Binreg in Stata: Odds Ratios, Risk Ratios, and Why Modified Poisson Is Preferred

1. Introduction

Binary outcomes are common in clinical and epidemiological research. Examples include disease status (yes/no), mortality (dead/alive), or treatment response (success/failure). In Stata, several commands can be used to analyze binary outcomes, including logistic, binreg, and glm with different families and links.

Although these commands may appear similar, they estimate different effect measures, rely on different assumptions, and can behave very differently in practice. This article clarifies what binreg does, how it compares with alternative commands, and why researchers often choose other approaches instead.

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2. What Is binreg?

binreg fits generalized linear models (GLMs) using the binomial family and allows the user to choose different link functions corresponding to different effect measures:

Importantly:

binreg always uses the binomial family.Only the link function changes.

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3. binreg, or vs logistic

Mathematical equivalence

binreg y x1 x2, or
logistic y x1 x2

These two commands:

• Fit the same model
• Use the same likelihood
• Produce identical estimates and standard errors

Therefore:

binreg, or is simply an alternative interface to logistic regression.

Practical implication

Because logistic is:

• More widely recognized
• More standard in reporting
• Better supported in teaching materials

👉 Logistic is generally preferred over binreg, or.

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4. binreg, rr: Log-Binomial Regression

What it tries to do

binreg y x1 x2, rr

This fits a log-binomial model:

log ( P ( Y = 1 ∣ X ) ) = Xβ

and reports:

RR = exp(β)

This is attractive because risk ratios are intuitive and collapsible, unlike odds ratios.

Why binreg and rr often fail

The problem is not conceptual but mathematical.

• The log link impliesμ = exp(Xβ)
• But in a binomial model,0 ≤ μ ≤ 1

If the model attempts to estimate μ > 1, the binomial likelihood becomes invalid. As a result:

• The optimization hits a boundary
• The model may fail to converge
• Estimates may be unstable or not produced

This problem is well known and occurs frequently when:

• Outcomes are common
• Effects are strong
• Multiple covariates are included

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5. Why Researchers Use Modified Poisson Instead

The alternative approach

glm y x1 x2, family(poisson) link(log) vce(robust) eform

This is known as modified Poisson regression.

Why this works

• The log link still models the mean as:μ = exp(Xβ)
• Poisson models do not restrict μ to be ≤ 1
• Therefore, the model converges reliably

Although Poisson is traditionally used for count data:

• With a binary outcome, the mean still equals the risk
• The coefficient (\exp(\beta)) still estimates a risk ratio

The variance is misspecified, but this is corrected using robust (sandwich) standard errors.

The mean model is correct, and the inference is valid.

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6. binreg, rd: Risk Difference Models

binreg y x1 x2, rd

This uses the identity link:

P ( Y = 1 ∣ X ) = Xβ

Advantages:

• Estimates absolute risk differences
• Collapsible and easy to interpret

Limitations:

• Predicted probabilities can fall below 0 or above 1
• Requires careful checking of predictions
• Less stable in complex models

Thus, risk difference models are typically used only in simpler settings or when absolute effects are explicitly required.

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7. Summary Comparison

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8. Practical Guidance for Readers

• If you want odds ratios → use logistic
• If you want risk ratios:
  • Avoid binreg, rr in most real datasets
  • Use modified Poisson with robust SE
• If you want risk differences → consider binreg, rd, but check predictions carefully

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9. Key Take-Home Message

binreg is a flexible binomial regression framework, but its log-link (RR) implementation is often numerically unstable. For this reason, modified Poisson regression has become the preferred method for estimating risk ratios from binary outcomes in modern epidemiology.