What is Marginalisation in Clinical Statistics?
On this page
Marginalisation refers to the process of transforming effect estimates derived from specific subgroups (i.e., conditional on covariates like age or sex) into a population-level average effect—that is, what would happen across the entire population.
💡 Why Do We Need Marginalisation?
When fitting a standard logistic regression, for example:
logistic outcome treat age sex
This produces a conditional odds ratio (OR) for treat:
- It estimates the effect of treatment conditional on being of the same age and sex.
- That is: “What is the effect of treatment among people who are the same in terms of age and sex?”
But often, our real-world question is:
“If we give the vaccine to everyone, how much will it reduce risk at the population level?”
This calls for a marginal OR—an estimate of the Average Treatment Effect (ATE) across the population.
🧮 How to Perform Marginalisation in Stata
Start with your logistic model that includes covariates:
logistic outcome treat age sex
This model predicts each person’s probability of the outcome, given their treatment and covariates.
Then use the margins command:
margins treat, predict(pr)
This command:
- Simulates the outcome for everyone as if they were treated (treat = 1),
- Then simulates the outcome for everyone as if they were not treated (treat = 0),
- Then compares the average predicted probabilities across those two scenarios.
The difference (or ratio) between these predictions represents the Marginal Risk Difference or Marginal OR.
📊 Comparison Table: Conditional vs. Marginal OR
| Feature | Conditional OR ✅ | Marginal OR ✅ |
| Focused on specific strata (e.g., age = 60, sex = male) | ✅ Yes | ❌ No |
| Applies to the full population | ❌ No | ✅ Yes |
| Directly output from logistic model | ✅ Yes | ❌ No |
| Requires margins command | ❌ No | ✅ Yes |
🎓 Definition Recap
Marginalisation is:
“The process of averaging model-based predictions across all levels of covariates to estimate population-level treatment effects.”
This helps translate regression outputs into clinically and policy-relevant quantities—especially for interpreting treatment effects across a diverse population.