1 M2 Medical Epidemiology Corrections for confounding. Effect Modification

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M2 Medical Epidemiology

Corrections for confounding.Effect Modification

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Corrections for Confounding Adjusting measures of frequency for confounding

– Direct rate adjustment– Indirect rate adjustment

Adjusting measures of association for confounding

By stratification– Specific vs. Crude association measures– Confounding vs. Effect modification– Mantel-Haenszel confounder-adjusted odds ratio– Fine stratification: matched pairs studies– When to use or avoid mantel-Haenszel methods

By multivariable statistical modeling– Multiple regression models for continuous outcomes– Multiple logistic regression models for dichotomous

outcomes

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Specific Vs. Crude Association MeasuresCrude rate, ratio, or proportion: calculated in an overall, heterogeneous population of interest.

Specific rate, ratio, or proportion: calculated in a subgroup that shares specific values or levels of some characteristic(s), e.g. age, sex, age and sex.

Crude odds ratio (OR) or relative risk (RR): calculated in an overall, heterogeneous population of interest, e.g. OR between smoking and lung cancer in CU.

Specific odds ratio (OR) or relative risk (RR): calculated in a subgroup that shares specific values or levels of some characteristic(s), e.g. OR between smoking and lung cancer among CU men (sex-specific), CU 50-60 year-old men (age by sex specific).

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Confounding Vs. Effect Modification

Effect Modifiers

When the degree of association between an exposure variable E and a disease outcome D

(as expressed by an odds ratio, relative risk or other appropriate parameter),

changes according to the value or level of a third variable M,

then M is called an “effect modifier” --

because M modifies the “effect” of E on D.

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Hypothetical Cohort Study with Effect Modification

Total

Poor Outcome

Good Outcome

New Rx 2000 30 1970 Standard Rx 2000 150 1850

RR for Poor outcome with new Rx is (30/2000)/ (150/2000)= 0.2

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Females

Total

Poor Outcome

Good Outcome


Males

Total

Poor Outcome

Good Outcome


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Females

Total

Poor Outcome

Good Outcome


RR for Females=0.4

Males

Total

Poor Outcome

Good Outcome


RR for Males=0.1

Gender is an effect modifier: it modifies the association between treatment and outcome.

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Confounding vs. Effect Modification Females

Disease Present

Disease Absent

Total 1000 2000 Exposed 200 300 Unexposed 800 1700 Males

Disease Present

Disease Absent

Total 500 1000 Exposed 200 150 Unexposed 300 850

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Confounding vs. Effect Modification

Gender is an effect modifier: it modifies the relationship between exposure and disease.

Hypothetical Case-Control Study with Effect Modification Females

Disease Present

Disease Absent


OR FOR FEMALES =(200X1700)/(300X800)= 1.41

Males

Disease Present

Disease Absent


OR FOR MALES =(200X850)/(150X300)= 3.78

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Confounding vs. Effect ModificationONE-MONTH INFANT SURVIVAL STATUS

SURVIVAL

AMOUNT OF CARE

DEAD ALIVE TOTAL MORTALITY (%)

LESS 20 373 393 5.1

MORE 6 316 322 1.9

CLINIC A

SURVIVAL

AMOUNT OF CARE DEAD ALIVE TOTAL MORTALITY (%)

LESS 3 176 179 1.7

MORE 4 293 297 1.4

CLINIC B

SURVIVAL


LESS 17 197 214 7.9

MORE 2 23 25 8.0

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Confounding vs. Effect Modification

ONE-MONTH INFANT SURVIVAL STATUS

SURVIVAL

AMOUNT OF CARE


LESS 20 373 393 5.1

MORE 6 316 322 1.9 RR=5.1/1.9=2.7

CLINIC A

SURVIVAL


LESS 3 176 179 1.7

MORE 4 293 297 1.4 RR=1.7/1.4=1.2

CLINIC B

SURVIVAL


LESS 17 197 214 7.9

MORE 2 23 25 8.0 RR=7.9/8.0=1.0

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SURVIVAL

AMOUNT OF CARE


LESS 200 3730 3930 5.1

MORE 60 3160 3220 1.9

CLINIC A

SURVIVAL


LESS 120 1760 1880 6.4

MORE 40 2840 2880 1.4

CLINIC B

SURVIVAL


LESS 80 1970 2050 3.9

MORE 20 320 340 5.9

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SURVIVAL

AMOUNT OF CARE


LESS 200 3730 3930 5.1

MORE 60 3160 3220 1.9 RR=5.1/1.9=2.7

CLINIC A

SURVIVAL


LESS 120 1760 1880 6.4

MORE 40 2840 2880 1.4 RR=6.4/1.4=4.6

CLINIC B

SURVIVAL


LESS 80 1970 2050 3.9

MORE 20 320 340 5.9 RR=3.9/5.9=0.7

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Confounding Vs. Effect Modification•What is effect modification?

Different relationships between exposure and disease in subgroups of the population, i.e. different specific measures of association at different levels of a stratification variable.

•How do you look for it?

•Stratify the data and

•Compare stratum-specific association measures to one another

•What do you do about it?

Report the stratum-specific association measures and ignore the crude association measure.

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Confounding Vs. Effect Modification•What is confounding?

Distortion of an exposure disease relationship by failure to account for a third variable related to both.

