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

Learning objectives

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

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

Concepts of confounding Response (R) Exposure (E)

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

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

Concepts of confounding MI 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=

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

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

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

Concepts of effect modification MI 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=

Phenylketonuria

Phenylketonuria

Counterfactual causal model: PKU

Oral contraceptives, smoking and CVD mortality

Pharmacogenetics – http://www.pharmgkb.org

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

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

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 = 10 + 40 = 50 No effect modification for incidence rate difference (ID)

Effect measure modification Z Z X Z Z X X X

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 = 10 + 40 = 50 Effect modification for incidence rate difference (ID)

Effect measure modification Z Z X Z Z X X X

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)

Effect measure modification Z Z X Z Z X X X

Effect measure modification Z Z X Z X Z X X

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?

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?

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?

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?

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?

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?

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?

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?

Additive model

Multiplicative model

Oral contraceptives, smoking and CVD mortality ID IR?

Oral contraceptives, smoking and CVD mortality

Oral contraceptives, smoking and CVD mortality Joint expected ID?

Oral contraceptives, smoking and CVD mortality Joint expected IR?

Threats to causal inference

Effect modification is a causal effect

Related concepts

Which is the relevant model? Additive vs. Multiplicative model

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

Qualitative interaction Y 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

Example of qualitative interaction

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

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 = 10 + 40 = 50 No effect modification for incidence rate difference (ID)

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 = 10 + 40 = 50 Effect modification for incidence rate difference (ID)

Example of Reciprocity of interaction

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.

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.

Hypothetical results (I)

Hypothetical results (II)

Hypothetical results (III)

Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults SBP = 97.31 + 0.6061·AGE + error N = 19,256

Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults SBP = 97.31 + 0.6061·AGE + error • Men • Women N = 19,256

Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults SBP = 99.48 + 0.6061·AGE – 4.0909·SEX + error M: SBP = 99.48 + 0.6061·AGE + error F: SBP = 99.48 + 0.6061·AGE – 4.0909 + error • Men • Women N = 19,256

Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults M: SBP = 106.19 + 0.4664·AGE + error F: SBP = 89.56 + 0.7279·AGE + error • Men • Women N = 19,256

Introducing interaction terms in regression models ID AGE SEX AGE·SEX 3 21 0 0 4 32 1 32 9 48 1 48 10 35 0 0 11 48 0 0 19 44 0 0 34 42 1 42 44 24 1 24 45 67 1 67 48 56 1 56

Interaction for continuous variables - Determinants of systolic blood pressure in NHANES III adults SBP = 106.19 + 0.4664·AGE – 16.6277·SEX + 0.2615·AGE·SEX + error FemalesMales N = 19,256

Interaction model for SBP vs. AGE and SEX SBP = 106.19 + 0.4664·AGE – 16.6277·SEX + 0.2615·AGE·SEX + error Coefficients: Value SE t P (Intercept) 106.1862 0.4352 244.0203 Age 0.4664 0.0084 55.7910 < 0.001 Sex -16.6277 0.5955 -27.9201 < 0.001 Age·Sex 0.2615 0.0114 22.8732 < 0.001

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

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

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

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

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

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

When do you believe the presence of effect modification?

Main points