Third Training Module, EpiSouth: Stratification, 15th to 19th June 2009 1/50
Stratification: Confounding, Effect
modificationThird training Module
EpiSouth
Madrid, 15th to 19th June, 2009
Dr D. Hannoun
National Institute of Public HealthAlgeria
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Introduction: GeneralityGenerality
Aims of analytical studies in epidemiology is to assess the association between two variables
• Is the association valid ? RD – RR – OR …
• is it causal ? Criterion of causality
In most case, we have to take in account a third (or more) variable that may affect the relationship studied
• Confounding bias +++
• Effect modification (Interaction) useful information +++:
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Introduction: GeneralityGenerality
Exposure Outcome
Vaccin efficacy Measle
Third variable• No effect: sexe (boy/girl)
• Intermediary v.: Antibodies rate
• Confounder: Mother education
• Effect modifier: Age VE is lower for children < 18 months
VE is the same for boy and girl
AR is a consequence of Vaccin
Effect observed is affected by ME
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Introduction: GeneralityGenerality
To avoid these complications we have many possibilities at essentially two steps :
• Step one in the study design
• Randomisation
• Restriction
• matching
• Step two in the analytical phase
• Standardization
• Stratification +++
• Multivariate analysis
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Stratification: Principle Principle
Principle :
• Create strata according to categories of the third variable
• Perfom analysis inside these strata
• Conclude about the studied relation inside the strata
• Forming «adjusted summary estimate»: concept of weighted average
• Assumption: weak variability in the strata
Stratification :
• To analyse effect modification
• To eliminate confounding
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Stratification: PrinciplePrinciple
To perform a stratified analysis, we have 6 steps :
1. Carry out simple analysis to test the association between the exposure and the disease and to Identify potential confounder
2. Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder
3. Carry out simple analysis to test the association between the exposure and the disease in each stratum
4. Test the presence or absence of effect modification between the variables
5. If appropriate, check for confounding and calculate a point estimate of overall effect (weighted average measure)
6. If appropriate, carry out and interpret an overall test for association
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Stratification: Step 1 – Example 1Step 1 – Example 1
Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study)
1. Crude analysis: Is there any association between vaccin efficacy and prevention of Measle ?
• RR = 0,55 [0,41-0,74] ; p < 10-5 VE = 1-RR = 45%
• There is an association between VE and Non occurrence of Measle
Measle+ Measle -
Vaccinated 72 79773
No vaccinated 116 71039
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Stratification: Step 1 – Example 1Step 1 – Example 1
Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study)
2. Identify potentiel confounder :
• Is the association real and valid or could be modify when we take in account a third factor : what about age ?
• We were interested in how the effects of a third variable, age at vaccination, may be influencing this relationship
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Stratification: Step 2 – Example 1Step 2 – Example 1
Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder
Example 1:
1. Number of categories of age : <1 year and 1-4 years
2. Create strata according to the number of categories
<1 yearMeasle+ Measle -
Vaccinated 38 35587
Not Vaccinated 30 24345
1 - 4 yearsMeasle+ Measle -
Vaccinated 34 44186
No vaccinated 86 46694
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Stratification: Step 3 – Example 1Step 3 – Example 1
Perfom analysis inside these strata1. In each strate
•Calculate the X2 to test the association•Estimate the RRi/ORi
<1 year
Measle+ Measle -
Vaccinated 38 35587
Not Vaccinated 30 24345
1 - 4 years
Measle+ Measle -
Vaccinated 34 44186
No vaccinated 86 46694
RRi = 0,87 [0,54 - 1,40] - VE= 13%
p = 0,55RRi = 0,42 [0,28 - 0,62] – VE= 58%
p < 10-8
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Stratification: Step 4 – Example 1Step 4 – Example 1
Test the presence or absence of interaction between the variables
• Appropriate tests
• Mantel-Haenszel test +++: the most commonly used
• Woolf test
• Breslow Day
• Tarone …
Spss tests
i i
2i2
)var(effect
effect)summary (effectΧ
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Stratification: Step 4 – Example 1Step 4 – Example 1
Test the presence or absence of interaction between the variables
• Breslow-Day: Test of homogeneity in strata :
• H0 : RR1 = RR2 Or OR1 = OR1
• =Χ2 test compared observed and expected counts
• It requires a large sample size within each stratum
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Stratification: Step 4 – Example 1Step 4 – Example 1
Test the presence or absence of interaction between the variables
Two possibilities
RR1 = RR2 or OR1 = OR2 RR1 RR2 or OR1 OR2
No Interaction: Third variable is Not an effect modifier
Presence of Interaction: Third variable could be effect modifier
Next step: Looking for confounding Trying to form adjusted measure
Stop here: Results only by strate No pooling measure
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Stratification: Step 4 – Example 1Step 4 – Example 1
Test the presence or absence of interaction …
Example 1: Homogeneity test: H0: RR<1year= RR1-4years (RR population)
– P < 10-4 statistical interaction +++
• There is interaction between age at vaccination and VE on the risk for Measle
• Age at vaccination modifies the effect of VE on the risk for Measle• Age at vaccination is an effect modifier for the relationship between VE and
Measle
• Not be appropriate to try to summarize these two effects, 0,87 and 0,42, into one overall number
• We should report the two stratum-specific estimates separately and stop here the analysis
0,87 ≠ 0,42 ????
