The third factor

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The third factor

• Effect modification
• Confounding factor FETP India

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Competency to be gained from this lecture

• Identify and describe an effect
  modificationEliminate a confounding factor

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Key elements

• Describing an effect modification
• Eliminating a confounding factor

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Stratification

• Sub-groups can be defined according to various
  characteristics in a population
• Age
• Sex
• Socio-economic status
• An association between a risk factor and an
  outcome may be studied within these various strata

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Key elements

• Describing an effect modification
• Eliminating a confounding factor

Effect modification
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Spotting effect modification in a stratified
analysis

• Effect modification ( Interaction) occurs when
  the answer about a measure of association is
• it depends
• Examples
• Efficacy of measles vaccine
• Variation according to the age
• Risk of myocardial infarction among women taking
  oral contraceptives
• Variation according to smoking habits

Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Death from diarrhoea according to breast-
feeding, Brazil, 1980s(Crude analysis)
Diarrhoea Controls Total No breastfeeding
120 136 256 Breastfeeding 50 204 254 Total 170 3
40 510
Odds ratio 3.6 95 CI 2.4- 5.5 p lt 0.0001
Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Death from diarrhoea according to breastfeeding,
Brazil, 1980s
Infants lt 1 month of age Cases Controls Total No
breastfeeding 10 3 13 Breastfeeding
7 68 75 Total 17 71 88 Infants 1 month of
age Cases Controls Total No breastfeeding
110 133 243 Breastfeeding 43 136 179 Total 153 2
69 422
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Death from diarrhoea according to breast
feeding, Brazil, 1980sAnalysis among infants lt
1 month of age
Cases Controls Total No breastfeeding
10 3 13 Breastfeeding 7 68 75 Total 17 71 88
Odds ratio 32.4 95 CI 6- 203 p lt 0.0001
Effect modification
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Death from diarrhoea according to breast
feeding, Brazil, 1980sAnalysis among infants
1 month of age
Cases Controls Total No breastfeeding
110 133 243 Breastfeeding 43 136 179 Total 153 2
69 422
Odds ratio 2.6 95 CI 1.7- 4.1 p lt 0.0001
Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Judge the heterogeneity of the measures of
association

• To be a difference, a difference should make a
  difference
• Review public health implications
• Odds ratios in the specific example
• Strata 1 OR 32 95 CI 6.0- 200
• Strata 2 OR 2.6 95 CI 1.7- 4.1

Effect modification
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Woolfs test for heterogeneity of the odds ratios

• Statistical testing of the heterogeneity of the
  odds ratios
• Lacks statistical power
• Calculation
• In statistical textbooks
• In the softwares analysis output
• Judgement is important

Effect modification
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Handling heterogeneous measures of association
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Describing an effect modification

• Conduct crude analysis
• Stratify data by suspected modifier
• Observe the association strata by strata
• Judge the heterogeneity of
• Odds ratios
• Relative risks
• Test a potential difference
• Report the effect modification

Effect modification
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Conclusion of the Brazilian case-control study on
breastfeeding and death from diarrhoea

• The protective efficacy of breastfeeding is more
  marked among infants under the age of one month
• This may correspond to a biological phenomenon
  that must be reported as part of the results

Effect modification
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Reporting results in the presence of an effect
modification

• Once the effect modification was detected the
  study population is split
• Results for the risk factor considered are
  reported stratum by stratum

Effect modification
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Vaccination against hepatitis B among
institutionalized children in Romania

• Hepatitis B is highly endemic in Romania
• Many children live in institutions
• Institutionalized children are at higher risk
• 1995 Hepatitis B immunization initiated
• 1997 Evaluation through serologic survey

Effect modification
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Hepatitis B vaccine efficacy among
institutionalized children over 6 months of age
, Romania, 1997

• Anti-HBc () Anti-HBc (-) RR 95 C.I.
• 3 doses 15 383 0.48 0.17-1.4
• lt 3 doses 4 47 Ref.
• Born after implementation of routine vaccination

HBVVaccine
Vaccine efficacy, 52, 95 CI 0-83
Effect modification
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Hepatitis B vaccine efficacy among
institutionalized children over 6 months of age
, by district, Romania, 1997

• Anti-HBc () Anti-HBc (-) RR 95 C.I.
• 3 doses 12 61 2.0 0.28-14
• lt 3 doses 1 11 Ref.
• 3 doses 3 322 0.12 0.0-0.6
• lt 3 doses 3 36 Ref.
• Wolf test for evaluation of interaction p 0.03
• Born after implementation of routine
  vaccination

District X
Others
Effect modification
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Hepatitis B vaccine efficacy among Romanian
children in institutions Conclusions

• The protective efficacy of hepatitis B vaccine
  appears low overall
• This overall low efficacy does not correspond to
  a biological phenomenon
• In fact, the efficacy is
• Normal in most districts (88)
• Low in district X
• This points towards programme errors that must be
  identified and prevented

Effect modification
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Describing an effect modificationSummary

• The analysis plan
• Anticipates effect modifiers to collect data
• The analysis
• Looks for effect modification to test it
• The report
• Breaks down the population in strata to report
  the effect modification

Effect modification
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Key elements

• Describing an effect modification
• Eliminating a confounding factor

Confounding factor
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What may explain an association between a risk
factor and an outcome?

