intermediate methods in observational epidemiology 2008 interaction

Intermediate methods in observational epidemiology

2008

Interaction

Threats to causal inferences in epidemiologic studies - outline

• Lack of precision

• Lack of internal validity – Selection bias– Information bias– Confounding

Interaction or “effect” modification is not on this list

Due to a study defect

Found in nature

Threats to Causal Inference in Epidemiologic Studies

The Sun, September 29, 1995

THUS, ASPIRIN MODIFIES THE “EFFECT” OF ANGER ON THE RISK OF A HEART ATTACK

The Sun, September 29, 1995

A BETTER DEFINITION FOR OBSERVATIONAL DATA: THUS, ASPIRIN MODIFIES THE STRENGTH OF THE ASSOCIATION OF ANGER WITH THE

RISK OF A HEART ATTACK

CHD

Anger

Aspirin

CHD

Anger

Interaction = “Effect” modification: The “effect” of the risk factor -- anger – on the outcome – CHD -- differs depending on the presence or absence of a third factor (effect modifier) --aspirin. The third factor (aspirin) modifies the “effect” of the risk factor (anger) on the outcome (CHD).

Note: to assess interaction, a minimum of 3 variables were needed in this study:•Aspirin•Anger•Coronary Heart Disease (CHD)

Weaker association

Stronger association

Heterogeneous Associations

Terminology

“Effect Modification”

“Interaction”

Heterogeneous Associations

Effect Modification

The “effect” of an exposure on an outcome depends on (is modified by) the level (or presence/absence) of a third factor.

The third factor modifies the effect of the exposure on the outcome.

Observed heterogeneity

• True (biological, sociological, psicological, etc.)

Other than true, it can be due to:

• Bias

• Confounding

• Chance

• Differences in level of exposure between the categories of the effect modifier

Risk associated with environmental exposure depends on genotype (gene-environment interaction)

• Individuals WITH this genotype WILL develop symptoms IF EXPOSED to phenylalanine.

• Individuals WITH this genotype WILL NOT develop symptoms WITHOUT exposure to phenylalanine.

• Individuals WITHOUT this genotype WILL NOT develop symptoms, even WITH exposure to phenylalanine.

• Both the gene AND environmental exposure are required for symptoms to occur.

PHENYLKETONURICS: CONTAINS PHENYLALANINE

One in 15,000 people may not properly metabolize phenylalanine, an essential amino acid found in aspartame.

True effect modification is NOT a nuisance to be eliminated

• Biases and confounding effects distort true causal associations

→ Strategies: avoid, eliminate, reduce, control

• Effect Modification is informative

– Provides insight into the nature of the relationship between exposure and outcome

– May be the most important result of a study

→ It should be reported and understood

FROM NOW ON, THE WORD “EFFECT(S)” WILL BE USED LOOSELY, EVEN WHEN DESCRIBING RESULTS OF OBSERVATIONAL RESEARCH

IN OTHER WORDS, FOR PRACTICAL PURPOSES, “EFFECT(S)” WILL REFER TO

ASSOCIATIONS THAT MAY OR MAY NOT BE CAUSAL

Word of caution: true effects cannot be inferred from observational data obtained in

single studies.

Interaction: Two definitions of the same phenomenon

• When the effect of factor A on the probability of the outcome Y differs according to the presence of Z (and vice-versa)

• When the observed joint effect of (at least) factors A and Z on the probability of the outcome Y is different from that expected on the basis of the independent effects of A and Z

Individual effects A Z

Expected joint effect A Z

Observed joint effect A + Z

No interaction

Observed joint effect A + Z +I

Synergism

Observed joint effect A + Z -I

Antagonism

Interaction


Interaction



No interaction


Synergism


Antagonism


Interaction



No interaction


Synergism


Interaction



No interaction


Synergism


Antagonism

How is effect measured in epidemiologic studies?

• If effect is measured on an additive or absolute scale (attributable risks) additive interaction assessment (Attributable Risk model: based on absolute differences between cumulative incidences or rates).

