Threats to causal inferences in epidemiologic studies - outline

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Threats to causal inferences in epidemiologic
studies - outline
Threats to Causal Inference in Epidemiologic
Studies

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

Interaction or effect modification is not on
this list
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The Sun, September 29, 1995
THUS, ASPIRIN MODIFIES THE EFFECT OF ANGER ON
THE RISK OF A HEART ATTACK
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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
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• Note to assess interaction, a minimum of 3
  variables were needed in this study
• Aspirin
• Anger
• Coronary Heart Disease (CHD)

Aspirin
Anger
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).
Stronger association
Weaker association
CHD
CHD
Heterogeneous Associations
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Terminology

• 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

• 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.
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Risk associated with environmental exposure
depends on genotype (gene-environment interaction)
One in 15,000 people may not properly metabolize
phenylalanine, an essential amino acid found in
aspartame.

• 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
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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

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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

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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.
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• 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

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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
Observed joint effect A Z -I
Antagonism Antagonism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
Observed joint effect A Z -I
Antagonism Antagonism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
Observed joint effect A Z -I
Antagonism Antagonism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z
Synergism Synergism Synergism
Observed joint effect A Z -I
Antagonism Antagonism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
Observed joint effect A Z
Antagonism Antagonism
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Interaction
Individual effects A Z
Expected joint effect A Z

Observed joint effect A Z A Z
No interaction No interaction
Observed joint effect A Z A Z I
Synergism Synergism Synergism
Observed joint effect A Z -I
Antagonism Antagonism
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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).

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• 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.
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First strategy to assess interactionEffect
Modification
ADDITIVE (attributable risk) interaction
Hypothetical example of presence of additive
interaction
Z A Incidence rate () ARexp to A ()
No No 5.0
No Yes 10.0
Yes No 10.0
Yes Yes 30.0
5.0
20.0
Conclude Because ARs associated with A are
modified by exposure to Z, additive interaction
is present.
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First strategy to assess interactionEffect
Modification
MULTIPLICATIVE (ratio-based) interaction
Hypothetical example of presence of
multiplicative interaction
Z A Incidence rate () RRA
No No 10.0
No Yes 20.0
Yes No 25.0
Yes Yes 125.0
2.0
5.0
Conclude Because RRs associated with A are
modified by exposure to Z, multiplicative
interaction is present.
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• 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

?
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Second strategy to assess interactioncomparison
of joint expected and joint observed effects
Additive interaction
5.0
5.0
25.0
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Second strategy to assess interactioncomparison
of joint expected and joint observed effects
Multiplicative interaction
2.0
2.5
12.5
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How can interaction be assessed in case-control
studies?
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Case-control study
Prospective study
First strategy to assess interactionEffect
Modification
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 Prospective Study Prospective Study Prospective Study
Z A Incidence rate () ARexp to A ()
No No 5.0 5.0
No Yes 10.0 5.0
Yes No 10.0 20.0
Yes Yes 30.0 20.0
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First strategy to assess interactionEffect
Modification
Case-control study
Layout of table to assess MULTIPLICATIVE
interaction
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Odds Ratios for the Association of Maternal
Smoking with Isolated Clubfoot, by Family History
of Clubfoot, Atlanta, Georgia, 1968-80
Family History Maternal smoking Cases Controls Odds RatiosMAT SMK
Yes Yes 14 7 (14/11)/(7/20) 3.64
No 11 20 (14/11)/(7/20) 3.64
No Yes 118 859 (118/203)/859/2143) 1.45
No 203 2 143 (118/203)/859/2143) 1.45
(Honein et al, Am J Epidemiol 2000152658-665)

