Effect Modification

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Effect Modification Confounding

• Kostas Danis
• EPIET Introductory course,
• Menorca 2012

2
Analytical epidemiology

• Study design cohorts case control
• cross-sectional studies
• Choice of a reference group
• Biases
• Impact
• Causal inference

• Stratification
• - Effect modification - Confounding
• Matching
• Multivariable analysis

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Cohort studies marching towards outcomes
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Cohort study
Non cases Risk
Total
Cases
100
Exposed
50 50 50
Not exposed
100
10 90 10
Risk ratio 50 / 10 5
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Source population
Cases
Exposed
Sample
Unexposed
Controls Sample of the denominator Representati
ve with regard to exposure
Controls
6
Controls are non cases
Cases
Low attack rate non-cases likely to represent
exposure in source pop
Sourcepopn
Non- cases
end
start
High attack rate non-cases unlikely to
represent exposure in source population
Cases
Non- cases
end
start
7
Case control study
Controls Odds ratio
Cases
a b
Exposed
OR (a/c) / (b/d) ad / bc
Not exposed
c d
ac
bd
Total
Odds of exposure
a/c
b/d
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Who are the right controls?
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Controls may not be easy to find
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Cross-sectional study Sampling
Sample
Sampling Population
Target Population
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Cross-sectional study
Non cases Prevalence
Total
Cases
1,000
Exposed
500 500 50
Not exposed
100 900 10
1,000
Prevalence ratio (PR) 50 / 10 5
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Should I believe my measurement?
Exposure Outcome
RR 4
13
Exposure
Outcome
Third variable
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Two main complications

• (1) Effect modifier
• (2) Confounding factor

- useful information - bias
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To analyse effect modification To eliminate
confounding


Solution stratification
stratified analysis Create strata according
to categories inside the range of values
taken by third variable
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Effect modification
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Effect modifier
Variation in the magnitude of measure of effect
across levels of a third variable.
Happens when RR or OR is different between
strata (subgroups of population)
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Effect modifier

• To identify a subgroup with a lower or higher
  risk ratio
• To target public health action
• To study interaction between risk factors

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Effect modification

Effect modifier Interaction
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Asbestos (As) and lung cancer (Ca)
Case-control study, unstratified data
As Ca Controls OR Yes 693
320 4.8 No 307 680 Ref. Total 1000
1000
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Asbestos Lung
cancer
Smoking
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Asbestos (As), smoking and lung cancer (Ca)
As Smoking Cases Controls OR Yes
Yes 517 160 8.9 Yes
No 176 160 3.0 No Yes
183 340 1.5 No
No 124 340 Ref.
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Physical activity and MI
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Physical
Infarction activity
Gender
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Vaccine efficacy
ARU ARV VE ----------------
ARU VE 1 RR
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Vaccine efficacy
VE 1 - RR 1 - 0.28 VE 72
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Vaccine
Disease
Age
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Vaccine efficacy by age group
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Effect modification

• Different effects (RR) in different strata (age
  groups)
• VE is modified by age
• Test for homogeneity among strata (Woolf test)

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Any statistical test to help us?

• Breslow-Day
• Woolf test
• Test for trends Chi square

Homogeneity
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How to conduct a stratified analysis?
Crude analysis

• Stratified analysis
• Do stratum-specific estimates look different?
• 95 CI of OR/RR do NOT overlap?
• Is the Test of Homogeneity significant?