• If effect is measured on a relative (ratio) scale (relative risks, odds ratios, etc.) multiplicative interaction assessment (Relative Risk model).

Two strategies to evaluate interaction based on different, but equivalent definitions:

• Effect modification (homogeneity/heterogeneity of effects)

• Comparison between joint expected and joint observed effects

The two definitions and strategies are completely equivalent. It is impossible to conclude that there is (or there is not) interaction using one strategy, and reach the opposite conclusion using the other strategy!

Thus, when there is effect modification, the joint observed and the joint expected effects will be different.

Hypothetical example of presence of additive interaction

Conclude: Because AR’s associated with A are modified by exposure to Z, additive interaction is present.

5.0

20.0

Z A Incidence rate (%) ARexp to A (%)

No No 5.0

Yes 10.0

Yes No 10.0

Yes 30.0

First strategy to assess interaction:Effect Modification

ADDITIVE (attributable risk) interaction

Hypothetical example of presence of multiplicative interaction

Z A Incidence rate (%) RRA

No No 10.0

Yes 20.0

Yes No 25.0

Yes 125.0

Conclude: Because RR’s associated with A are modified by exposure to Z, multiplicative interaction is present.

2.0

5.0


MULTIPLICATIVE (ratio-based) interaction

Two strategies to evaluate interaction based on different, but equivalent definitions:

• Effect modification (homogeneity/heterogeneity of effects)

• Comparison between joint expected and joint observed effects

Factor Z

Factor A

Incidence (%)

Obs. Strat. ARA

Observed ARvs(--)

No 5.0 Reference No Yes 10.0

5.0

No 10.0 Yes Yes 30.0

20.0

5.05.0

25.0 10.0

Expected

Second strategy to assess interaction:comparison of joint expected and joint observed effects

Additive interaction

Conclude:Because the observed joint AR is different from that expected by adding the individual AR’s, additive interaction is present(that is, the same conclusion as when looking at the stratified AR’s)

Joint observedobserved AR = 25%Joint expectedexpected AR = ARA+Z- + ARA-Z+= 10%

Factor Z

Factor A

Incidence (%)

Obs. Strat. RRA

RRvs(--)


2.0

No 25.0 Yes Yes 125.0

5.0

5.0

2.02.5

12.5

Second strategy to assess interaction:comparison of joint expected and joint observed effects

Multiplicative interaction

Conclude:Because the observed joint RR is different from that expected by multiplying the individual RR’s, there is multiplicative interaction(that is, the same conclusion as when looking at the stratified RR’s)

Joint observedobserved RRA+Z+ = 12.5

Joint expectedexpected RRA+Z+ = RRA+Z- × RRA-Z+= 2.0 × 2.5 = 5.0

How can interaction be assessed in case-control studies?


Case-control study

Prospective Study

Z A Incidence rate (%) ARexp to A (%)

No No 5.0

5.0Yes 10.0

Yes No 10.0

20.0Yes 30.0

Additive interaction cannot be assessed in case-control studies by using the effect modification (homogeneity/heterogeneity) strategy, as no incidence measures are available to calculate attributable risks in the exposed

Prospective study


Layout of table to assessMULTIPLICATIVE interaction

Case-control study

Factor Z

Factor A

Cases

Controls

Stratified ORA

What does it mean?

No No Yes

Effect of A in the absence of Z

No Yes Yes

Effect of A in the presence of Z

Family History Maternal smoking Cases Controls Odds RatiosMAT SMK

Yes Yes 14 7 (14/11)/(7/20)= 3.64

No 11 20

No Yes 118 859 (118/203)/859/2143)= 1.45No 203 2 143

(Honein et al, Am J Epidemiol 2000;152:658-665)

Odds Ratios for the Association of Maternal Smoking with Isolated Clubfoot, by Family History of Clubfoot, Atlanta, Georgia, 1968-80

Hypothesis: Family history of clubfoot is a potential modifier of the association of maternal smoking with clubfoot.

• Use the “effect” modification strategy to evaluate the presence of multiplicative interaction. For this strategy, two reference categories are used.

