1. Kanguk Samsung Hospital, Sungkyunkwan University
Effect Modification
Seungho Ryu, MD, PhD
Kanguk Samsung Hospital,
Sungkyunkwan University

2. Learning objectives

3. Factors X M Y Z C Exposure factor Mediating factor Outcome factor
Effect
modifier C
Confounding
factor

4. Confounders have to …
Cause the disease (or be a surrogate measure of a cause) AND
Be associated with exposure (i.e., be distributed differently between exposed and unexposed), AND
Not affected by exposure (i.e., not be an intermediate variable in the causal pathway)
Note: the 3 conditions are necessary for a variable to be a confounder

5. Concepts of confounding
Response (R)
Exposure (E)

6. Concepts of confounding
C is associated with E
C causes R
 CONFOUNDING
Response (R)
C = 1
C = 0
Exposure (E)

7. Concepts of confounding
C is associated with E
C causes R
 CONFOUNDING
Response (R)
C = 1
C = 0
Exposure (E)

8. Concepts of confoundingMI
No MI
Coffee 90 60
No coffee
Odd ratio (OR)=
Smokers
Nonsmokers MI
No MI
Coffee 80 40 10 20
No Coffee
OR in smokers=
OR in nonsmokers=

10. Mediator Mediators are: Affected by exposure
On causal pathway between exposure and disease
Cause of disease
Mediators are intermediate variables, translating at least part of the effect of exposure on disease

11. Causal diagram – Physical activity, HDL cholesterol, and MI
Low physical activity
Low HDL cholesterol
Myocardial infarction
Low physical activity is a cause low HDL cholesterol
Low HDL cholesterol is a cause of myocardial infarction
HOWEVER, low HDL cholesterol is an intermediate variable in the causal pathway between physical activity and myocardial infarction

16. Obesity
(X)
Age, Sex, ……….
Glucose,
Blood pressure
Etc.
Coronary artery calcification
(Y)

18. Concepts of effect modificationMI
No MI
Coffee 90 60
No coffee
Odd ratio (OR)=
Smokers
Nonsmokers MI
No MI
Coffee 50 15 40 45
No Coffee 10 33 57
OR in smokers=
OR in nonsmokers=

19. Phenylketonuria

20. Phenylketonuria

21. Counterfactual causal model: PKU

22. Oral contraceptives, smoking and CVD mortality

23. Pharmacogenetics – http://www.pharmgkb.org

29. Effect modification - concept
Definition based on homogeneity or heterogeneity of effects
Interaction occurs when the effect of a risk factor X on the risk of an outcome Y is not homogenous in strata formed by a third variable Z. (Z: effect modifier)
Effect of X | Z ≠ Effect of X | Z

30. Effect modification - concept
Definition based on the comparison between observed and expected joint effects
Interaction occurs when the observed and expected joint effect of X and Z differs from that expected on the basis of their independent effects.
Effect of X and Z ≠ Effect of X | Z + Effect of Z | X

31. Effect measure modification (additive model)
Exposure Z
Exposure X
Outcome (incidence per 1,000py)
IDx
(by Z-group) (per 1,000py)
IDxy
(per 1,000py) No 10
0 (ref)
Yes 20 50 40 60
Joint expected IDxy = = 50
No effect modification for incidence rate difference (ID)

32. Effect measure modificationZ Z X Z Z X X X

33. Effect measure modification(additive model)
Exposure Z
Exposure X
Outcome (incidence per 1,000py)
IDx
(by Z-group) (per 1,000py)
IDxy
(per 1,000py) No 10
0 (ref)
Yes 20 50 40
100 90
Joint expected IDxy = = 50
Effect modification for incidence rate difference (ID)

34. Effect measure modificationZ Z X Z Z X X X

35. Effect modification (multiplicative model)
Exposure Z
Exposure X
Outcome (incidence per 1,000py)
IRx
(by Z-group) (per 1,000py)
IRxy
(per 1,000py) No 10
1 (ref)
Yes 20 2 50 5
100
Joint expected IRxy = 2 X 5 = 10
No effect modification for incidence rate ratio (IR)

36. Effect measure modificationZ Z X Z Z X X X

37. Effect measure modificationZ Z X Z X Z X X

38. Additive model or Multiplicative model? Effect modification?
Examples 1 Z X
Incidence rate
(per 1000)
difference No
10.0
0 (ref)
Yes
20.0
30.0
40.0
Additive model or Multiplicative model? Effect modification?