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Stratification: Step 1 – Example 2Step 1 – Example 2
Example 2 : Investigation of Effectiveness of AZT in preventing HIV seroconversion after a needlestick (case control study)
1. Crude analysis: Is there any association between AZT and prevention of HIV seroconversion after a needlestick in health care workers ?
• ORcrude = 0,61 [0,26-1,44] ; p = 0,25
• No evidence of a benefit from AZT
• the authors stratified by the severity of the needlestick
HIV+ HIV-
AZT + 8 130
AZT - 19 189
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Stratification: Steps 2 and 3 – Example 2Steps 2 and 3 – Example 2
Divide the sample in strata, according to the number of categories of the confounder and perfom analysis inside …
1. Categories of severity of needlestick : minor and major severity
2. Create strata according to the number of categories
3. In each strate test the association and Estimate the RDi/RRi/ORi
Minor severity
HIV+ HIV -
AZT + 1 90
AZT - 3 161
Major severity
HIV+ HIV -
AZT + 7 40
AZT - 16 28
ORminor = 0,60 [0.06-5,81] – p = 1No association
ORmajor = 0,31 [0,11- 0,84] – p =0,02Presence of association
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Stratification: Step 4 – Example 2Step 4 – Example 2
Test the presence or absence of interaction between the variables
• Test of homogeneity in strata : H0 : ORminor = ORmajor ?
• p = 0,59 Breslow-Day test is not significant
No statistical interaction
Paradoxal result ?
• We assume there is no effect modification between severity of needlestick and AZT on the risk of HIV
• We could try to summarize these two effects, 0,60 and 0.31, into one overall number Construct a weighted average estimate
• Go to step 5
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Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
•Two steps
•Forming adjusted summary estimate
•Compare adjusted summary estimate to crude estimate
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Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
1.Forming an adjusted summary estimate
•It is the first step to assess the presence of confounding
•Properties:• Summary measure
• = weigthed average measure of the effect of exposure: RDi - RRi - ORi … according to the size of each stratum
•Weight depends upon a lot of factors:
• measure of association: RD – RR – OR…• nature of data: qualitative, quantitative• purpose of the analysis: follow-up study, case control study…
•Methods: • Mantel-Haenszel +++ • Woolf, Miettinen
RR/OR
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i
0iii
i
iia n
ncwavec
w
RRwRR
i i
1i1i
ii
i i
0i0i
ii
a
n
m*n
c
n
m*n
aRR
Strate i of FDis+ Dis -
E + ai bi noi
E - ci di n1i
moi m1i ni
Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
1.Estimation of RRa : Follow up study
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Strate i of FDis+ Dis -
E + ai bi noi
E - ci di n1i
moi m1i ni
Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
1.Estimation of ORa : Case control study
ORMH = ai di bi ci
ni ni
ORMH = wwii OR ORii / wwii Avec wAvec wii = b = bii c cii / n / nii
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Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
2. Identify confounding
• Compare the crude measure of effect to Adjusted measure of effect:
• H0 : RRMH = RRcrude or ORMH = ORcrude
• No statistical test to help us
• Confounding can be judged present when adjusted RRMH or ORMH is different from crude effect
• = (ORMH - ORcrude ) / ORcrude
• Arbitrary cut-off: >15-20 %or >20-30 %
• Interpretation
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Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
Two possibilities
< 15-20 % > 15-20 %
No confounding Presence of confounding
Use RRcrude or ORcrude
To measure the relationUse RRMH or ORMH
To measure the relation
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Stratification: Step 5 – Example 2Step 5 – Example 2
If appropriate, check for confounding
Be careful! We should report the adjusted measure:
• Only if we haven’t detected interaction: RRi or ORi are homogenous among strata
• And if we have detected confounding
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Stratification: Step 5 – Example 2Step 5 – Example 2
Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers
1. Estimation of ORa adjusted
ni = 255 ; OR = 0,60 ni = 92 ; OR = 0,31
Minor severity
HIV+ HIV -
AZT + 1 90
AZT - 3 161
Major severity
HIV+ HIV -
AZT + 8 40
AZT - 16 28
ORMH = 0,34 [0,14 – 0,87]
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Stratification: Step 5 – Example 2Step 5 – Example 2
Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health…
2. Identify confounding