Conclusion: Because the stratified ORs are different (heterogeneous), there is multiplicative interaction.

Now evaluate the same hypothesis using the second strategy: comparison between joint observed and joint expected “effects”.

Factor Z Factor A Cases Controls OR What does it mean?

No No 1.0

Yes OR+-

Yes No OR-+

Yes OR++

Case-Control Study

Second strategy to assess interaction: comparison between joint observed and joint expected effects

Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction

Note common reference category


No No 1.0

Yes OR+-

Yes No OR-+

Yes OR++

Case-Control Study




No No 1.0 Reference

Yes OR+-

Yes No OR-+

Yes OR++

Case-Control Study




No No 1.0 Reference

Yes OR+- Indep. effect of A

Yes No OR-+

Yes OR++

Case-Control Study




No No 1.0 Reference


Yes No OR-+ Indep. effect of Z

Yes OR++

Case-Control Study




No No 1.0 Reference



Yes OR++ Joint effects of A and Z

Case-Control Study




No No 1.0 Reference




Case-Control Study



Under ADDITIVE MODEL: Exp’d OR++ = OR+- + OR-+ - 1.0

)()()(. IncIncIncIncIncIncExpdARExpected

Inc

Inc

Inc

Inc

Inc

Inc

Inc

Inc

Inc

Inc

Inc

Inc

0.1 RRRRRR

If disease is “rare” (e.g., <5%):

0.1 OROROR

Derivation of formula for expected joint OR

observed

RR++ RR+- 1.0 RR-+ 1.01.0

Derivation of formula: Expected OR++ = OR+- + OR-+ - 1.0

Intuitive graphical derivation:

OR

1.0

OR--

Baseline

2.0

Baseline + Excess due to A

OR+-

EXCA

BL

[EXCA+BL] + [EXCZ+BL] - BL

3.5

Exp’dOR++

EXCZ

EXCA

BL

2.5

Baseline + Excess due to Z

OR-+

EXCZ

BLBL

Two baselines!

One baseline has to be removed

Expected OR++= OR+- + OR-+ - 1.0

OR

1.0

2.02.5

3.5 3.5

OR-- OR-+ OR+- Exp’dOR++

Observed OR++

Conclude:If the observed joint OR is the same as the expected under the additive model, there is no additive interaction

OR

1.0

2.02.5

3.5

6.0

OR-- OR-+ OR+- Exp’dOR++

Observed OR++

Conclude:If the observed joint OR is different than the expected under the additive model, there is additive interaction

Excess due tointeraction (“interaction term”)

Excess due to thejoint effects of A and Z

Family history of clubfoot

Maternal smoking

Cases Controls Stratified ORs

ORs using No/No as the reference

categoryExpected under the ADDITIVE

model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45

No 203 2,143 1.0 (reference)(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152:658-65.)

Odds Ratios for the association among isolated clubfoot, maternal smoking, and a family history of clubfoot, Atlanta, Georgia, 1968-80

Effect Modification Strategy

1.0

1.0


Maternal smoking




model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45



Effect Modification Strategy

1.0

1.0

Two reference categories


Maternal smoking




model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45



Second Strategy: Comparison between joint expected and joint observed effects -- allows assessment of both ADDITIVE and MULTIPLICATIVE interactions--

1.0

1.0


Maternal smoking




model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45




Independent effect of family history (i.e., in the absence of maternal smoking)

1.0

1.0


Maternal smoking




model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45




Independent effect of maternal smoking (i.e., in the absence of family history)

1.0

1.0


Maternal smoking




model

Yes Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45




Joint effect of family history and maternal smoking

1.0

1.0


Maternal smoking


Observed ORs using No/No as the reference

category

Expected under the ADDITIVE

model

Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45







Yes 6.26

1.45 + 5.81 – 1.0=

Conclude: Since the observed joint OR(20.3) is different from the joint OR expected under the additive model (6.26), there is additive interaction