• 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.
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0
Yes OR-
Yes No OR-
Yes OR
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0
Yes OR-
Yes No OR-
Yes OR
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR-
Yes No OR-
Yes OR
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR- Indep. effect of A
Yes No OR-
Yes OR
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR- Indep. effect of A
Yes No OR- Indep. effect of Z
Yes OR
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR- Indep. effect of A
Yes No OR- Indep. effect of Z
Yes OR Joint effects of A and Z
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR- Indep. effect of A
Yes No OR- Indep. effect of Z
Yes OR Joint effects of A and Z
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Derivation of formula for expected joint OR
observed
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Derivation of formula Expected OR OR-
OR- - 1.0
Intuitive graphical derivation
OR
1.0
BL
OR--
Baseline
Expected OR OR- OR- - 1.0
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OR
Observed OR
3.5
3.5
2.5
2.0
1.0
OR--
OR-
OR-
Expd OR
Conclude If the observed joint OR is the same as
the expected under the additive model, there is
no additive interaction
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Observed OR
6.0
OR
3.5
2.5
2.0
1.0
OR--
OR-
OR-
Expd OR
Conclude If the observed joint OR is different
than the expected under the additive model, there
is additive interaction
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Effect Modification Strategy
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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 2000152658-65.)
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Effect Modification Strategy
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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)
Two reference categories
(Honein et al. Family history, maternal smoking,
and clubfoot an indication of gene-environment
interaction. Am J Epidemiol 2000152658-65.)
44
Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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 2000152658-65.)
45
Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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 2000152658-65.)
Independent effect of family history (i.e., in
the absence of maternal smoking)
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Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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 2000152658-65.)
Independent effect of maternal smoking (i.e., in
the absence of family history)
47
Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs ORs using No/No as the reference category Expected 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 2000152658-65.)
Joint effect of family history and maternal
smoking
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Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs 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
No 203 2,143 1.0 (reference)
Yes
(Honein et al. Family history, maternal smoking,
and clubfoot an indication of gene-environment
interaction. Am J Epidemiol 2000152658-65.)
Joint effect of family history and maternal
smoking
Independent effect of family history (i.e., in
the absence of maternal smoking)
Independent effect of maternal smoking (i.e., in
the absence of family history)
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
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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
Factor Z Factor A Cases Controls OR What does it mean?
No No 1.0 Reference
Yes OR- Indep. effect of A
Yes No OR- Indep. effect of Z
Yes OR Joint effects of A and Z
Under MULTIPLICATIVE MODEL Expd OR OR-
? OR-
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Second Strategy Comparison between joint
expected and joint observed effects -- allows
assessment of both ADDITIVE and MULTIPLICATIVE
interactions--
Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot Maternal smoking Cases Controls Stratified ORs 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
No 203 2,143 1.0 (reference)
Yes
(Honein et al. Family history, maternal smoking,
and clubfoot an indication of gene-environment
interaction. Am J Epidemiol 2000152658-65.)
Joint effect of family history and maternal
smoking
Independent effect of family history (i.e., in
the absence of maternal smoking)
Independent effect of maternal smoking (i.e., in
the absence of family history)
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).
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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
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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.
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Further issues for discussion

• Quantitative vs. qualitative interaction

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Odds Ratios for the association among isolated
clubfoot, maternal smoking, and a family history
of clubfoot, Atlanta, Georgia, 1968-80
Family history of clubfoot 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 2000152658-65.
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Reproductive Health Study, retrospective study of
1,430 non-contraceptive parous women, Fishkill,
NY, Burlington, VT, 1989-90.
Smoking Caffeine No. pregnancies Delayed conception ORcaffeine P value
No No 575 47 1.0
301mg/d 90 17 2.6 1.4, 5.0
Yes No 76 15 1.0
301mg/d 83 11 0.6 0.3, 1.4
(Modified from Stanton CK, Gray RH. Am J
Epidemiol 19951421322-9)
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When there is qualitative interaction in one
scale (additive or multiplicative), it must also
be present in the other
Qualitative Interaction Qualitative Interaction Qualitative Interaction Qualitative Interaction 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
A- 6.0 Reference 1.0
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When there is qualitative interaction in one
scale (additive or multiplicative), it must also
be present in the other
Z
Risk of outcome
Z-
A-
A
Qualitative Interaction Qualitative Interaction Qualitative Interaction Qualitative Interaction 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
A- 6.0 Reference 1.0
Interaction in both scales
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When there is qualitative interaction in one
scale (additive or multiplicative), it must also
be present in the other
Another type of qualitative interaction
effectof A is flat in one stratum of the effect
modifier in the other stratum, an association is
observed
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When there is qualitative interaction in one
scale (additive or multiplicative), it must also
be present in the other
Another type of qualitative interaction
effectof A is flat in one stratum of the effect
modifier in the other stratum, an association is
observed
Gene
Risk of outcome
No
Yes
Phenylalanine Intake

• Individuals WITH this genotype WILL develop
  symptoms IF EXPOSED to phenylalanine (P) ? OR or
  RR gtgt 1.0, ARexpgtgt0
• Individuals WITHOUT this genotype WILL NOT
  develop symptoms, even WITH exposure to
  phenylalanine ? OR or RR 1.0

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Further issues for discussion

• Quantitative vs. qualitative interaction
• Reciprocity of interaction

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

• The 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.

