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I am trying to find out how to correctly interpret the coefficients for a Poisson regression. My main outcome of interest is the number of antibiotics prescribed (count) or the rate of antibiotics prescribed (number of antibiotics prescribed divided by the total number of prescriptions in one calendar year). My main research question is looking at whether a practice's centrality measure is associated antibiotics prescribing. Covariates in my model include a GP dummy, Charlson comorbidity score. I have used the count as my outcome variable with the total number of prescriptions as an offset, and a quasi-Poisson specification to account for the overdispersion. My regression is as follows:

log(Number of of antibiotics prescribed) =  β0+ β1×centrality
       measure+ β2×GP(dummy)+ β3×Charlsonscore + 
       log⁡(# of total medications prescribed) 

Right now, I'm struggling to interpret the coefficients of my model. Would 1 unit increase in centrality measure equate to e^β1 in number of antibiotics prescribed?

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Interpretation of coefficients in a Poisson rate regression fitted with quasi-likelihood is identical with interpretation when using maximum likelihood. The only thing that changes is the standard errors, the estimated coefficients are the same.

For interpretation of the coefficients, tat are answered at

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