• Compare the ORMH = 0,34 With ORcrude = 0,61
• = (ORMH - ORcrude ) / ORcrude = 44 %
• > 15-20 % We conclude that severity of needlestick is a confounder
• After adjusting for severity of needlestick, we obtain a reduction of the magnitude of the relation between AZT and prevention of the HIV seroconversion
• Conclusion : The good summary measure to use is the adjusted ORMH = 0,34
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Stratification: Step 6 – Example 2Step 6 – Example 2
If appropriate, carry out and interpret an overall test for association
1. Verify the relationship between the exposure and the outcome after adjusting on a third variable
• H0 : RRMH = 1or ORMH = 1
• Statistical test Mantel-Haenszel
• it follows a chi-square distribution of 1 ddl, regardless of the number of strata
2. Intervalle estimates of of RRa or ORa adjusted
2MHχ
1,961
RR 2
MHχ
1,961
OR
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Stratification: Step 6 – Example 2Step 6 – Example 2
Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers
1. Verify the relationship between the AZT and the HIV seroconversion after adjusting on the severity of needlestick
• H0 : ORMH = 1
• p = 0,036 Mantel-Haenszel test is significant
• Conclusion:
• After adjustement for severity of needlestick, we have an association between AZT and HIV
• When we have adjusted for severity of needlestick the OR decreased from 0,61 to 0,34 but became significant
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Confounding: Definition: Definition
= Stratum specific-estimates are from the crude estimate
= Distortion of measure effect because of a third factor
• Due to differences in the distribution of an extraneous factor in the exposed and unexposed group
Example:
• Individuals who are vaccinated tend to be healthier than individuals who are not vaccinated
Overestimation of the vaccin efficacy
Influenza Vaccine in elderly subjects
ARI death
Health status: 58%
74,7%
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Confounding: Definition: Definition
Be careful!
• Confounding is a concept
• Factor responsible for confounding is called a confounder or a confounding variable
• Confounder factor confounds the association of interest: It confounds an estimate
Examples:
1. Health status confonds the estimation of vaccine efficacy on ARI death
2. Needlestick confonds the estimation of AZT in preventing HIV seroconversion
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Confounding: Definition: Definition
When we have confounding:
• The observed association between exposure and disease can be attributed totally or in part to the effect of confounder
• Overestimation of the true association between exposure and disease occurs:
• Underestimation of the true association between exposure and disease occurs:
• Direction of observed effect could change
Crude effect > Adjusted Effect
Crude effect < Adjusted Effect
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Confounding: CriteriaCriteria
To be a confounding factor, The variable must be:
1. Associated with the outcome independently of exposure= risk factor for the disease even in the absence of exposure
• e.g. needlestick is asociated with the risk of HIV independently of exposure (prescription of AZT)
Exposure: AZT
Outcome: HIV
Confounder: Severity of needlestickIn cohort
studyIn case control
study
ORCD/Ē 1 ORCD/Ē 1
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Confounding: CriteriaCriteria
To be a confounding factor, The variable must be:
2. Associated with the exposure in the study population without being the consequence of exposure= Different distribution of the third variable in the exposed and unexposed group
• occurrence of needlestick is associated with the prescription of AZT
• Individuals with minor needlestich have lower probability to take AZT
Exposure: AZT
Outcome: HIV
Confounder: Severity of needlestick
ORCE 1
In cohort study
In case control study
ORCE/Ḋ 1
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Confounding: CriteriaCriteria
To be a confounding factor, The variable must be:
3. Not an intermediate link in the causal pathway between the exposure and the disease
Exposure: AZT
Confounder: Severity of needlestick
Outcome: HIV
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Confounding: CriteriaCriteria
To be a confounder, the variable must be presented the three criteria
Exposure: AZT
Outcome: HIV
Confounder: Severity of needlestick
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Confounding : How to identify confounderHow to identify confounder
Compare :
• Crude effect of measure association : RD - RR - OR
• To adjusted measure of effect : RDA - RRMH - ORMH
How ?