YES EFFECT MODIFICATION (Report estimates by
stratum)
NO Check for confounding (compare crude RR/OR
with MH RR/OR)
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Stratified analysis Effect Modification
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Death from diarrhea according to breast feeding,
Brazil, 1980s(Crude analysis)
Diarrhea Controls OR (95 CI) No breast
feeding 120 136 3.6 (2.4-5.5) Breast feeding
50 204 Ref
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No breast
Diarhoea feeding
Age
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Death from diarrhea according to breast feeding,
Brazil, 1980s
Infants lt 1 month of age Cases
Controls OR (95 CI) No breast
feeding 10 3
32 (6-203) Breast feeding 7
68 Ref Infants 1
month of age Cases Controls
OR (95 CI) No breast feeding 110
133 2.6 (1.7-4.1) Breast
feeding 43 136
Ref
Woolf test (test of homogeneity)p0.03
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Risk of gastroenteritis by exposure, Outbreak X,
Place, time X (crude analysis)
Exposed Exposed Exposed
Exposure Yes Yes No RR (95 CI)
Exposure n AR () n AR() RR (95 CI)
pasta 94 77 7 4.2 18.0 (8.8-38)
tuna 49 68 49 24 2.9 (2.1-3.8)
RR Risk Ratio
AR Attack Rate
95 CI 95 confidence interval of the RR
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Tuna
gastroenteritis
Pasta
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Risk of gastroenteritis by exposure, Outbreak X,
Place, time X (stratified analysis)
Pasta Yes Cases
Total AR () RR (95 CI) Tuna
43 52 83
1.1 (0.9-1.3) No tuna
46 60 77
Ref Pasta No Cases
Total AR () RR (95 CI)
Tuna 4 17
24 11 (2.6-46) No tuna
3 144 2
Ref
Woolf test (test of homogeneity) p0.0007
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Tuna, pasta and gastroenteritis
Tuna Pasta Cases AR()
RR Yes Yes 43 83
42 Yes No 4 23
12 No Yes 46
76 38 No No 3
2 Ref.
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Risk of HIV by injecting drug use (idu),
surveillance data, Spain, 1988-2004
Cases Total AR
() RR (95 CI) Idu 268 2,732
9.8 3.9 (3.3-4.4) No idu
484 18,822 2.5 Ref
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idu hiv
gender
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Risk of HIV by injecting drug use (idu), Spain,
1988-2004 (stratified analysis)
Males Cases Total
AR () RR (95 CI) idu
86 693 12
20 (14-28) No idu 52
8,306 0.6
Ref Females Cases
Total AR () RR (95 CI)
idu 182 2,039
8.9 2.3 (1.9-2.6) No idu
432 10,576 4.1
Ref
Woolf test (test of homogeneity) p0.00000
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Idu, gender and hiv
Idu Male Cases AR()
RR Yes Yes 86 12.4
3.0 Yes No 182 8.9
2.2 No Yes 52 0.6
0.14 No No 432 4.1
Ref.
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Confounding
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Confounding

• Distortion of measure of effect because of a
  third factor
• Should be prevented
• Needs to be controlled for

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Confounding
Skate- boarding
Chlamydia
Age
Age not evenly distributed between the
2 exposure groups - skate-boarders, 90 young -
Non skate-boarders, 20 young
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Exposure
Outcome (coffee)
(Lung cancer)
Third variable (smoking)
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Grey hair
stroke
Age
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Birth order
Down syndrom
Age or mother
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Confounding
To be a confounding factor, 2 conditions must be
met
Exposure
Outcome
Third variable
Be associated with exposure - without
being the consequence of exposure
Be associated with outcome -
independently of exposure
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Exposure
Outcome Hypercholesterolaemia
Myocardial infarction
Third factor Atheroma
Any factor which is a necessary step in the
causal chain is not a confounder
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Salt
Myocardial
infarction
Hypertension
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The nuisance introduced by confounding factors

• May simulate an association
• May hide an association that does exist
• May alter the strength of the association
• Increased
• Decreased

Confounding factor
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Apparent association
Ethnicity
Pneumonia

Crowding
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Altered strength of association
Crowding
Pneumonia

Malnutrition
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How to prevent/control confounding?

• Prevention
• Randomization (experiment)
• Restriction to one stratum
• Matching
• Control
• Stratified analysis
• Multivariable analysis

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Are Mercedes more dangerous than Porsches?
95 CI 1.3 - 1.8
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Car type
Accidents
Confounding factor Age of driver
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Crude RR 1.5 Adjusted RR 1.1 (0.94 - 1.27)
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Incidence of malaria according to the presence of
a radio set, Kahinbhi Pradesh
Crude data Malaria Total AR
RR Radio set 80 520 15
0.7 No radio 220 1080
20 Ref
RR 0.7 95 CI 0.6- 0.9 p lt 0.02
95 CI 0.6 - 0.9
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Radio
Malaria
Confounding factor Mosquito net
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Crude RR 0.7 Adjusted RR 1.01
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To identify confounding

• Compare crude measure of effect (RR or OR)
• to
• adjusted (weighted) measure of effect
• (Mantel Haenszel RR or OR)

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Any statistical test to help us?

