Calculating adjusted R(2) measures for Poisson regression models

In regression models not only the parameter estimates and significances of explanatory variables are of interest, but also the degree to which variation in the dependent variable can be explained by covariates. In recent publications, an R(2) measure based on deviance was recommended for Poisson regression models, one of the most frequently used modelling tools in epidemiological studies. However, when sample size is small relative to the number of covariates in the model, simple R(2) measures may be seriously inflated and may need to be adjusted according to the number of covariates in the model. We present a SAS-macro that calculates adjustments for the R(2) measures in Poisson regression models based on log-likelihood and on sums of squares. The proposed measures are applied to real data sets and their performance is discussed.