Calculating adjusted R(2) measures for Poisson regression models

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Regression models assess explanatory variable significance and variance explained.
• R-squared measures, particularly deviance-based R-squared, are used for Poisson regression.
• Standard R-squared can be inflated in Poisson regression with small sample sizes relative to covariates.

Purpose of the Study:

• To address the inflation of R-squared measures in Poisson regression models.
• To present a SAS macro for calculating adjusted R-squared measures.
• To evaluate the performance of adjusted R-squared measures using real data.

Main Methods:

• Development of a SAS macro for adjusted R-squared calculation.
• The macro computes adjustments based on log-likelihood and sums of squares.
• Application and discussion of proposed measures on real epidemiological datasets.

Main Results:

• A SAS macro is presented for calculating adjusted R-squared in Poisson regression.
• The macro provides adjustments for R-squared measures to account for model complexity.
• Performance of the adjusted measures is discussed in the context of real data.

Conclusions:

• Adjusted R-squared measures are crucial for accurate variance explanation in Poisson regression.
• The proposed SAS macro offers a practical solution for addressing R-squared inflation.
• These adjusted measures improve the reliability of model evaluation in epidemiological studies.