39. Additive model or Multiplicative model? Effect modification?
Examples 2 Z
Incidence rate (per 1000)
Incidence rate
difference (per 1000) No
5.0
0 (ref)
Yes
10.0
30.0
20.0
Additive model or Multiplicative model? Effect modification?

40. Incidence rate ratio (per 1000)
Examples 3 Z A
Incidence rate (per 1000)
Incidence rate ratio (per 1000) No
10.0
1.0
Yes
20.0
2.0
25.0
50.0
Additive model or Multiplicative model? Effect modification?

41. Incidence rate ratio (per 1000)
Examples 4 Z A
Incidence rate (per 1000)
Incidence rate ratio (per 1000) No
10.0
1.0
Yes
20.0
2.0
25.0
125.0
5.0
Additive model or Multiplicative model? Effect modification?

42. Examples 5
Observed incidence rate /1000
Observed incidence rate difference (ID) /1000 X Z - +
10.0
30.0
0 (ref)
20.0
40.0
Additive model or Multiplicative model? Joint expected incidence rate difference (ID)?
Effect modification?

43. Examples 6
Observed incidence rate /1000
Observed incidence rate difference (ID) /1000 X Z - +
10.0
30.0
0 (ref)
20.0
60.0
50.0
Additive model or Multiplicative model? Joint expected incidence rate difference (ID)?
Effect modification?

44. Observed incidence rate /1000 Observed incidence rate ratio (IR) /1000
Examples 7
Observed incidence rate /1000
Observed incidence rate ratio (IR) /1000 X Z - +
10.0
30.0
1 (ref)
3.0
20.0
60.0
2.0
6.0
Additive model or Multiplicative model? Joint expected incidence rate ratio (IR)?
Effect modification?

45. Observed incidence rate /1000 Incidence rate ratio (per 1000)
Examples 8
Observed incidence rate /1000
Incidence rate ratio (per 1000) X Z - +
10.0
30.0
1 (ref)
3.0
20.0
90.0
2.0
9.0
Additive model or Multiplicative model? Joint expected incidence rate ratio (IR)?
Effect modification?

46. Additive model

47. Multiplicative model

48. Oral contraceptives, smoking and CVD mortalityID
IR?

49. Oral contraceptives, smoking and CVD mortality

50. Oral contraceptives, smoking and CVD mortality
Joint expected ID?

51. Oral contraceptives, smoking and CVD mortality
Joint expected IR?

52. Threats to causal inference

53. Effect modification is a causal effect

54. Related concepts

55. Which is the relevant model? Additive vs. Multiplicative model

56. Incidence rate difference (ID) Incidence rate ratio (IR)
Hypothetical example of additive interaction without multiplicative interaction
Family history
Smoking
Incidence / 100
Incidence rate difference (ID)
Incidence rate ratio (IR) No
5.0
0 (ref)
1 (ref)
Yes
10.0
2.0
20.0
40.0

57. Qualitative interactionY Y
Z+ (IR>1.0, ID>0)
Z+ (IR>1.0, ID>0)
Z- (IR<1.0, ID<0)
Z- (IR=1.0, ID=0) X- X+ X- X+
X = exposure of interest
Z = effect modifier
Y = risk of outcome

58. Example of qualitative interaction

59. Example of qualitative interaction
Coronary heart disease event-free survival according to anger proneness among non-hypertensive (A) and among hypertensive (B)

