What is Marginalisation in Clinical Statistics?

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.

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💡 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.

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🧮 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.

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📊 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

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🎓 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.