1.0

1.0


No No 1.0 Reference






Under ADDITIVE MODEL: Exp’d OR++ = OR+- + OR-+ - 1.0

Under MULTIPLICATIVE MODEL: Exp’d OR++ = OR+- OR-+

Case-Control Study


Maternal smoking


Observed ORs using No/No as the reference

category

Expected under the MULTIPL.

model

Yes 14 7 3.64 20.30

No 11 20 5.81

No Yes 118 859 1.45 1.45







Yes 8.42

5.81 x 1.45=

Conclude: Since the observed joint OR(20.3) is different from the joint OR expected under the multiplicative model (8.4), there is multiplicative interaction. This inference is consistent with the inference made based on the effect modification strategy (heterogeneity of odds ratios when examining strata of family history).

1.0

1.0

Back to the terms...• Synergism or Synergy: The observed joint “effect” is

greater than that expected from the individual “effects”.

Which is equivalent to saying that the “effect” of A in the presence of Z is stronger than the “effect” of A when Z is absent.

• Antagonism: The observed joint “effect” is smaller than that expected from the individual “effects”.

Which is equivalent to saying that the “effect” of A in the presence of Z is weaker than the “effect” of A when Z is absent

Note: the expressions “synergism/antagonism” and “effect modification” should ideally be reserved for situations in which one is sure of a causal connection. In the absence of evidence supporting causality, it is preferable to use terms such as “heterogeneity”

Back to the terms...• Synergism or Synergy: The observed joint “effect” is

greater than that expected from the individual “effects”.

Which is equivalent to saying that the “effect” of A in the presence of Z is stronger than the “effect” of A when Z is absent.

• Antagonism: The observed joint “effect” is smaller than that expected from the individual “effects”.

Which is equivalent to saying that the “effect” of A in the presence of Z is weaker than the “effect” of A when Z is absent

Note: some investigators reserve the term, “synergy” to define biological interaction.

Further issues for discussion

• Quantitative vs. qualitative interactionQuantitative vs. qualitative interaction


Maternal smoking Cases Controls

Stratified ORmaternal

smk

Yes Yes 14 7 3.64

No 11 20

No Yes 118 859 1.45

No 203 2,143

Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152:658-65.


Quantitative Interaction:

Both ORs are in the same

direction(>1.0), but they are

heterogeneous (different)

Smoking Caffeine No. pregnancies Delayed conception* ORcaffeine P value

No No 575 47 1.0

301+mg/d 90 17 2.6 1.4, 5.0

Yes No 76 15 1.0

301+mg/d 83 11 0.6 0.3, 1.4

Qualitative Interaction: Odds ratios are not only different: they have different directions (>1, and <1). Smoking modifies the effect of caffeine on delayed conception in a qualitative manner.

(Modified from: Stanton CK, Gray RH. Am J Epidemiol 1995;142:1322-9)

Reproductive Health Study, retrospective study of 1,430 non-contraceptive parous women, Fishkill, NY, Burlington, VT, 1989-90.

A- A+

Ris

k of

ou

tcom

e

Z-

Z+ RRA

>1

<1

ARA

Positive (>0)

Negative (<0)

Z+Z-

Qualitative Interaction

Effect Modifier Risk Factor Incidence/1000 ARA RRA

Z+ A+ 10.0 +5/1000 2.0

A- 5.0 Reference 1.0

Z- A+ 3.0 -3/1000 0.5


Interaction in both scales

When there is qualitative interaction in one scale (additive or multiplicative), it must also be

present in the other



A- A+

Ris

k of

ou

tcom

e

Z-

Z+ RRA

>1

<1

ARA

Positive (>0)

Negative (<0)

Z+Z-

Qualitative Interaction

Effect Modifier Risk Factor Incidence/1000 ARA RRA

Z+ A+ 10.0 +5/1000 2.0


Z- A+ 3.0 -3/1000 0.5


Interaction in both scales

A- A+

Ris

k of

ou

tcom

e

Z-

Z+ ARA

Positive (>0)

Null (=0)

RRA

>1

=1

Z+Z-

Another type of qualitative interaction: “effect”of A is flat in one stratum of the effect modifier; in the other stratum, an association is observed