• Take in account only = (ORMH - ORcrude ) / ORcrude
• If > 15-20 % Presence of confounding
• If < 15-20 % No confounding
Statistical test must be avoided to identify confounding
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Effect modification
= Variation in the magnitude of measure of effect across levels of a third variable
• Tetracycline discolours teeth in children but not in adults
Tetracyclines
Age: children/adults
Vocabulary:
• Effect modification is a concept, also called effect measure modification, interaction or heterogeneity of effect
• Factor responsible for effect modification is called an effect modifier it modifies the effect of exposure on the outcome
Teeth coloration
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Effect modification: Interaction/synergismInteraction/synergism
Synergism= action of separates substances that in combination produce an effect greater than any component taken alone
Interaction
• quantitative relationship not necessarily related to basic biologic mechanisms
• Is a characteristic of the OBSERVED data
• is model-dependent
Effect modification
• Estimate depends on the presence/absence of another factor
• Is a characteristic of the POPULATION from the data came
• is effect measure-dependent
The two factors act at different levels of the processus
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Effect modification:Additive/multiplicativeAdditive/multiplicative
Remarks:
• Absence of interaction, when we use risk DIFFERENCE:
RAAB = RAA + RAB
Interaction, in this case, is called Additive interaction
OR
• Absence of interaction, when we use risk RATIO:
RRAB = RRA * RRB
Interaction, in this case, is called Multiplicative interaction
OR
RDAB > RDA + RDB RDAB > RDA + RDB
RRAB > RRA * RRB RRAB< RRA * RRB
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Effect modification: Additive/multiplicativeAdditive/multiplicative
exposedunexposed
0,05
0,15
0,150,45
RR = 3
RR = 3
Ris
k of
dis
eas
e
Ris
k of
dis
eas
e
0,05
0,15
RR = 3 – RD = 0,1
0,250,15
RR = 1,7 – RD = 0,1
Additive interactionNo multiplicative
interaction
Multiplicative interactionNo additive interaction
Third variable present
Third variable absent
unexposed exposed
RD = 0,3
RD = 0,1
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Effect modification:Additive/multiplicativeAdditive/multiplicative
Remarks:
• Assessment of interaction depends of the measure association used effect measure modification
• When you talk about intercation always precise the measure of association used
• When we have an effect, absence of multiplicative interaction implies presence of additive interaction and vice versa
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Effect modification : PropertiesProperties
Effect modification is not a bias but useful information
•Identification of subgroups with a lower or higher risk
•Targeting public health action
•Better understand of the disease: biological mechanism
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Effect modification : PropertiesProperties
To identify a subgroup with a lower or higher risk
• Example 1 : Influenza :
• Important complications for old people, for person with cardiac and pulmonary disease or diabetus…
• The risk of complication is more higher for these categories of people
• Age and comorbidity are effect modifiers for influenza
To target public health action
• Example 1 : Influenza
• Vaccination is recommanded for :
Old person,
Person with cardiac and pulmonary disease
Diabetus …
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Effect modification : How to assess it ? : How to assess it ?
Any statistical test to help us in assessing effect modification ?
• Yes: many tests to verify the homogeneity of the strata +++
• But not sufficient
•Clinical/biological decision rather than statistical
•Taking in account the magnitude of the effect modification
•Statistical tests depend on the size of the study
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Report effect modification or not ?
What is the decision ?
Potential effect modifier present
Potential effect modifier absent
P value for heterogeneity test
Report or ignore interaction
4,2 4,5 0,40
4,3 4,6 0,001
4,0 25,0 0,001
4 25,0 0,10
Ignore
Ignore
Report
Report
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Effect modification/ConfoundingEffect modification
Belongs to nature
Rare
≠ effects in ≠ strata
Must report stratum-specific estimates separately
Useful information
• ↗knowledge of biological mechanism
• Allows targeting of public health action
Confounding
Belongs to study
Frequent
Specific effects ≠ crude measure
Should report an adjusted weighted estimate
Distorsion of effect: bias
• Creates confusion in data
• ≠ distribution of the conf. in the exposed and unexposed group
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Effect modification/Confounding
Effect modification
Not
Could be controlled only if we have take in account in the study design phase
Statistical test for interaction
Confounding
Be prevented in the study design
Be controlled in the analytical phase
No statistical test for confounding
Both confounding and effect modification
• must be interpreted and take in account according to the knowledge of physiopathologic mechanism
• Determination is dependent on choice of effect measure : RD – RR – OR …
• Effect modification and confounding can exist separately or together
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General framework for stratification
In the study design phase:• Decide which variables to control for
In the implementation phase:• Measure the confounders or other variables needed to block path
In the analytical phase: • Assess clinical, statistical and practical consideration
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Crude analysis
Specific estimates among strata
Yes= Effect
modification
No= No effect
modification
Estimate adjusted estimate Crude estimate
Yes = Confounding No = No Confounding
Report stratum-specific estimates – No
pooled measure
Report adjusted estimate, 95% CI, p
value of χ2MH
Report crude estimate, 95% CI, p
value
Stratification
Specific estimates in each strata
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Stratification: Conclusion Conclusion
Stratification is useful tool to assess the real effect of exposure on the disease
But, its have some limits:
• Possibility of insufficient data when we have several strata
• Tool developped only for categorical variable
• Precision of the adjusted summary measure could be affected with overcontrolled
• Only possible to adjust for a limited number of confounders simultaneously
Necessity of other tools