Causal inference involves using directed acyclic graphs (DAGs) and the potential outcomes model to assess effect modification (EM) from a causal perspective. DAGs can help identify confounding and selection bias. The potential outcomes model distinguishes statistical from causal interaction and allows estimating average risk or risk differences to determine if causal interaction is present on the additive scale. Studies should minimize bias, control confounding, and quantify uncertainty to best assess causal EM.

1. Outline
1. What does causal inference entail?
2. Using directed acyclic graphs
a. DAG basics
b. Identifying confounding
c. Understanding selection bias
3. Causal perspective on effect modification
a. Brief recap of effect modification (EM)
b. Linking EM in our studies to reality
c. Types of interaction
d. Causal interaction / EM
1. Sufficient cause model (“causalpies”)
2. Potential outcomes model (“causal types”)
e. Choosing which measure of interaction to estimate and report
4. Integrating causal concepts into your research

2. Potential Outcomes Model & EM
• Calculate RRs from a real world study
– Adjust for confounding
– Consider role of bias
– Quantify role of chance (e.g., confidence interval)
• The RR for the relation between X and Y was
different between people of Z=1 and Z=0
• This suggests heterogeneity in the measure of
association between X and Y by values of Z
• No connection back to causal interaction

3. Potential Outcomes Model & EM
• Calculate ARs from a real world study
– Adjust for confounding
– Consider role of bias
– Quantify role of chance (e.g., confidence interval)
• The AR for the relation between X and Y was
different between people of Z=1 and Z=0
• This suggests the presence of causal interaction
between X and Z
– Have to consider bias, control confounding, quantify role
of random error and state assumptions

4. 39
Assessing EM on the additive scale using relative scale
estimation methods
• What if you want or need to estimate measures of association
on a relative scale, but you want to assess interaction on the
additive scale?
• Estimate the Relative Excess Risk due to Interaction
(RERI) RERI = RR11-‐RR10-‐RR01+1
NOTE: Recoding may be necessary for preventive exposures
• RERI>0 implies that AR11 ≠ AR01+ AR10
– Interaction is present on the additive scale
• RERI=0 implies that AR11 = AR01+ AR10
– Interaction is not present on the additive scale
Read more: VanderWeele (2009). Sufficient Cause Interactions and Statistical Interactions.
Epidemiology20:6-‐13.

5. What’s the best we can do to assess
EM?
• Be clear about whether we are purely
assessing EM from a statistical perspective or
if we intend to make causal inferences
• Be thougheul about which scale we choose to
assess interaction on
• Attempt to minimize sources of bias and error
in our studies

6. Outline
1. What does causal inference entail?
2. Using directed acyclic graphs
a. DAG basics
b. Identifying confounding
c. Understanding selection bias
3. Causal perspective on effect modification
a. Brief recap of effect modification (EM)
b. Linking EM in our studies to reality
c. Types of interaction
d. Causal interaction / EM
1. Sufficient cause model (“causalpies”)
2. Potential outcomes model (“causal types”)
e. Choosing which measure of interaction to estimate and report
4. Integrating causal concepts into your research