Assessment of Heterogeneity of Effects

Understanding Interaction in Epidemiological Studies

Kamarul Imran Musa, Universiti Sains Malaysia

Learning Objectives

By the end of this session, you will be able to:

  1. Understand ‘Interaction’ in epidemiological studies

  2. Identify ‘Interaction’ in epidemiological studies

  3. Handle, interpret, prevent and control ‘Interaction’ in epidemiological studies

Introduction to Interaction

Interaction (Effect Modification):

  • A situation where two or more risk factors modify the effect of each other regarding the occurrence or level of a given outcome

  • Must be distinguished from confounding

MacMahon’s Definition

“When the incidence rate of disease in the presence of two or more risk factors differs from the incidence rate expected to result from their individual effects.”

Key Concepts

For Dichotomous Variables:

  • Effect of exposure on outcome differs depending on whether another variable (effect modifier) is present or absent

For Continuous Variables:

  • Effect of exposure on outcome depends on the level of another variable

Minimum Requirements:

  • Three factors needed: Factor A (main risk factor), Y (outcome), Z (effect modifier)

Types of Interaction

Positive Interaction (Synergism):

  • Effect modifier strengthens (accentuates) the effect of exposure
  • Combined effect is greater than expected

Negative Interaction (Antagonism):

  • Effect modifier diminishes or eliminates the effect of exposure
  • Combined effect is less than expected

Important

The challenge: Determining what we would expect from individual effects

Assessment Framework

Key Question:

Does the magnitude or direction of effect of A on Y vary according to the occurrence of variable Z?

Example: Diabetes is a stronger risk factor for CHD in women than in men → Gender modifies the effect of diabetes on CHD risk

Two Approaches to Detection

1. Additive Interaction:

  • Based on absolute difference (attributable risk model)
  • Examines if attributable risk varies across strata of Z

2. Multiplicative Interaction:

  • Based on relative difference (ratio model)
  • Examines if relative risk varies across strata of Z

Tip

Both models provide different but complementary information

Additive Interaction: Definition

Present when:

Attributable risk in those exposed to factor A (ARexp) varies as a function of variable Z

Formula:

ARexp = (Risk in exposed) - (Risk in unexposed)

Key Feature:

  • Focuses on absolute differences in risk
  • More relevant for public health interventions

Example: No Additive Interaction

Z A Incidence rate (per 1000) Attributable risk (per 1000)
No No 10.0 Reference
Yes 20.0 10.0
Yes No 30.0 Reference
Yes 40.0 10.0

Interpretation: Attributable risk is constant (10.0) regardless of Z status → No additive interaction

Example: Additive Interaction Present

Z A Incidence rate (per 1000) Attributable risk (per 1000)
No No 5.0 Reference
Yes 10.0 5.0
Yes No 10.0 Reference
Yes 30.0 20.0

Interpretation: Attributable risk varies (5.0 vs 20.0) by Z status → Additive interaction present

Multiplicative Interaction: Definition

Present when:

Relative risk between exposed and unexposed to factor A differs as a function of variable Z

Formula:

RR = (Risk in exposed) / (Risk in unexposed)

Key Feature:

  • Focuses on relative differences in risk
  • Commonly assessed in statistical models

Example: No Multiplicative Interaction

Z A Incidence rate (per 1000) Relative risk
No No 10.0 1.0
Yes 20.0 2.0
Yes No 25.0 1.0
Yes 50.0 2.0

Interpretation: Relative risk is constant (2.0) regardless of Z status → No multiplicative interaction

Example: Multiplicative Interaction Present

Z A Incidence rate (per 1000) Relative risk
No No 10.0 1.0
Yes 20.0 2.0
Yes No 25.0 1.0
Yes 125.0 5.0

Interpretation: Relative risk varies (2.0 vs 5.0) by Z status → Multiplicative interaction present

Comparing Expected vs Observed Effects

Additive Model - Expected Joint Effect:

Expected AR = ARA + ARZ (minus baseline to avoid double counting)

Multiplicative Model - Expected Joint Effect:

Expected RR = RRA × RRZ

Interpretation

  • Observed > Expected: Positive interaction (synergism)
  • Observed < Expected: Negative interaction (antagonism)
  • Observed ≈ Expected: No interaction

Classic Example: Smoking and Asbestos

Deaths from Lung Cancer (per 100,000):

Cigarette Smoking Asbestos Exposure
No Yes
No 11.3 58.4
Yes 122.6 601.6

Analysis:

  • Expected additive: 58.4 + 122.6 - 11.3 = 169.7
  • Observed: 601.6
  • Strong synergistic interaction!

