stratification: confounding , effect modification

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


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 +++:



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



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


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


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


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



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



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




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


RRi = 0,87 [0,54 - 1,40] - VE= 13%

p = 0,55RRi = 0,42 [0,28 - 0,62] – VE= 58%

p < 10-8



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




• 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




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



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 ????



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


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




• 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



If appropriate, check for confounding

•Two steps

•Forming adjusted summary estimate

•Compare adjusted summary estimate to crude estimate




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


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



1.Estimation of RRa : Follow up study


Strate i of FDis+ Dis -

E + ai bi noi

E - ci di n1i

moi m1i ni



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




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




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




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



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]



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



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



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


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%



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



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


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




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




3. Not an intermediate link in the causal pathway between the exposure and the disease

Exposure: AZT


Outcome: HIV



To be a confounder, the variable must be presented the three criteria

Exposure: AZT

Outcome: HIV



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


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


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


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


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


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


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


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 …


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


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


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


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


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


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


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

stratification: confounding , effect modification

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