Let's start with two definitions.

- Effect modification
- Effect modification occurs when a factor (an effect modifier) modifies the causal relationship between a risk factor and the outcome.

For example, immunization status is a strong effect modifier of the relationship between exposure to a specific pathogen and subsequent disease from that pathogen. As an effect modifier, immunization status then modifies the biologic response of the person. The presence of effect modification supports a causal relationship because it implies a biologically plausible process.

- Statistical interaction
- Statistical interaction is a term that is often used to describe a similar feature of data. Statistical interaction is consistent with effect modification but does not necessarily mean that there is a difference in the biologic response depending on exposure status.

#### Consequences of not identifying an effect modifier

If effect modification is not recognized, the estimator of the association of the risk factor with the outcome (e.g., RR) becomes a weighted average between the RR in one level of X (e.g., immunized) and the RR from another level of X (not immunized).

#### Methods to take effect modification into account

When designing and conducting a study:

- Conceptualize which factors (variables) might be effect modifiers
- Do not match on a potential effect modifier
- Collect information on potential effect modifiers (the more the better!)
- Consider powering the study to be able to test effect modifiers (rule of thumb – 4 times the sample size as would be required to test the presence of effect modification)

In the analysis of a study:

- Conceptualize potential effect modifiers, using your knowledge of the area of research, prior experience (from yourself and others). Ask a sequence of questions (e.g. For exposure E, disease D and factor X, a potential effect modifier: is there an association between E and D? is it biologically plausible that the association betwen E and D differs for levels of X? can such a difference be detected in this study?)
- Estimate a crude (unadjusted) association between exposure and disease.
- Stratifiy by potential effect modifiers to get stratum specific estimators. Compare/test significance of differences between stratum-specific estimators.
- Use a statistical model with interaction term.

#### Judgment

- If the stratum-specific estimators are significantly different from each other, the stratified variable is likely to be a major effect modifier.
- Statistical methods (Breslow-Day Test for Homogeneity of the ORs from Extended Mantel-Haenszel method, -2 log likelihood test from logistic regression) are available to test the statistical significance of potential effect modifiers, and to calculate the estimators of Exposure-Disease association according to the levels of significant effect modifiers.
- Most epidemiological studies are not designed to have enough statistical power to statistically identify potential effect modifiers (often not the primary objective).

**Note!**

**Absence of evidence is not the same as Evidence of absence**.

“The interactions between Exposure and race, sex… in association with Disease were statistically tested by introducing interaction-terms into the logistic regression models, and none of them were found to be statistically significant at p < 0.15 level”.

An effect modifier is a real or hypothesized relationship in *nature*, not just observed in a dataset, as compared to a confounder. Once identified as an effect modifier, a variable is not treated as a confounder.

#### Example

Here is an example of effect modification:

DIABETES (DIABETES)

Incident CHD | |||
---|---|---|---|

Frequency Percent Row Pct Col Pct |
0 | 1 | Total |

0 | 1191 | 25 | 1216 |

1 | 93 | 13 | 106 |

Total | 1248 | 38 | 1322 |

**\(CI_0 = 2.06\%\) **

**\(CI_1 = 12.26\%\)**

**RR = 6.00**

**Odds ratio = 6.66**

DIABETES (DIABETES)

Incident CHD | |||
---|---|---|---|

Frequency Percent Row Pct Col Pct |
0 | 1 | Total |

0 | 1003 | 70 | 1073 |

1 | 77 | 12 | 89 |

Total | 1080 | 82 | 1162 |

**\(CI_0 = 6.52\%\) **

**\(CI_1 = 13.48\%\)**

**RR = 2.07**

**Odds ratio = 2.23**

Combining both sexes, the OR = 4.30. Thus, sex modifies the effect of diabetes on incident CHD.