Ris

k of

ou

tcom

e Gene+ ARA

Positive (>0)

Null (=0)

RRA

>1

=1

Z+Z-

Another type of qualitative interaction: “effect”of A is flat in one stratum of the effect modifier; in the other stratum, an association is observed

• Individuals WITH this genotype WILL develop symptoms IF EXPOSED to phenylalanine (P) OR or RR >> 1.0, ARexp>>0

• Individuals WITHOUT this genotype WILL NOT develop symptoms, even WITH exposure to phenylalanine OR or RR= 1.0



Phenylalanine Intake

No Yes

Gene-


• Quantitative vs. qualitative interaction

• Reciprocity of interactionReciprocity of interaction

If Z modifies the effect of A on disease Y, then Z will necessarily modify the effect of Z on disease Y

Reciprocity of interactionThe decision as to which is the “principal” variable and which is the

effect modifier is arbitrary, because if A modifies the effect of Z, then Z modifies the effect of A.

Factor Z

Factor A

Incidence (%)

Stratified RRA

RRvs(--)


2.0 2.0

No 25.0 2.5 Yes Yes 125.0

5.0 12.5

Z modifies the effect of A

Factor A Factor Z Incidence (%)Stratified

RRZ RRvs(--)

No 10.0 ReferenceNoYes 25.0 2.5 2.5No 20.0 2.0YesYes 125.0 6.25 12.5

A modifies the effect of Z



• Reciprocity of interaction

• Interaction is not confounding

Pair No. Case Control OR by sex

1 (male) + -

2 (male) + -

3 (male) - +

4 (male) + -

5 (male) + +

6 (female) - -

7 (female) + -

8 (female) - +

9 (female) + +

10 (female) - -

Total (Pooled) Odds Ratio 4/2= 2.0

INTERACTION IS NOT CONFOUNDING

Hypothetical example of matched case-control study (matching by gender) of the relationship of risk factor X (e.g., alcohol drinking ) and disease Y (e.g., esophageal cancer)


1 (male) + -

3/1 = 3.02 (male) + -

3 (male) - +

4 (male) + -

5 (male) + +

6 (female) - -

7 (female) + -

8 (female) - +

9 (female) + +

10 (female) - -






1 (male) + -

3/1 = 3.02 (male) + -

3 (male) - +

4 (male) + -

5 (male) + +

6 (female) - -

1/1= 1.07 (female) + -

8 (female) - +

9 (female) + +

10 (female) - -







• Interpretation and uses of interactionInterpretation and uses of interaction– Additive interaction as “public health Additive interaction as “public health

interaction”interaction” (term coined by Rothman)

Additive interaction as “Public Health interaction”

Incidence per 100

Family history (EM)

Smoking (RF)

Stratified ARSmk%

Stratified RRSmk

5.0 No No

10.0 Yes

5.0

2.0

20.0 Yes No

30.0 Yes

10.0

1.5

Incidence of disease “Y” by smoking and family history of “Y”

Thus, if there are enough subjects who are positive for both variables and if resources are limited, smokers with a positive family history should be regarded as the main “target” for prevention examine the prevalence of (Fam Hist+ and Smk+ ) and estimate the attributable risk in the population

Positive additive interaction (synergism), but negative

multiplicative interaction (antagonism)

EM- effect modifierRF- risk factor of interest

Current Smoking Status

Low Vitamin C intake (mg/day)

Odds Ratio

No No 1.0

Yes No 6.8

No Yes 1.8

Yes Yes 10.6

Joint effects of current cigarette smoking and low consumption of vitamin C (≤ 100 mg/day) with regard to adenocarcinoma of the salivary gland, San Francisco-Monterey

Bay area, California, 1989-1993

(Horn-Ross et al. Diet and risk of salivary gland cancer. Am J Epidemiol 1997;146:171-6)

Additive Model:Expected joint Odds Ratio = 6.8 + 1.8 – 1.0= 7.6

Positive additive interaction=

“Public Health interaction”

