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

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

a) Frequency matching

Age Cases (years) 0-14 50 15-29 30 30-44 15 45+ 5

TOTAL 100

a) Frequency matching

Age Cases Controls(years) unmatched 0-14 50 20 15-29 30 20 30-44 15 20 45+ 5 40

TOTAL 100 100

a) Frequency matching

Age Cases Controls(years) unmatched matched 0-14 50 10 5015-29 30 25 3030-44 15 25 1545+ 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

a) Frequency matching: analysis

• keep stratification by age group

0-14 years Exposed Cases Controls Total Yes 45(a) 30(b) 75No 5(c) 20(d) 25Total 50 50 100(ni)

5.19

100150100900

i

i

ncbnda

a) Frequency matching: analysis

15-29 years Exposed Cases Controls Total Yes 15(a) 4(b) 19No 15(c) 26(d) 41Total 30 30 60(ni)

same process for each age group

0.15.6

606060390

i

i

ncbnda

etcetcORMH

15.15.69

b) individual matching

Each pair could be considered one stratum

4 possible outcomes per pairExposure

+ -Case 1 0Control 1 0

b) individual matching

Each pair could be considered one stratum

4 possible outcomes per pairExposure

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

b) individual matching

Each pair could be considered one stratum

4 possible outcomes per pairExposure

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

b) individual matching

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

b) individual matching

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

b) individual matching

If change way of presenting case and control data to show in pairs

ControlsExposed 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 3Cases

- 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