1. Intermediate methods in observational epidemiology 2008
Interaction

2. Threats to causal inferences in epidemiologic studies - outline
Threats to Causal Inference in Epidemiologic Studies
Threats to causal inferences in epidemiologic studies - outline
Lack of precision
Lack of internal validity
Selection bias
Information bias
Confounding
Due to a study defect
Found in nature
Interaction or “effect” modification is not on this list

4. The Sun, September 29, 1995
THUS, ASPIRIN MODIFIES THE “EFFECT” OF ANGER ON THE RISK OF A HEART ATTACK

5. 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

6. Heterogeneous Associations
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).
Weaker association
Stronger association
CHD
CHD
Heterogeneous Associations

7. Terminology “Effect Modification” “Interaction”
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.

8. 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

9. 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

10. 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

11. 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.

12. 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

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

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

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

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

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

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

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

20. 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).

21. 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.

22. First strategy to assess interaction: Effect Modification
ADDITIVE (attributable risk) interaction
Hypothetical example of presence of additive interaction Z A
Incidence rate (%)
ARexp to A (%) No
5.0
Yes
10.0
30.0
5.0
20.0
Conclude: Because AR’s associated with A are modified by exposure to Z, additive interaction is present.

23. First strategy to assess interaction: Effect Modification
MULTIPLICATIVE (ratio-based) interaction
Hypothetical example of presence of multiplicative interaction Z A
Incidence rate (%)
RRA No
10.0
Yes
20.0
25.0
125.0
2.0
5.0
Conclude: Because RR’s associated with A are modified by exposure to Z, multiplicative interaction is present.

24. Effect modification (homogeneity/heterogeneity of effects)
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 

25. Second strategy to assess interaction: comparison of joint expected and joint observed effects
Additive interaction
10.0
Expected
5.0
5.0
25.0
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 observed AR = 25%
Joint expected AR = ARA+Z- + ARA-Z+= 10%

26. Multiplicative interaction
Second strategy to assess interaction: comparison of joint expected and joint observed effects
Multiplicative interaction
2.0
5.0
2.5
12.5
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 observed RRA+Z+ = 12.5
Joint expected RRA+Z+ = RRA+Z- × RRA-Z+= 2.0 × 2.5 = 5.0

27. How can interaction be assessed in case-control studies?

28. First strategy to assess interaction: Effect Modification
Case-control study
Prospective study
First strategy to assess interaction: Effect 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 Z A
Incidence rate (%)
ARexp to A (%) No
5.0
Yes
10.0
20.0
30.0

29. First strategy to assess interaction: Effect Modification
Case-control study
First strategy to assess interaction: Effect Modification
Layout of table to assess
MULTIPLICATIVE interaction

30. Odds Ratios for the Association of Maternal Smoking with Isolated Clubfoot, by Family History of Clubfoot, Atlanta, Georgia,
Family History
Maternal smoking
Cases
Controls
Odds RatiosMAT SMK
Yes 14 7
(14/11)/(7/20)= 3.64 No 11 20
118
859
(118/203)/859/2143)= 1.45
203
2 143
(Honein et al, Am J Epidemiol 2000;152: )
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”.

31. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
Factor Z
Factor A
Cases
Controls OR
What does it mean? No
1.0
Yes
OR+-
OR-+
OR++

32. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Yes
OR+-
OR-+
OR++

33. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
OR-+
OR++

34. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
Indep. effect of A
OR-+
OR++

35. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
Indep. effect of A
OR-+
Indep. effect of Z
OR++

36. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
Indep. effect of A
OR-+
Indep. effect of Z
OR++
Joint effects of A and Z

37. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
Indep. effect of A
OR-+
Indep. effect of Z
OR++
Joint effects of A and Z
Under ADDITIVE MODEL: Exp’d OR++ = OR+- + OR

38. If disease is “rare” (e.g., <5%):
Derivation of formula for expected joint OR
observed
RR++
1.0
RR+-
1.0
RR-+
1.0
If disease is “rare” (e.g., <5%):

39. Derivation of formula: Expected OR++ = OR+- + OR-+ - 1.0
Intuitive graphical derivation: OR
3.5
Exp’d
OR++
EXCZ
EXCA BL
2.5
Baseline + Excess due to Z
OR-+
EXCZ BL
2.0
Baseline + Excess due to A
OR+-
EXCA BL
1.0 BL
OR--
Two baselines!
Baseline
[EXCA+BL] + [EXCZ+BL] - BL
One baseline has to be removed
Expected OR++= OR+- + OR

40. OR
Observed OR++
3.5
3.5
2.5
2.0
1.0
OR--
OR-+
OR+-
Exp’d
OR++
Conclude:
If the observed joint OR is the same as the expected under the additive model, there is no additive interaction

41. Observed OR++
6.0 OR
Excess due to
interaction (“interaction term”)
3.5
Excess due to the
joint effects of A
and Z
2.5
2.0
1.0
OR--
OR-+
OR+-
Exp’d
OR++
Conclude:
If the observed joint OR is different than the expected under the additive model, there is additive interaction

42. Effect Modification Strategy
Odds Ratios for the association among isolated clubfoot, maternal smoking, and a family history of clubfoot, Atlanta, Georgia,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )

43. Effect Modification Strategy
Odds Ratios for the association among isolated clubfoot, maternal smoking, and a family history of clubfoot, Atlanta, Georgia,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
Two reference categories
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )

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,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )

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,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )
Independent effect of family history (i.e., in the absence of maternal smoking)

46. 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,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )
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,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORs
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
118
859
1.45
203
2,143
1.0 (reference)
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )
Joint effect of family history and maternal smoking

48. 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,
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
118
859
1.45
203
2,143
1.0 (reference)
Yes
6.26
– 1.0=
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )
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

49. Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction
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
1.0
Reference
Yes
OR+-
Indep. effect of A
OR-+
Indep. effect of Z
OR++
Joint effects of A and Z
Under ADDITIVE MODEL: Exp’d OR++ = OR+- + OR
Under MULTIPLICATIVE MODEL: Exp’d OR++ = OR+-  OR-+

50. 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,
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
118
859
1.45
203
2,143
1.0 (reference)
Yes
8.42
5.81 x 1.45=
1.0
(Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152: )
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).

51. 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”

52. 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.

53. Further issues for discussion
Quantitative vs. qualitative interaction

54. Odds Ratios for the association among isolated clubfoot, maternal smoking, and a family history of clubfoot, Atlanta, Georgia,
Family history of clubfoot
Maternal smoking
Cases
Controls
Stratified ORmaternal smk
Yes 14 7
3.64 No 11 20
118
859
1.45
203
2,143
Quantitative Interaction: Both ORs are in the same direction(>1.0), but they are heterogeneous (different)
Honein et al. Family history, maternal smoking, and clubfoot: an indication of gene-environment interaction. Am J Epidemiol 2000;152:

55. Reproductive Health Study, retrospective study of 1,430 non-contraceptive parous women, Fishkill, NY, Burlington, VT,
Smoking
Caffeine
No. pregnancies
Delayed conception*
ORcaffeine
P value No
575 47
1.0
301+mg/d 90 17
2.6
1.4, 5.0
Yes 76 15 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)

56. When there is qualitative interaction in one scale (additive or multiplicative), it must also be present in the other A- A+
Risk of
outcome 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-
3.0
-3/1000
0.5
6.0
Interaction in both scales

57. 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
Effect Modifier
Risk Factor
Incidence/1000
ARA
RRA Z+ A+
10.0
+5/1000
2.0 A-
5.0
Reference
1.0 Z-
3.0
-3/1000
0.5
6.0
Interaction in both scales

58. When there is qualitative interaction in one scale (additive or multiplicative), it must also be present in the other
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 A- A+
Risk of
outcome Z- Z+

59. When there is qualitative interaction in one scale (additive or multiplicative), it must also be present in the other
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
Gene+
Risk of
outcome
Gene- No
Yes
Phenylalanine Intake
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

60. 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

61. 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
A modifies the effect of Z

62. Further issues for discussion
Quantitative vs. qualitative interaction
Reciprocity of interaction
Interaction is not confounding

63. 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)
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. 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)
Pair No.
Case
Control
OR by sex
1 (male) + -
3/1 = 3.0
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

65. 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)
Pair No.
Case
Control
OR by sex
1 (male) + -
3/1 = 3.0
2 (male)
3 (male)
4 (male)
5 (male)
6 (female)
1/1= 1.0
7 (female)
8 (female)
9 (female)
10 (female)
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”
Incidence of disease “Y” by smoking and family history of “Y”
Positive additive interaction (synergism), but negative multiplicative interaction (antagonism)
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. Current Smoking Status Low Vitamin C intake (mg/day) Odds Ratio
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,
Current Smoking Status
Low Vitamin C intake (mg/day)
Odds Ratio No
1.0
Yes
6.8
1.8
10.6
(Horn-Ross et al. Diet and risk of salivary gland cancer. Am J Epidemiol 1997;146:171-6)
Additive Model:
Expected joint Odds Ratio = – 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 1995;142:1322-9
Reproductive Health Study, retrospective study of 1,430 non-contraceptive parous women, Fishkill, NY, Burlington, VT,
“…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  ) + (0.2  0.02)]  100= 3.6%
1.6
Unexposed
0.1
[(0.10  0.04) + (0.90  0.02)]  100 = 2.2%
1.0
Women
0.20
[(0.20  0.04) + (0.80  0.02)]  100= 2.4%
[(0.20  0.04) + (0.80  0.02)]  100= 2.4%

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

75. Non-differential misclassification within each stratum
Smokers:
Cases
Controls
Sensitivity
0.80
Specificity
0.85
Non-smokers:
0.95
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
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

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. 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,
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
(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)

78. Usually drank liquor with nonalcoholic mixers (n= 163)
Oral cancer odds ratios* related to excessive consumption of diluted and undiluted forms of liquor by liquor drinkers Puerto Rico,
Usually drank liquor with nonalcoholic mixers (n= 163)
Usually drank liquor straight (undiluted) (n= 206)
Drinks/week
Odds Ratio (95% CI)
>0 - <8
1.0 (reference)
64 - <137
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
1.5
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 SURE…Think 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 OR’s stratified according to the matching variable)
Cannot be assessed under the additive model, because the expected joint OR is undefined:
Exp’d OR++ = OR+- + OR
Set to be 1.0, by definition

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!