# Unadjusted rates vs. observed rates?

by Nw2this   Last Updated September 11, 2019 16:19 PM - source

In poisson and negative binomial rate models, should the observed rate be the same as the unadjusted rate (in model with only 1 variable)?

Should you report these unadjusted rates from a model with a single variable if there is over-dispersion? Or should these mini-models be held to the same standards as your larger multivariable model.

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#### Answers 1

They'll be the same.

Yes, overdispersion doesn't mean that the rate: $$\frac{\# \text{events} }{\# \text{person-time}}$$ is not a useful quantity.

Think about it practically, if you look at hospital admissions in a cohort that comprises healthy patients and, say, patients with hepatitis B, the hep B patients will be readmitted at a much higher rate. So there is dispersion in the count process.

Suppose the healthy folks are hospitalized once every 50 years whereas a Hep B patient is hospitalized twice every year. If 100,000 healthy patients are in my catchment and only 500 hep B patients. If I am a hospital administrator, it's useful to know these stratified rates and prevalence, but it doesn't change the fact that I expect 6,000 admits a year rather than 5,050.

AdamO
September 11, 2019 16:00 PM