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Careful use of pseudo R ‐squared measures in epidemiological studies
Author(s) -
Heinzl Harald,
Waldhör Thomas,
Mittlböck Martina
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2168
Subject(s) - interpretability , covariate , poisson distribution , categorical variable , poisson regression , mathematics , statistics , event (particle physics) , bernoulli's principle , generalized linear model , econometrics , computer science , medicine , artificial intelligence , population , physics , environmental health , quantum mechanics , engineering , aerospace engineering
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, π ), are arbitrarily combined into binomially distributed ones, B( n , π ), which are then approximated by the Poisson model. Copyright © 2005 John Wiley & Sons, Ltd.