Causal Interaction in Clinical Epidemiology: Additive Interaction, RERI, AP, and Synergy Index

Introduction

In clinical epidemiology, most diseases arise from the combined influence of multiple exposures rather than a single cause. Understanding how these exposures act together is essential for identifying causal mechanisms and designing effective prevention strategies.

Causal interaction refers to a situation in which two exposures jointly influence an outcome in a way that differs from what would be expected based on their individual effects. This concept is central to causal inference, where the goal is to determine whether observed associations reflect true causal relationships rather than confounding, bias, or chance.

A general causal framework can be expressed as:

Y = f (X_{1}, X_{2}, X_{1} \times X_{2} \mid confounders)

where X1 and X2 are exposures and X1×X2 represents their joint effect.

Definition of Causal Interaction

Causal interaction occurs when the combined effect of two exposures cannot be explained by simply adding or multiplying their individual effects.

For example:

X1 : Smoking
X2 : Air pollution
Y : Lung disease

If individuals exposed to both smoking and air pollution have a risk that is greater (or smaller) than expected from each exposure alone, interaction is present. This joint effect reflects how multiple determinants operate together in disease causation.

Scales of Interaction

Interaction can be evaluated on two complementary scales: multiplicative and additive.

Multiplicative Interaction

Multiplicative interaction assesses whether the combined effect differs from the product of individual effects. It is typically evaluated using regression models such as logistic, Poisson, or Cox regression, through inclusion of an interaction term.

Although widely used, multiplicative interaction primarily reflects statistical relationships and may not directly correspond to biological or clinical relevance.

Additive Interaction

Additive interaction assesses whether the combined effect exceeds the sum of individual effects. This scale is more relevant for clinical and public health decision-making because it quantifies excess risk attributable to the joint exposure.

Additive interaction addresses practical questions such as how much additional disease burden arises when exposures occur together and how many cases could be prevented by eliminating one exposure.

Measures of Additive Interaction

Three measures are commonly used to quantify additive interaction:

1. Relative Excess Risk due to Interaction (RERI)

R E R I = R R_{11} - R R_{10} - R R_{01} + 1

RERI represents the excess risk attributable specifically to the interaction between exposures.

RERI > 0: positive interaction (synergy)
RERI = 0: no interaction
RERI < 0: antagonism

2. Attributable Proportion (AP)

A P = \frac{R E R I}{R R_{11}}

AP indicates the proportion of disease among individuals exposed to both factors that is due to their interaction.

3. Synergy Index (SI)

S I = \frac{R R_{11} - 1}{(R R_{10} - 1) + (R R_{01} - 1)}

SI reflects the strength of the interaction:

SI > 1: synergy
SI = 1: no interaction
SI < 1: antagonism

Illustrative Example

Consider the following:

Exposure	Risk Ratio (RR)
None	1
Smoking only	2
Pollution only	2
Both	6

Calculations:

RERI=6-2-2+1=3
AP=3/6=0.5
SI=(6-1)/[(2-1)+(2-1)]=2.5

These results indicate a positive additive interaction. Specifically, half of the disease risk among individuals exposed to both factors is attributable to their interaction, and the combined effect is substantially greater than expected.

Interaction vs Effect Modification

Interaction should be distinguished from effect modification.

Causal interaction concerns how two exposures jointly affect an outcome.
Effect modification refers to variation in the effect of one exposure across levels of another variable.

For example, smoking and asbestos jointly increasing lung cancer risk represents interaction, whereas a drug working differently in men and women represents effect modification.

Interpretation and Limitations

Although measures such as RERI, AP, and SI provide insight into potential biological synergy, valid causal interpretation requires:

Clear temporality (exposure precedes outcome)
Adequate control of confounding
Appropriate study design (e.g., cohort study with individual-level data)

Without these conditions, observed interaction may reflect association rather than true causal co-action.

Conclusion

Causal interaction is a fundamental concept in clinical epidemiology that explains how multiple exposures jointly influence disease risk. While multiplicative interaction is commonly assessed in statistical models, additive interaction provides more clinically meaningful information by quantifying excess risk attributable to combined exposures.

Measures such as RERI, AP, and SI allow researchers to evaluate this excess risk and identify synergistic relationships. However, careful attention to study design and causal assumptions is essential to ensure valid interpretation.

Key Takeaways

Causal interaction describes joint effects of exposures on an outcome
Additive interaction is most relevant for clinical and public health decisions
RERI quantifies excess risk due to interaction
AP shows the proportion of risk attributable to interaction
SI measures the strength of synergy
Valid causal interpretation depends on proper design and confounding control