60. Reciprocity of interaction
Exposure Z
Exposure X
Outcome (incidence per 1,000py)
IDz
(by x-group) (per 1,000py)
IDxy
(per 1,000py) No 10
0 (ref)
Yes 20 50 40 60
Joint expected IDxy = = 50
No effect modification for incidence rate difference (ID)

61. Reciprocity of interaction
Exposure Z
Exposure X
Outcome (incidence per 1,000py)
IDx
(by Z-group) (per 1,000py)
IDxy
(per 1,000py) No 10
0 (ref)
Yes 20 50 40
100 80 90
Joint expected IDxy = = 50
Effect modification for incidence rate difference (ID)

62. Example of Reciprocity of interaction

63. Interaction, Confounding effects and Adjustment
When a variable is found to be both a confounding variable and an effect modifier, adjustment for this variable is contraindicated.
This notion is even more important in qualitative interaction.

64. Z-adjusted RR or Z-specific RR?
Suspected effect modifier (Z)
Should a weighted average (Z-adjusted) effect be reported?
Absent
Present
2.3
2.6
2.0
20.0
0.5
3.0
4.5
Yes. Even if the difference in RRs is statistically significant
Z-adjusted RR may not be appropriate No
Perhaps.

65. Hypothetical results (I)

66. Hypothetical results (II)

67. Hypothetical results (III)

68. Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults
SBP = ·AGE + error
N = 19,256

69. Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults
SBP = ·AGE + error
• Men
• Women
N = 19,256

70. Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults
SBP = ·AGE – ·SEX + error
M: SBP = ·AGE + error
F: SBP = ·AGE – error
• Men
• Women
N = 19,256

71. Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults
M: SBP = ·AGE + error
F: SBP = ·AGE + error
• Men
• Women
N = 19,256

72. Introducing interaction terms in regression models
ID AGE SEX AGE·SEX

73. Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults
SBP = ·AGE – ·SEX ·AGE·SEX + error
FemalesMales
N = 19,256

74. Interaction model for SBP vs. AGE and SEX
SBP = ·AGE – ·SEX ·AGE·SEX + error
Coefficients:
Value SE t P
(Intercept)
Age < 0.001
Sex < 0.001
Age·Sex < 0.001

75. Interpreting Interaction
Heterogeneity due to random variability
Heterogeneity due to confounding
Heterogeneity due to differential bias
Heterogeneity due to differential intensity of exposure
Interaction and host factors

76. Heterogeneity due to random variability
Sample size inevitably decreases as more strata are created in subgroup analysis
Heterogeneity would occur by chance alone
Subgroup analysis should be regarded as an exploratory strategies
Detection of heterogeneity should be address vis-à-vis its plausibility

77. Heterogeneity due to confounding
Gender/smoking
Coffee intake
Cases
Control
Odds ratio
Female /nonsmoker
Yes 10
1.0 No 90
Total
100
Male/total 38 22
2.2 62 78
Gender/smoking
Coffee intake
Cases
Control
Odds ratio
Male /nonsmoker
Yes 35 15
1.0 No
Total 70 30
Male/smoker 3 7 27 63

78. Heterogeneity due to differential bias
Risk of miscarriage per 100 pregnancies in relation to maternal years of education
White
Black
Black / White ratio No
Risk
/100
Total
325
7.7 93
5.5
0.7
Mother’s years of education
<9 12
10.4 -
10-11 52
8.0 15
4.5
0.6
111
6.3 44
4.7
0.7
≥13
150
9.2 33
9.5
1.0

79. Heterogeneity due to differential intensity of exposure
Apparent interaction can occur when there is heterogeneity in the levels of exposure to the risk factor according to the effect modifier
Potential effect modification by gender of the relationship of smoking to respiratory disease may be created or exaggerated by the fact that the level of exposure to smoking is higher in men than in women

80. Interaction and host factors
Biological mechanism of effect modification can vary at the metabolic or cellular level.
Phenylketonuria
Endogenous hormones
Relative low risk of coronary heart disease in white women at similar levels of exposure to traditional CVD risk factors as men

82. When do you believe the presence of effect modification?

83. Main points