The third factor Effect modification Confounding factor FETP India.

The third factor

Effect modificationConfounding factor

FETP India

Competency to be gained from this lecture

Identify and describe an effect modification

Eliminate a confounding factor

Key elements

• Describing an effect modification• Eliminating a confounding factor

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

Key elements


Effect modification

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

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

Diarrhoea Controls Total

No breastfeeding 120 136 256

Breastfeeding 50 204 254

Total 170 340 510

Death from diarrhoea according to breastfeeding, Brazil, 1980s

(Crude analysis)

Odds ratio: 3.6; 95% CI: 2.4- 5.5; p < 0.0001

Effect modification





Effect modification

Infants < 1 month of age

Cases Controls Total



Total 17 71 88

Infants ≥ 1 month of age




Total 153 269 422

Death from diarrhoea according to breastfeeding, Brazil, 1980s





Effect modification




Total 17 71 88

Death from diarrhoea according to breast feeding, Brazil, 1980s:

Analysis among infants < 1 month of age

Odds ratio: 32.4; 95% CI: 6- 203; p < 0.0001

Effect modification




Total 153 269 422

Death from diarrhoea according to breast feeding, Brazil, 1980s:

Analysis among infants ≥ 1 month of age

Odds ratio: 2.6; 95% CI: 1.7- 4.1; p < 0.0001

Effect modification





Effect modification

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





Effect modification

Woolf’s 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 software’s analysis output

• Judgement is important

Effect modification

Handling heterogeneous measures of association

Eff ect modifi cat ion

ORs / RRs 95% C. I.do not overlap


Wool f 's test signifi cant

Discuss lack of powerof Wol lf 's test

Eff ect modifi cat ionunl ikely

Wool f 's test not signifi cant

Use Wool f 's test

ORs / RRs C. I.do overlap

ORs / RRs arediff erent across st rata





Effect modification

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

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

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

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

< 3 doses 4 47 Ref.

* Born after implementation of routine vaccination

Vaccine efficacy, 52%, 95% CI 0-83%

HBVVaccine

Effect modification

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< 3 doses 1 11 Ref.

3 doses 3 322 0.12 0.0-0.6< 3 doses 3 36 Ref.

Wolf test for evaluation of interaction: p = 0.03

* Born after implementation of routine vaccination

Dis

tric

t X

Oth

ers

Effect modification

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

Describing an effect modification:Summary

• 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

Key elements


Confounding factor

What may explain an association between a risk factor and an

outcome?? Chance? Bias? Third factor? Causal association

Confounding factor

Exposure

Characteristics of a third, confounding factor

• Associated with the exposure Without being a consequence of exposure

• Associated with the outcome Independently from the exposure

Outcome

Confounding factor

Confounding factor

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

Outcome

Example of confounding factor

Exposure 1Apparent association

Confounding factor

Confounding factor

Pneumonia

Example of confounding factor (1)

EthnicityApparent association

Crowding

Confounding factor

Pneumonia

Example of confounding factor (2)

CrowdingAltered strength of

association

Malnutrition

Confounding factor

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

Controlling a confounding factor

• Stratification• Restriction• Matching • Randomization • Multivariate analysis

Confounding factor

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

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

Incidence of malaria according to the presence of a radio set,

Kahinbhi Pradesh

Crude dataMalaria 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 < 0.02

Confounding factor


Kahinbhi Pradesh

Strata 1: Sleeping under a mosquito netMalaria 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 < 0.97Confounding factor


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 < 0.95

Confounding factor

Mantel-Haenszel adjusted relative risk

RR M-H=aixL0i) / Ti]

ci xL1i) / Ti]

Confounding factor

Malaria and radio sets: Conclusion

• No association between radio and malaria within each strata

• The new adjusted relative risk replaces the crude one

MalariaRadio setsApparent association

Mosquito nets

Confounding factor

OR M-H=ai.di) / Ti]

bi.ci) / Ti]

Mantel-Haenszel adjusted odds ratio

Confounding factor



Confounding factor

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


Transfusion 3 1 4

Non-transfusion 69 189 258

Total 72 190 262

Odds ratio: 8.2; 95% CI : 0.8-220

Acute hepatitis B and receiving a transfusion in Moldova, 1994-1995

Confounding factor

Acute hepatitis B and receiving a transfusion in Moldova, 1994-1995 (According to receiving injections)

Case Control Total

Transfusion 3 1 6

No transfusion 22 6 28

Total 25 7 32

Case Control Total

Transfusion 0 0 0

No transfusion 47 183 230

Total 47 183 230

Odds ratio: -

Injections No injections

Odds ratio: 0.8,

95% CI: 0.1-24.9

Confounding factor



Confounding factor

Matching

• Stratification conducted initially at the stage of the study design of a case control study

• Stratified analysis (matched) necessary

Confounding factor



Confounding factor

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



Confounding factor

Multivariate analysis

• Mathematical model• Simultaneous adjustment of all

confounding and risk factors • Can address effect modification

Confounding factor

Taking into account a third factor in practice

1. Think of potential confounding factors 2. Collect accurate data on them 3. Conduct crude analysis4. Stratify5. Look for effect modification

• Are the RR or OR different to each other?

6. If effect modification: • Report• Do not adjust

7. Control confounding factors through adjustment• If applicable

Before the study

During the analysis

Analyzing a third factor

Report ONE crude OR/ RR

Third factor does not play a role

Strata ORs / RRs similar to crude(Crude value fal ls between strata)

El iminate the confoudingReport ONE adj usted OR / RR

Adj ust using theM-H technique

Confounding factor

Strata ORs / RRs diff erent f rom crude(Crude value does not fal l between strata)

Ident ical ORs / RRs across strata

Report MULT IPLE ORs / RRs for each stratum

Stop the analysis.DO NOT adj ust!


Diff erent ORs / RRs across strata

Examine ORs / RRs in each st ratum

Examine crude OR / RR

Take-home messages

• Describe effect modifications The analysis must TEST for their

occurrences

• Control confounding factors The analysis must ELIMINATE their influence

The third factor Effect modification Confounding factor FETP India.

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