1. Intermediate methods in observational epidemiology 2008 Interaction

2. 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

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. 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

7. 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

8. 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.

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. Individual effectsAZ Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism Observed joint effectA + Z-I Antagonism Interaction

14. Individual effectsAZ Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism Observed joint effectA + Z-I Antagonism Interaction

15. Individual effectsAZ Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism Observed joint effectA + Z-I Antagonism Interaction

16. Individual effectsAZ Interaction Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z Synergism Observed joint effectA + Z-I Antagonism

17. Individual effectsAZ Interaction Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism

18. Individual effectsAZ Interaction Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism Observed joint effectA + Z Antagonism

19. Individual effectsAZ Interaction Expected joint effectAZ Observed joint effectA + Z No interaction Observed joint effectA + Z+I Synergism Observed joint effectA + 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. 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 ZAIncidence rate (%)AR exp to A (%) No 5.0 Yes10.0 YesNo10.0 Yes30.0 First strategy to assess interaction: Effect Modification ADDITIVE (attributable risk) interaction

23. Hypothetical example of presence of multiplicative interaction ZAIncidence rate (%)RR A No 10.0 Yes20.0 YesNo25.0 Yes125.0 Conclude: Because RR’s associated with A are modified by exposure to Z, multiplicative interaction is present. 2.0 5.0 First strategy to assess interaction: Effect Modification MULTIPLICATIVE (ratio-based) interaction

24. 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. 5.0 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) observed Joint observed AR = 25% expected Joint expected AR = AR A+Z- + AR A-Z+ = 10%

26. 5.0 2.0 2.5 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) observed Joint observed RR A+Z+ = 12.5 expected Joint expected RR A+Z+ = RR A+Z- × RR A-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 ZAIncidence rate (%)AR exp to A (%) No 5.0 Yes10.0 YesNo10.0 20.0 Yes30.0 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

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

30. Family HistoryMaternal smokingCasesControlsOdds Ratios MAT SMK Yes 147(14/11)/(7/20)= 3.64 No1120 NoYes118859(118/203)/859/2143) = 1.45 No2032 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”.

31. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0 YesOR +- YesNoOR -+ YesOR ++ 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

32. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0 YesOR +- YesNoOR -+ YesOR ++ 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

33. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- YesNoOR -+ YesOR ++ 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

34. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- Indep. effect of A YesNoOR -+ YesOR ++ 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

35. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- Indep. effect of A YesNoOR -+ Indep. effect of Z YesOR ++ 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

36. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- Indep. effect of A YesNoOR -+ Indep. effect of Z YesOR ++ Joint effects of A and Z 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

37. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- Indep. effect of A YesNoOR -+ Indep. effect of Z YesOR ++ Joint effects of A and Z 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 Under ADDITIVE MODEL: Exp’d OR ++ = OR +- + OR -+ - 1.0

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

39. 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 +- EXC A BL [EXC A +BL] + [EXC Z +BL] - BL 3.5 Exp’d OR ++ EXC Z EXC A BL 2.5 Baseline + Excess due to Z OR -+ EXC Z BL Two baselines! One baseline has to be removed Expected OR ++ = OR +- + OR -+ - 1.0

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

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

42. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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

43. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Two reference categories

44. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- 1.0

45. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- Independent effect of family history (i.e., in the absence of maternal smoking) 1.0

46. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- Independent effect of maternal smoking (i.e., in the absence of family history) 1.0

47. Family history of clubfoot Maternal smoking CasesControlsStratified ORs ORs using No/No as the reference category Expected under the ADDITIVE model Yes 1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- Joint effect of family history and maternal smoking 1.0

48. Family history of clubfoot Maternal smoking CasesControlsStratified ORs Observed ORs using No/No as the reference category Expected under the ADDITIVE model Yes1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- 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) 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

49. Factor ZFactor ACasesControlsORWhat does it mean? No 1.0Reference YesOR +- Indep. effect of A YesNoOR -+ Indep. effect of Z YesOR ++ Joint effects of A and Z Second strategy to assess interaction: comparison between joint observed and joint expected effects Layout of table to assess both ADDITIVE and MULTIPLICATIVE interaction Under ADDITIVE MODEL: Exp’d OR ++ = OR +- + OR -+ - 1.0 Under MULTIPLICATIVE MODEL: Exp’d OR ++ = OR +-  OR -+ Case-Control Study

50. Family history of clubfoot Maternal smoking CasesControlsStratified ORs Observed ORs using No/No as the reference category Expected under the MULTIPL. model Yes1473.6420.30 No11205.81 NoYes1188591.45 No2032,1431.0 (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 Second Strategy: Comparison between joint expected and joint observed effects - - allows assessment of both ADDITIVE and MULTIPLICATIVE interactions-- 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) 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

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 interactionQuantitative vs. qualitative interaction

54. Family history of clubfoot Maternal smoking CasesControls Stratified OR maternal smk Yes 1473.64 No1120 NoYes1188591.45 No2032,143 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 Quantitative Interaction: Both ORs are in the same direction(>1.0), but they are heterogeneous (different)

55. SmokingCaffeineNo. pregnanciesDelayed conception*OR caffeine P value No 575471.0 301+mg/d90172.61.4, 5.0 YesNo76151.0 301+mg/d83110.60.3, 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.

