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I am reporting the results of an analysis where we tested the effect of various demographic predictors on the number of counselling sessions undertaken by participants during a clinical trial. I ran a Poisson regression with number of sessions as the outcome variable. To control for exposure I included an additional predictor, the log of the number of weeks each person was enrolled in the trial.

I have read e.g. here that including this offset variable effectively turns the count into a rate.

My questions is rather than including the offset variable as a predictor, why not simply convert the count outcome variable itself into a rate?

For example in my study I could just divide the number of counselling sessions by the number of weeks attended. Is there a good reason not to do this and instead use the offset variable?

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The principal reason is to be able to use a Poisson likelihood function. The same reason would apply with a negative binomial likelihood function, or any other count likelihood when using a generalized linear model with a log link function. Using a calculated rate directly as a response, you lose that opportunity. For details see When to use an offset in a Poisson regression?

For one, if the data really are generated by some Poisson process, presumably a Poisson likelihood is better, simply because it is the correct one! And, even if it is not strictly a Poisson process, a Poisson distribution (or some other count data distribution) is probably a better approximation.

Not strictly related to this (it is more related to the use of a log link function, which could also be used with a Gaussian likelihood): Counts is an extensive variable, see Goodness of fit and which model to choose linear regression or Poisson

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    $\begingroup$ Thank you @kjetl b halvorsen. Why is it so bad to lose the opportunity to use the Poisson likelihood function? Is it better for rates than a Gaussian? e.g. does the Poisson handle large amount of zero counts better than a Gaussian? $\endgroup$ – llewmills Mar 10 at 11:29

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