What Is Collapsibility in Clinical Statistics?
- Mayta
- Jun 23
- 2 min read
Collapsibility is a property of effect measures that determines whether the measure changes when you (statistically) adjust or don’t adjust for covariates, even in the absence of confounding.
✅ Collapsible Measure
Example: Risk Difference (RD) or Mean Difference (MD)
Property:
If no confounding, the crude (unadjusted) effect estimate equals the adjusted effect estimate.
That is:
Why? Because RD and MD are linear, and averaging over subgroups does not distort the overall effect.
❌ Non-Collapsible Measure
Example: Odds Ratio (OR) or Hazard Ratio (HR)
Property:
Even if there’s no confounding, adjusting for covariates changes the effect estimate.
That is:
Why? These are non-linear transformations of the data (log-odds, log-hazard) and inherently distort when marginalizing.
🧪 Illustrative Stata Examples
Crude vs Adjusted (Collapsible case)
regress BDI6mo treat
regress BDI6mo treat BDI0 age sex
If treat is your intervention and BDI6mo your outcome (e.g., depression score),
The β for treat changes little: ➡️ Mean Difference is collapsible
Crude vs Adjusted (Non-Collapsible case)
logistic outcome treat
logistic outcome treat BDI0 age sex
The ORs differ: ➡️ Odds Ratio is non-collapsible, even if covariates aren't confounders.
🔁 What Is Marginalisation?
Marginalisation is the process of recovering population-average (marginal) effects from conditional (adjusted) regression models.
In other words:
“Given I fitted a logistic model adjusting for covariates, what is the overall effect of treat averaged over the covariate distribution?”
📦 In Stata:
logistic outcome treat age sex
margins r.treat, predict(pr) // Predicted risk
margins r.treat, predict(or) // Marginal OR
marginsplot // Visualize marginal effects
This tells you: “On average, what is the risk/OR if everyone received the treatment vs. control?”
🔑 Summary Table
Concept | Meaning |
Collapsible | Effect estimate doesn't change with covariate adjustment (e.g., RD) |
Non-collapsible | Effect changes due to mathematical form, not confounding (e.g., OR) |
Marginalisation | Transforming model-based (conditional) effects into population averages |
🧠 Secret Insight from CECS Logic
Always distinguish change due to bias (confounding) vs change due to non-collapsibility.
Marginal effects are policy-relevant; conditional effects are decision-support relevant.
Collapsibility is mathematical. Confounding is causal. Don’t confuse them.
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