56. A- A+ Risk of outcome Z- Z+ Qualitative Interaction Effect ModifierRisk FactorIncidence/1000AR A RR A Z+A+10.0+5/10002.0 A-5.0Reference1.0 Z-A+3.0-3/10000.5 A-6.0Reference1.0 Interaction in both scales When there is qualitative interaction in one scale (additive or multiplicative), it must also be present in the other

57. A- A+ Risk of outcome Z- Z+ Qualitative Interaction Effect ModifierRisk FactorIncidence/1000AR A RR A Z+A+10.0+5/10002.0 A-5.0Reference1.0 Z-A+3.0-3/10000.5 A-6.0Reference1.0 Interaction in both scales

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

59. Risk of outcome Gene+ 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, AR exp >>0 Individuals WITHOUT this genotype WILL NOT develop symptoms, even WITH exposure to phenylalanine  OR or RR= 1.0 When there is qualitative interaction in one scale (additive or multiplicative), it must also be present in the other Phenylalanine Intake No Yes Gene-

60. Further issues for discussion 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

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. Pair No.CaseControlOR 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 Ratio4/2= 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)

64. Pair No.CaseControlOR 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 Ratio4/2= 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)

65. Pair No.CaseControlOR 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 Ratio4/2= 2.0 INTERACTION IS NOT CONFOUNDING

66. Further issues for discussion 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” –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” 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 modifier RF- risk factor of interest

68. Current Smoking Status Low Vitamin C intake (mg/day) Odds Ratio No 1.0 YesNo6.8 NoYes1.8 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 Conclude: For Public Health purposes, ignore negative multiplicative interaction, and focus on smokers for prevention of low vitamin C intake Negative multiplicative interaction

69. Further issues for discussion 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 (“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, 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 interactionInterpretation and uses of interaction –Additive interaction as “public health interaction” –Biological interaction –Statistical interaction (not causal) Differential confoundingDifferential confounding

72. Prevalence of G IncidenceRelative Risk Men Exposed0.8 [(0.8  0.04 ) + (0.2  0.02)]  100= 3.6% 1.6 Unexposed0.1 [(0.10  0.04) + (0.90  0.02)]  100 = 2.2% 1.0 Women Exposed0.20 [(0.20  0.04) + (0.80  0.02)]  100= 2.4% 1.0 Unexposed0.20 [(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

73. Further issues for discussion 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

74. Smoking StatusBMI statusCasesControlsOdds Ratio SmokersOverweight2001002.25 Not overweight800900 Non-smokersOverweight2001002.25 Not overweight800900 Example of effect of misclassification of overweight by smoking category, on the Odds Ratios

75. Smokers Smokers:CasesControls Sensitivity0.80 Specificity0.85 Non-smokers Non-smokers:CasesControls Sensitivity0.95 Specificity0.98 Smoking StatusBMI statusCasesControlsOdds Ratio TRUE SmokersOverweight2001002.25 Not overweight800900 Non-smokersOverweight2001002.25 Not overweight800900 Non-differential misclassification within each stratum Values of indices of validity different between smokers and non-smokers Smokers Over- weight CasesControlsOR MISCL Yes2802151.4 No720785 Non-Smokers Over- weight CasesControlsOR MISCL Yes2061132.0 No794887

76. Further issues for discussion 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 Differential misclassification across strata of the effect modifier The dose (amount of exposure) may be higher in one stratum than in the other

77. Maximum wind speed Number of days% of epidemic daysOR ≤ 12 miles/hour*9925.74.4 > 12 miles/hour33902.01.7 No soy25481.81.0 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)

78. Usually drank liquor with nonalcoholic mixers (n= 163) Usually drank liquor straight (undiluted) (n= 206) Drinks/weekOdds Ratio (95% CI) >0 - <81.0 (reference) 64 - <1371.17.3 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

79. GenderSmokingRelative Risk ManYes3.0 No1.0 WomanYes1.5 No1.0 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.

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 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  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 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  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. 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 -+ - 1.0 Set to be 1.0, by definition –Cannot be assessed under the additive model, because the expected joint OR is undefined:

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!