•How do you look for it?

•Stratify the data and

•Compare stratum-specific association measures to the crude measure from the pooled data.

•What do you do about it?

Adjust for it!

HOW?

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Mantel-Haenszel Confounder-adjusted Odds Ratio•An adjusted odds-ratio (analogous to a directly-adjusted rate, but for representing association)

•Replaces the crude odds-ratio to correct for confounding (just as the adjusted rate replaces the crude rate under similar conditions)

•As the adjusted rate, is obtained by •dividing data into subgroups, that is, by stratifying

and•reassembling data from the subgroups in a special way

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Mantel-Haenszel Confounder-adjusted Odds RatioOdds-ratio for a single table=ad/bc

Consider stratified data

a1 b1

c1 d1

T1

a2 b2 a b

c2 d2 c d

T2 T

a3 b3

c3 d3

T3

etc.

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Mantel-Haenszel Confounder-adjusted Odds Ratioa1 b1

c1 d1

T1

a2 b2 a b

c2 d2 c d

T2 T

a3 b3

c3 d3

T3

etc.

CRUDE odds-ratio=ad/bc = (ai)(di)/(bi)(ci), where the summations are over all strata.

Mantel-Haenszel adjusted odds-ratio=(aidi/Ti)/( bici/Ti), where the summations are also over all strata.

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Mantel-Haenszel Confounder-adjusted Odds Ratio

Mantel-Haenszel adjusted odds-ratio=(aidi/Ti)/( bici/Ti),

= (a1d1/T1)+ (a2d2/T2)+ (a3d3/T3) + etcdivided by

(b1c1/T1)+ (b2c2/T2)+ (b3c3/T3) + etc

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Mantel-Haenszel Analysis

Lung cancer Present

Lung cancer Absent

Total 300 300 Drinks alcohol 210 120 Does not drink 90 180

Crude OR = (210 180)/(120 90) = 3.5

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Mantel-Haenszel AnalysisHypothetical Case-Control Study with Confounding Smokers

Disease Present

Disease Absent

Total

Total 245 96 341 Exposed 197 77 Unexposed 48 19

OR FOR SMOKERS = (197X19)/(77X48)=12500/500=1.01

Non-smokers

Disease Present

Disease Absent

Total

Total 55 204 259 Exposed 13 43 Unexposed 42 161

OR FOR NON-SMOKERS = (13X161)/(43X42)=1.18

Mantel-Haenszel OR = 197x19/341+13x161/259

Divided by 77X48/341+43x42/259

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Mantel-Haenszel Confounder-adjusted Odds Ratio

197x19/341+13x161/259 77X48/341+43x42/259

= 3743/341+2093/259

3696/341+1806/259

= 11.0+8.1 =19.1/18.0=1.06

11.0+7.0Compare to Crude OR of 3.5

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Mantel-Haenszel Analysis: Matched Studies

1 0

0 1

2

0 1 a b

1 0 c d

2 T

1 1

0 0

2

0 0

1 1

2

etc.

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MH OR = 1x1/2 + 0x0/2 + 1x0/2 + 0x1/2 0x0/2 + 1x1/2 + 0x1/2 +1x0/2

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Uninformative Concordant positive Cas Cntr EX U Concordant negative E U

Informative Discordant, case exposed Discordant, control exposed

1 1

0 0

0 0

1 1

1 0

0 1

0 1

1 0

Four types of matched pairs:

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For concordant pairs– ad=bc=0, so they contribute nothing to the Mantel-Haenszel odds

ratio

– each count is equal to its expectation, so they contribute nothing to the Mantel-Haenszel test statistic

For discordant pairs

the Mantel-Haenszel odds ratio simplifies to

Number of discordant pairs with case exposed/Number of discordant

pairs with control exposed

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Mantel-Haenszel Methods: When to Use

•When effect modification seems absent or minimal and confounding may be present.

•Then compare the adjusted OR to the crude OR.

•If different, confounding is present

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Mantel-Haenszel Methods: When to Avoid Avoid the Mantel-Haenszel or any single summary of

association when stratum-specific association measures differ substantially and sample sizes are moderate to large. Report the stratum-specific results.

Especially when stratum-specific association measures are in opposite directions, e.g. OR or RR>1 in some strata and <1 in others. In this case, major effects may be missed because positive associations in some strata can be cancelled out by negative associations in other strata.

Report the stratum-specific results, perform tests of statistical significance for the effect modification and, if these are positive, look for explanations.

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Hypothetical Case-Control Study

FemalesDiseasePresent

DiseaseAbsent Total

Exposed 25 5 30Unexposed 75 45 120Total 100 50 150

OR FOR FEMALES = 3.00

MalesDiseasePresent

DiseaseAbsent Total

Exposed 15 45 60Unexposed 70 135 205Total 85 180 265

OR FOR MALES = 0.64

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Can You Have Both Confounding and Effect Modification? Yes. Difficult to see. But in extreme cases is easy to see. Example Crude RR=0.7

RR in men is 2.0RR in women is 4.0

2 is different from 4, hence EM You are not allowed to use adjustment to

summarize (average) the 2 and 4. But you know that the effect is RR >1 in both genders. So, gender has distorted the RR

Documents

1 M2 Medical Epidemiology Corrections for confounding. Effect Modification