Conditional vs. Marginal Odds Ratios: Why Your Logistic Regression May Be Lying to You

👩‍⚕️ The Situation

You’re analyzing your study: Did Drug A reduce the risk of infection compared to Drug B?

You run a logistic regression, adjust for age, sex, and comorbidities, and find an odds ratio (OR) of 2.5.

You interpret this as:

“Patients on Drug A are 2.5 times more likely to get infected.”

But here’s the twist:

❗ That OR isn’t the effect in your population. It’s the effect after adjusting for everything. And it doesn’t equal the overall population effect.

🔄 Meet the Two ORs

Type	What it really means	How you get it
Conditional OR	Odds of outcome within covariate strata (e.g., same age, same sex)	Logistic regression (standard output)
Marginal OR	Odds of outcome averaged across the population	Requires special methods (like G-computation or IPTW)

🧠 Why They’re Not the Same

Logistic regression is “non-collapsible.”Even if there’s no confounding, the adjusted OR (conditional) is still different from the marginal one.

That’s like saying:

“Even if no one's cheating, your class average will still change when you adjust for who sat in the front row.”

📉 In simpler terms:

Conditional ORs are great for individual-level prediction.
Marginal ORs are needed for policy, public health, or "what if we changed the treatment for everyone?" questions.

🔬 Example

Suppose:

Risk of outcome in group A = 20%
Risk in group B = 10%
Risk Ratio (RR) = 2.0
Odds Ratio (OR) = 2.25

If you run logistic regression adjusting for a covariate, you might get:

Conditional OR = 3.0
But the Marginal OR (true population effect) is still 2.25

➡️ Your model overstates the effect.

✅ What Should You Do?

If you need population-level impact:

Use methods that recover marginal effects:

G-computation (simulate outcomes for all with and without exposure)
IPTW (reweight the sample like a pseudo-RCT)
Log-binomial or Poisson (with robust SEs) if estimating risk ratios instead

If you just want risk prediction for individuals:

Standard logistic regression is fine. But don’t interpret the OR as a population effect.

💡 TL;DR

Conditional OR ≠ Marginal OR — even without confounding!
Logistic regression gives conditional results.
If you're interested in what would happen to the population, you need extra steps.

📎 Bonus: Cheat Sheet

Model	Target Effect	Collapsible?	OK for Marginal?
Logistic	Conditional OR	❌ No	❌ Needs correction
Log-binomial	Risk Ratio	✅ Yes	✅ Yes
Poisson (robust)	Risk Ratio (approx)	✅ Yes	✅ Yes
Linear Probability	Risk Difference	✅ Yes	✅ Yes

👋 Got data and want to try this out? I can walk you through how to code G-computation or compare OR vs RR on your own dataset.

Just say the word.

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