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