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Parameter estimation and goodness-of-fit in log binomial regression.

L Blizzard¹, D W Hosmer

¹Menzies Research Institute, University of Tasmania, Hobart, Australia. Leigh.Blizzard@utas.edu.au

Biometrical Journal. Biometrische Zeitschrift

|March 21, 2006

Summary

The log binomial regression model, used for risk estimation, frequently fails to converge or produces invalid probabilities. Alternative methods also show limitations, suggesting caution in its application.

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Area of Science:

Biostatistics
Epidemiology
Statistical Modeling

Background:

Logistic regression over-estimates risk for non-rare outcomes.
Log binomial regression is increasingly used for accurate risk estimation.
Performance and diagnostics of log binomial models are understudied.

Purpose of the Study:

Compare log binomial regression with alternative methods.
Evaluate model performance, goodness-of-fit, and diagnostics.
Provide guidance on appropriate use of risk estimation models.

Main Methods:

Extensive simulations to compare three statistical models.
Log binomial regression.
Logistic regression (Schouten et al., 1993).
Poisson regression (Zou, 2004; Carter et al., 2005).

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Main Results:

Log binomial regression showed high failure rates (up to 59%).
Alternative methods also produced invalid probabilities (up to 78%).
Coefficient and standard error estimates were similar across models.
Goodness-of-fit tests had modest power.

Conclusions:

Log binomial regression is not recommended for uncritical use due to performance issues.
Alternative methods also exhibit limitations in risk estimation.
Careful model selection and validation are crucial for reliable risk estimates.