I am analysing a binary outcome from a cohort study, adjusting for
continuous and categorical covariates including two stratification
variables. Given the prospective nature of the study, I would prefer to
estimate relative risks, rather than using logistic regression to obtain
odds ratios, and hence have tried Poisson and binomial (log link) modeling.
I get very similar results with both, but both show underdispersion
(defined as deviance/df) and non-normally distributed deviance residuals.
My questions are
a) whether the Poisson model can be used for a binary outcome (I have seen
this done in the past) or whether binomial modeling is strictly more correct
b) whether evidence of underdispersion and non-normally distributed
deviance residuals is indicative of a poor fit in these two models, or
whether it is simply an artifact of the binary outcome.
Many thanks, Susanna.
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