Multiplicative Model:Expected joint Odds Ratio = 6.8 1.8 = 12.4

ConcludeConclude: For Public Health purposes, ignore negative multiplicative interaction, and focus on : For Public Health purposes, ignore negative multiplicative interaction, and focus on smokers for prevention of low vitamin C intakesmokers for prevention of low vitamin C intake

Negative multiplicative interaction





• Interpretation and uses of interactionInterpretation and uses of interaction

– Additive interaction as “public health interaction”

– Biological interaction (“synergy”)

Am J Epidemiol 1995;142:1322-9

Smoking Caffeine No. pregnanciesDelayed

conception>12 months

StratifiedORA 95% CI

No 575 47No301 mg/d 90 17 2.62 1.36-4.98

No 76 15Yes301 mg/d 83 11 0.62 0.27-1.45

Reproductive Health Study, retrospective study of 1,430 non-contraceptive parous women, Fishkill, NY, Burlington, VT, 1989-90.

“…An interaction between caffeine and smoking is also biologically plausible. Several studies have shown that cigarette smoking significantly increases the rate of caffeine metabolism […]. The accelerated caffeine clearance in smokers may explain why we failed to observe an effect of high caffeine consumption on fecundability among women who smoked cigarettes.”

This interaction can be properly named, “synergy”, as it has a strong biological plausibility





• Interpretation and uses of interactionInterpretation and uses of interaction– Additive interaction as “public health interaction” – Biological interaction– Statistical interaction (not causal)

• Differential confoundingDifferential confounding

Prevalence of G

Incidence Relative Risk

MenMen

Exposed 0.8 [(0.8 0.04 ) + (0.2 0.02)] 100= 3.6%

1.6

Unexposed 0.1 [(0.10 0.04) + (0.90 0.02)] 100 = 2.2%

1.0

WomenWomen

Exposed 0.20 [(0.20 0.04) + (0.80 0.02)] 100= 2.4%

1.0

Unexposed 0.20 [(0.20 0.04) + (0.80 0.02)] 100= 2.4%

1.0

• No association between the exposure (e.g., chewing gum) and the disease (e.g., liver cancer)• Unaccounted-for confounder (e.g., a genetic polymorphism G)• Incidence of the disease by G:

G+ = 0.04 G- = 0.02

Example of confounding resulting in apparent interaction


• Quantitative vs. qualitative interaction • Reciprocity of interaction• Interaction is not confounding • Interpretation and uses of interactionInterpretation and uses of interaction

– Additive interaction as “public health interaction” – Biological interaction– Statistical interaction (not causal)

• Differential confounding across strata of the effect modifier

• Misclassification resulting from different sensitivity and specificity values of the variable under study across strata of the effect modifier

Smoking Status BMI status Cases Controls Odds Ratio

Smokers Overweight 200 100 2.25

Not overweight 800 900

Non-smokers Overweight 200 100 2.25


Example of effect of misclassification of overweight by smoking category, on the Odds Ratios

SmokersSmokers: Cases Controls

Sensitivity 0.80 0.80

Specificity 0.85 0.85

Non-smokersNon-smokers: Cases Controls

Sensitivity 0.95 0.95

Specificity 0.98 0.98

Smoking Status BMI status Cases Controls Odds RatioTRUE

Smokers Overweight 200 100 2.25


Non-smokers Overweight 200 100 2.25


Non-differential misclassification within each stratum

Values of indices of validity different between smokers and non-smokers

Smokers

Over- weight

Cases Controls ORMISCL

Yes 280 215 1.4

No 720 785

Non-Smokers

Over- weight

Cases Controls ORMISCL

Yes 206 113 2.0

No 794 887

Further issues for discussion• Quantitative vs. qualitative interaction • Reciprocity of interaction • Interaction is not confounding• Interpretation and uses of interactionInterpretation and uses of interaction


