Careful use of pseudo R-squared measures in epidemiological studies

Many epidemiological research problems deal with large numbers of exposed subjects of whom only a small number actually suffers the adverse event of interest. Such rare events data can be analysed by employing an approximate Poisson model. The objective of this study is to challenge the interpretability of the corresponding Poisson pseudo R-squared measure. It will lack sensible interpretation whenever the approximate Poisson outcome is generated by counting the number of events within covariate patterns formed by cross-tabulating categorical covariates. The failure is caused by the immanent arbitrariness in the definition of the covariate patterns, that is, independent Bernoulli events, B(1,pi), are arbitrarily combined into binomially distributed ones, B(n,pi), which are then approximated by the Poisson model.