• Chance
• Bias
• Third factor
• Causal association

Confounding factor
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What may explain an association between a risk
factor and an outcome?

• Chance
• Bias
• Third factor
• Causal association

Confounding factor
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Characteristics of a third, confounding factor

• Associated with the exposure
• Without being a consequence of exposure
• Associated with the outcome
• Independently from the exposure

Exposure
Outcome
Confounding factor
Confounding factor
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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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Example of confounding factor
Outcome
Exposure 1
Confounding factor
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Example of confounding factor (1)
Pneumonia
Ethnicity
Confounding factor
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Example of confounding factor (2)
Pneumonia
Crowding
Confounding factor
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Eliminating confounding in the pneumonia example

• Estimate the strength of the association between
  malnutrition and pneumonia
• Estimate the strength of the association between
  crowding and pneumonia
• Adjusted for the effect of malnutrition
• Eliminate the confounding effect of crowding on
  the false association between ethnicity and
  pneumonia

Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Adjustment to eliminate confounding

• Examine strength of association across strata
• Check for the absence of effect modification
• If there is an effect modification, break in
  various strata, report. End of the story
• Observation of a strength of association
• Homogeneous across strata
• Different from the crude measure
• Calculate weighted average of stratum-specific
  measures of association

Confounding factor
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Malaria and radio sets

• Hypothesis Could radio waves be a repellent for
  female anopheles?
• Cohort study on the risk factors for malaria in
  an endemic area

Confounding factor
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Incidence of malaria according to the presence of
a radio set, Kahinbhi Pradesh
Crude data Malaria No malaria Total Radio 80 440
520 No radio 220 860 1080 Total 300 1300 1600
RR 0.7 95 CI 0.6- 0.9 p lt 0.02
Confounding factor
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Incidence of malaria according to the presence of
a radio set, Kahinbhi Pradesh
Strata 1 Sleeping under a mosquito
net Malaria No malaria Total Radio 30 370 400 No
radio 50 630 680 Total 80 1000 1080
RR 1.02 95 CI 0.7- 1.6 p lt 0.97
Confounding factor
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Incidence of malaria according to the presence of
a radio set, Kahinbhi Pradesh
Strata 2 Sleeping without a mosquito net
Malaria No malaria Total Radio 50 70 120 No
radio 170 230 400 Total 220 300 520
RR 0.98 95 CI 0.8- 1.2 p lt 0.95
Confounding factor
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Mantel-Haenszel adjusted relative risk
????aixL0i) / Ti ????ci xL1i) / Ti
RR M-H
Confounding factor
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Malaria and radio sets Conclusion

• No association between radio and malaria within
  each strata
• The new adjusted relative risk replaces the crude
  one

Radio sets
Malaria
Confounding factor
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Mantel-Haenszel adjusted odds ratio
????ai.di) / Ti ????bi.ci) / Ti
OR M-H
Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Hepatitis B and blood transfusion in Moldova

• Hepatitis B virus infection is highly endemic in
  Moldova
• Routes of transmission are unknown
• A case control study was initiated to assess
  potential modes of transmission

Confounding factor
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Acute hepatitis B and receiving a transfusion in
Moldova, 1994-1995
Cases Controls Total Transfusion 3 1 4 Non-trans
fusion 69 189 258 Total 72 190 262 Odds ratio
8.2 95 CI 0.8-220
Confounding factor
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Acute hepatitis B and receiving a transfusion in
Moldova, 1994-1995 (According to receiving
injections)
Injections
No injections
Case Control Total Transfusion 0 0 0 No
transfusion 47 183 230 Total 47 183 230 Odds
ratio -
Case Control Total Transfusion 3 1 6 No
transfusion 22 6 28 Total 25 7 32
Odds ratio 0.8, 95 CI 0.1-24.9
Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Matching

• Stratification conducted initially at the stage
  of the study design of a case control study
• Stratified analysis (matched) necessary

Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Randomization

• Distribution of exposure of interest at random in
  the study population for a prospective cohort
• An association between an exposure and a
  confounding factor will be
• Secondary to chance alone
• Improbable

Confounding factor
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Controlling a confounding factor

• Stratification
• Restriction
• Matching
• Randomization
• Multivariate analysis

Confounding factor
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Multivariate analysis

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

Confounding factor
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Taking into account a third factor in practice

• Think of potential confounding factors
• Collect accurate data on them
• Conduct crude analysis
• Stratify
• Look for effect modification
• Are the RR or OR different to each other?
• If effect modification
• Report
• Do not adjust
• Control confounding factors through adjustment
• If applicable

Before the study
During the analysis
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Analyzing a third factor
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Take-home messages

• Describe effect modifications
• The analysis must TEST for their occurrences
• Control confounding factors
• The analysis must ELIMINATE their influence