• Differential confounding across strata of the effect modifier

• Differential misclassification across strata of the effect modifier

• The dose (amount of exposure) may be higher in one stratum than in the other

Maximum wind speed

Number of days % of epidemic days OR

≤ 12 miles/hour* 992 5.7 4.4

> 12 miles/hour 3390 2.0 1.7

No soy 2548 1.8 1.0

12 miles/hour = 19.3 km/hour

Asthma epidemic day = 64 or more visits for asthma during 1 day

Odds ratios for asthma epidemic days and number of days with presence of vessels carrying soy at the harbor, adjusted for year, New

Orleans, Louisiana, 1957-1968

(White et al. Reexamination of epidemic asthma in New Orleans, Louisiana, in relation to the presence of soy at the harbor. Am J Epidemiol 1997;145:432-8)

Usually drank liquor with nonalcoholic mixers (n= 163)

Usually drank liquor straight (undiluted) (n= 206)

Drinks/week Odds Ratio (95% CI) Odds Ratio (95% CI)

>0 - <8 1.0 (reference) 1.0 (reference)

64 - <137 1.1 7.3

Oral cancer odds ratios* related to excessive consumption of diluted and undiluted forms of liquor by liquor drinkers Puerto Rico, 1992-1995

*Adjusted for age, tobacco use, consumption of raw fruits and vegetables, and educational level

Gender Smoking Relative Risk

Man Yes 3.0

No 1.0

Woman Yes 1.5

No 1.0

Exposure intensity and interaction

Are you surprised??

When studying effects of smoking in men and women, the category “smoker” is related to more cigarettes/day in men than in women. Thus, the observed odds ratios may be heterogeneous because of different levels of smoking exposure between men and women, and not because men are more susceptible to smoking-induced disease.

Further Issues for Discussion• Quantitative Vs qualitative interaction• Reciprocity of interaction• Interaction is not confounding• Interpretation and uses of interaction

– Additive interaction as “public health interaction

– Biological interaction

– Statistical interaction

– More on biological interaction• Consistent with pathophysiologic mechanisms

• Confirmed by animal studies

• Best model?– NO ONE KNOWS FOR SURE…Think about specific conditions

Problem: Epidemiology usually assesses proximal causes X1X2 X3. Y

Further issues for discussion• Quantitative vs. qualitative interaction • Reciprocity of interaction • Interpretation and uses of interactionInterpretation and uses of interaction


• Differential confounding across strata of the effect modifier • Differential misclassification across strata of the effect modifier • The dose (amount of exposure) may be higher in one stratum than in

the other• Biologic interaction:

– Consistent with pathophysiologic mechanisms (biologic plausibility)

– Confirmed by animal studies– What is best model from the biologic viewpoint?

No one knows for sure… Think about the specific condition under study – Examples: trauma, cancer

Problem: Epidemiology usually assesses proximal cause X1 X2 X3 Y

Further issues for discussion• Quantitative vs. qualitative interaction • Reciprocity of interaction • Interpretation and uses of interactionInterpretation and uses of interaction


• Differential confounding across strata of the effect modifier • Differential misclassification across strata of the effect modifier • The dose (amount of exposure) may be higher in one stratum than in

the other • Biologic interaction• Matching and interaction

Matching and interaction

• In a matched case-control study, the interaction between the exposure of interest and the matching variable…

– Can be assessed under the multiplicative model, using the effect modification strategy (i.e., looking at the heterogeneity of the OR’s stratified according to the matching variable)

Exp’d OR++ = OR+- + OR-+ - 1.0Set to be 1.0, by definition

– Cannot be assessed under the additive model, because the expected joint OR is undefined:

Conclusion

• If heterogeneity is present… is there interaction?

– What is the magnitude of the difference? (p-value?)

– Is it qualitative or just quantitative?– If quantitative, is it additive or multiplicative?– Is it biologically plausible?

• If we conclude that there is interaction, what should we do?

– Report the stratified measures of association … The interaction may be the most important finding of the study!

intermediate methods in observational epidemiology 2008 interaction

Documents

effect of anger

true effect modification

effect modifier slide

interaction slide

control effect modification

factor effect modifier

risk factor anger

factor aspirin