Z modifies the effect of A
62
Further issues for discussion

• Quantitative vs. qualitative interaction
• Reciprocity of interaction
• Interaction is not confounding

63
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)
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
64
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)
INTERACTION IS NOT CONFOUNDING
Pair No. Case Control OR by sex
1 (male) - 3/1 3.0
2 (male) - 3/1 3.0
3 (male) - 3/1 3.0
4 (male) - 3/1 3.0
5 (male) 3/1 3.0
6 (female) - -
7 (female) -
8 (female) -
9 (female)
10 (female) - -
Total (Pooled) Odds Ratio 4/2 2.0
65
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)
INTERACTION IS NOT CONFOUNDING
Pair No. Case Control OR by sex
1 (male) - 3/1 3.0
2 (male) - 3/1 3.0
3 (male) - 3/1 3.0
4 (male) - 3/1 3.0
5 (male) 3/1 3.0
6 (female) - - 1/1 1.0
7 (female) - 1/1 1.0
8 (female) - 1/1 1.0
9 (female) 1/1 1.0
10 (female) - - 1/1 1.0
Total (Pooled) Odds Ratio 4/2 2.0
66
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 (term coined by Rothman)

67

• Additive interaction as Public Health
  interaction

EM- effect modifier RF- risk factor of interest
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
68
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
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
(Horn-Ross et al. Diet and risk of salivary gland
cancer. Am J Epidemiol 1997146171-6)
Additive Model Expected joint Odds Ratio 6.8
1.8 1.0 7.6
Positive additive interaction Public Health
interaction
Negative multiplicative interaction
Multiplicative Model Expected joint Odds Ratio
6.8 ? 1.8 12.4
Conclude For Public Health purposes, ignore
negative multiplicative interaction, and focus on
smokers for prevention of low vitamin C intake
69
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 (synergy)

70
Am J Epidemiol 19951421322-9
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
71
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 (not causal)
• Differential confounding

72
Example of confounding resulting in apparent
interaction

• 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

Prevalence of G Incidence Relative Risk
Men
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
Women
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
73
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 (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

74
Example of effect of misclassification of
overweight by smoking category, on the Odds Ratios
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
Not overweight 800 900
75
Smokers Smokers Cases Controls
Sensitivity 0.80 0.80
Specificity 0.85 0.85
Non-smokers Non-smokers Cases Controls
Sensitivity 0.95 0.95
Specificity 0.98 0.98
Values of indices of validity different between
smokers and non-smokers
Non-differential misclassification within each
stratum
Smoking Status BMI status Cases Controls Odds RatioTRUE
Smokers Overweight 200 100 2.25
Not overweight 800 900
Non-smokers Overweight 200 100 2.25
Not overweight 800 900
Smokers Smokers
Over- weight Cases Controls ORMISCL
Yes 280 215 1.4
No 720 785
Non-Smokers Non-Smokers
Over- weight Cases Controls ORMISCL
Yes 206 113 2.0
No 794 887
76
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 (not causal)
• 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

77
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
Maximum wind speed Number of days of epidemic days OR
12 miles/hour 992 5.7 4.4
gt 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
(White et al. Reexamination of epidemic asthma in
New Orleans, Louisiana, in relation to the
presence of soy at the harbor. Am J Epidemiol
1997145432-8)
78
Oral cancer odds ratios related to excessive
consumption of diluted and undiluted forms of
liquor by liquor drinkers Puerto Rico, 1992-1995
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)
gt0 - lt8 1.0 (reference) 1.0 (reference)
64 - lt137 1.1 7.3
Adjusted for age, tobacco use, consumption of
raw fruits and vegetables, and educational level
79
Exposure intensity and interaction
Gender Smoking Relative Risk
Man Yes 3.0
No 1.0
Woman Yes 1.5
No 1.0
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.
Are you surprised??
80
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 SUREThink about specific
  conditions
• Problem Epidemiology usually assesses proximal
  causes X1?X2? X3.? Y

81
Further issues for discussion

• Quantitative vs. qualitative interaction ?
• Reciprocity of interaction
• Interpretation and uses of interaction
• Additive interaction as public health
  interaction ?
• Biological interaction
• Statistical interaction (not causal)
• 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
82
Further issues for discussion

• Quantitative vs. qualitative interaction ?
• Reciprocity of interaction ?
• Interpretation and uses of interaction
• Additive interaction as public health
  interaction ?
• Biological interaction
• Statistical interaction (not causal)
• 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

83
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 ORs
  stratified according to the matching variable)

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

Expd OR OR- OR- - 1.0
84
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!