• When is ORMH different from crude OR ?

10 - 20
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Mantel-Haenszel summary measure

• Adjusted or weighted RR or OR
• Advantages of MH
• Zeroes allowed

S (ai di) / ni OR MH ------------------------
--- S (bi ci) / ni
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Mantel-Haenszel summary measure

• Mantel-Haenszel (adjusted or weighted) OR

n1
Cases
Controls
Exp
a2
(a1 x d1) / n1 ORMH
----------------------------------------

(a2 x d2) / n2
b2
(b2 x c2) / n2
(b1 x c1) / n1
d2
Exp-
c2
n2
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How to conduct a stratified analysis?
Crude analysis

• Stratified analysis
• Do stratum-specific estimates look different?
• 95 CI of OR/RR do NOT overlap?
• Is the Test of Homogeneity significant?

YES EFFECT MODIFICATION (Report estimates by
stratum)
NO Check for confounding (compare crude RR/OR
with MH RR/OR)
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Risk of gastroenteritis by exposure, Outbreak X,
Place, time X (crude analysis)
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Stratified Analysis
gt 10-20
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Examples of stratified analysis
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• Effect modifier
• Belongs to nature
• Different effects in different strata
• Simple
• Useful
• Increases knowledge of biological mechanism
• Allows targeting of PH action
• Confounding factor
• Belongs to study
• Weighted RR different from crude RR
• Distortion of effect
• Creates confusion in data
• Prevent (protocol)
• Control (analysis)

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Analyzing a third factor
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How to conduct a stratified analysis

• Perform crude analysisMeasure the strength of
  association
• List potential effect modifiers and confounders
• Stratify data according topotential modifiers or
  confounders
• Check for effect modification
• If effect modification present, show the data by
  stratum
• If no effect modification present, check for
  confoundingIf confounding, show adjusted dataIf
  no confounding, show crude data

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How to define the strata?

• Strata defined according to third variable
• Usual confounders (e.g. age, sex,
  socio-economic status)
• Any other suspected confounder, effect modifier
  or additional risk factor
• Stratum of public health interest
• For two risk factors
• stratify on one to study the effect of the second
  on outcome
• Two or more exposure categories
• each is a stratum
• Residual confounding ?

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Logical order of data analysis

• How to deal with multiple risk factors
• Crude analysis
• Multivariable analysis
• 1. stratified analysis
• 2. modelling
• linear regression
• logistic regression

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Multivariate analysis

• Mathematical model
• Simultaneous adjustment of all confounding and
  risk factors
• Can address effect modification

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A train can mask a second train
A variable can mask another variable
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Back-up slides
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Risk factors for Salmonella enteritidis
infections, France, 1995
Delarocque-Astagneau et al Epidemiol. Infect
1998121561-7
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Cases of Salmonella enteritidis gastroenteritis
according to egg storage and season
Summer Cases Controls OR (95CI)
Duration of storage
gt 2 weeks 12 2 7.4 (1.5-69.9)
lt 2 weeks 52 64 7.4 (1.5-69.9)
Other seasons Other seasons Other seasons Other seasons
Duration of storage
gt 2 weeks 7 3 2.6 (0.5-16.8)
lt 2 weeks 32 36 2.6 (0.5-16.8)
All seasons All seasons All seasons All seasons
gt 2 weeks 19 5 4.5 (1.5 16.1)
lt 2 weeks 84 100 4.5 (1.5 16.1)
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Duration
Salmonellosis of storage
Season
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Cases of Salmonella enteritidis gastroenteritis
according to egg storage and season
Summer (A) Long storage (B) Cases Control OR OR
Yes Yes 12 2 ORAB 6.8
Yes No 52 64 ORA 0.9
No Yes 7 3 ORB 2.6
No No 32 36 Ref Ref
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Advantages Disadvantages of Stratified Analysis

• Advantages
• straightforward to implement and comprehend
• easy way to evaluate interaction
• Disadvantages
• only one exposure-disease association at a time
• requires continuous variables to be grouped
• Loss of information possible residual
  confounding
• deteriorates with multiple confounders
• e.g. suppose 4 confounders with 3 levels
• 3x3x3x381 strata needed
• unless huge sample, many cells have 0 and
  strata have undefined effect measures