Application in Cohort Studies

Example: Gender and Diabetes on Post-Stenting Mortality

Homogeneity Strategy:

  • Compare AR and RR across strata of effect modifier
  • Assess if measures are heterogeneous

Findings:

  • Women with diabetes: AR = 6.2, RR = 2.5
  • Men with diabetes: AR = 2.0, RR = 1.5
  • Conclusion: Gender modifies diabetes effect

Application in Case-Control Studies

Important Limitation:

  • Can only assess multiplicative interaction
  • Absolute risk measures usually not available
  • Cannot calculate attributable risk directly

Example: Oral Contraceptives and Smoking on MI

Heavy Smoking OC Use Odds Ratio
No No 1.0
Yes 4.5
Yes No 1.0
Yes 5.6

Interpretation: Weak multiplicative interaction (4.5 vs 5.6)

Additive vs Multiplicative Models

Which Model to Use?

Additive Model:

  • Public health perspective
  • Disease prevention focus
  • Identifies populations at highest absolute risk

Multiplicative Model:

  • Statistical convenience
  • Common in regression models
  • Mantel-Haenszel adjustment

Warning

If only multiplicative interaction is assessed, additive interaction may be missed!

Interaction vs Confounding

Key Differences:

Feature Confounding Interaction
Nature Undesirable distortion Part of causal web
Goal Control/eliminate Identify/describe
Implication Threatens validity Scientific interest
Action Adjust in analysis Report stratified results

Important

When a variable is both a confounder and effect modifier: Do NOT adjust!

Statistical Evaluation

Decision Framework:

  1. Test for heterogeneity
  2. Assess statistical significance
  3. Consider sample size
  4. Evaluate biological plausibility

Recommendations:

  • Large studies: Small heterogeneity may be ignored if not biologically plausible
  • Small studies: Substantial heterogeneity should be considered even if not statistically significant

Presenting Effect Modification and Interaction

Importance of Proper Presentation

Why Presentation Matters:

  • Facilitates understanding of complex relationships
  • Ensures transparency in research
  • Guides clinical and public health decisions
  • Prevents misinterpretation of findings

Note

Following Knol & VanderWeele (2012) recommendations enhances the quality and reproducibility of epidemiological research

Key Principles for Reporting

1. Report Both Scales:

  • Present both additive and multiplicative interaction when possible
  • Each scale provides unique information

2. Stratified Results:

  • Always show stratum-specific estimates
  • Do not rely solely on adjusted estimates

3. Clear Terminology:

  • Use consistent definitions (interaction vs effect modification)
  • Specify the scale being assessed

Measures of Additive Interaction

Three Key Measures:

  1. RERI (Relative Excess Risk due to Interaction)
    • RERI = RR11 - RR10 - RR01 + 1
    • RERI = 0 indicates no additive interaction
  2. AP (Attributable Proportion)
    • AP = RERI / RR11
    • Proportion of risk due to interaction
  3. S (Synergy Index)
    • S = (RR11 - 1) / (RR10 + RR01 - 2)
    • S = 1 indicates no synergy

Interpreting Interaction Measures

RERI Interpretation:

  • RERI > 0: Positive interaction (synergism)
  • RERI < 0: Negative interaction (antagonism)
  • RERI = 0: No additive interaction

Synergy Index (S) Interpretation:

  • S > 1: Synergism
  • S < 1: Antagonism
  • S = 1: No interaction

Tip

Confidence intervals should be presented for all measures

Common Pitfalls to Avoid

1. Testing Interaction Only on One Scale

  • May miss important interactions on the other scale

2. Not Reporting Stratum-Specific Estimates

  • Makes interpretation difficult for readers

3. Confusing Interaction with Confounding

  • These are conceptually different phenomena

4. Over-reliance on P-values

  • Small studies may have true interaction without significance
  • Large studies may have statistical but not practical significance

Best Practices for Tables

Example Table Structure:

Exposure A Modifier Z Cases Controls OR (95% CI)
No No n₁ n₂ 1.0 (Reference)
Yes No n₃ n₄ OR₁ (CI₁)
No Yes n₅ n₆ OR₂ (CI₂)
Yes Yes n₇ n₈ OR₃ (CI₃)

Include:

  • RERI (95% CI)
  • AP (95% CI)
  • P-value for multiplicative interaction

Summary and Key Messages

  1. Interaction reveals how risk factors work together

  2. Two scales of measurement: additive and multiplicative

  3. Both scales provide important information

  4. Confounding and interaction are distinct phenomena

  5. Report stratified results when interaction is present

  6. Biological plausibility should guide interpretation

Tip

Always consider both public health and statistical perspectives!

References

Main Reading:

  • Szklo M, Nieto FJ. Epidemiology: Beyond the Basics (3rd edition), Chapter 6: Defining and Assessing Heterogeneity of Effects: Interaction

Additional Resources:

  • Gordis L. Epidemiology, Chapter 15
  • Knol MJ, VanderWeele TJ. Recommendations for presenting analyses of effect modification and interaction. Int J Epidemiol 2012;41(2):514-520

Practice:

  • Apply these concepts using simulated scenarios in your assignments