi x ci) / 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 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