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

Matching(in case control studies)

James Stuart, Fernando SimónEPIET

Dublin, 2006

Remember confounding…

Confounding factor is variable independently associated with

• exposure of interest• outcome

that distorts measurement of association

Control of confounders

In the study design

• Restriction• Matching

In the analysis

• Stratification• Multivariate analysis

Matching

Selection of controls to match specific

characteristics of cases

a) Frequency matchingSelect controls to get same distribution of

variable as cases (e.g. age group)

b) Individual matchingSelect a specific control per case by

matching variable (e.g. date of birth)

… but matching introduces bias

because controls are no longer representative of source population

to remove this selection bias

• Stratify analysis by matching criteria

matched design matched analysis

• Can not study the effect of matching variables on the outcome

a) Frequency matching

useful if distribution of cases for a confounding variable differs markedly from distribution of that variable in source population


Age Cases

(years)

0-14 50

15-29 30

30-44 15

45+ 5

TOTAL 100


Age Cases Controls

(years) unmatched

0-14 50 20

15-29 30 20

30-44 15 20

45+ 5 40

TOTAL 100 100


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

a) Frequency matching: analysis

• Mantel-Haenszel Odds Ratio (weighted)

• Conditional logistic regression for

multiple variables

][

][

i

iMH ncb

ndaOR


• keep stratification by age group

0-14 years

Exposed Cases Controls Total

Yes 45(a) 30(b) 75

No 5(c) 20(d) 25

Total 50 50 100(ni)

5.1

9

100150

100900

i

i

ncb

nda


15-29 years

Exposed Cases Controls Total

Yes 15(a) 4(b) 19

No 15(c) 26(d) 41

Total 30 30 60(ni)

same process for each age group

0.1

5.6

6060

60390

i

i

ncb

nda

etc

etcORMH

15.1

5.69

b) individual matching

Each pair could be considered one stratum

4 possible outcomes per pair

Exposure

+ -

Case 1 0

Control 1 0




Exposure

+ - + -

Case 1 0 1 0

Control 1 0 0 1




Exposure

+ - + - + -

Case 1 0 1 0 0 1

Control 1 0 0 1 0 1


Each pair can be considered as one stratum

4 possible outcomes per pairExposure

+ - + - + - + -Case 1 0 1 0 0 1 0 1Control 1 0 0 1 0 1 1 0

ad = zero unless case exposed, control not exposed bc = zero unless control exposed, case not exposed


The only pairs that contribute to OR are discordant

ORMH= sum of discordant pairs where case exposed sum of discordant pairs where control exposed

][

][

i

iMH ncb

ndaOR


If change way of presenting case and control data

to show in pairs

Controls

Exposed Unexposed

Exposed e f (ad=1)

Cases

Unexposed g (bc = 1) h

ORMH = sum of discordant pairs where case exposed sum of discordant pairs where control exposed

= f/g

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 8pairs case not/control exp 1

OR= = = 8

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

Analysis: GP and age matched controls

swimming pool exposure

Controls+ -

+ 1 15Cases

- 1 3

OR = f/g = 15/1 = 15.0

Analysis: friend controls

swimming pool exposure

Controls

+ -

+ 13 3

Cases

- 1 3

OR = 3/1 = 3.0

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.

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

Over-matching

• exposure to the risk factor of interest

• under-estimates true association

• may fail to find true association

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

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

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