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I am working on formulating a regression problem where my dependent variable is the number of heart disease cases (count data) in a population. I am looking to do an ecological poisson-based regression.

I have crude rate per 100,000 population for smoking, where:

crude rate = (total number of smokers / total number of persons in the population) x 100,000

I would like to know if it is possible to directly use ' crude rates' as an independent, explanatory variable in my regression problem. Generally speaking, I know in regression problems 'percentages' can be used, but not sure about 'rates'. Any insights are welcome.

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According to this source, "Rates are a special type of ratio that incorporate the dimension of time into the denominator".

"For example: A mortality rate is the proportion of deaths occurring over a span of time in a population. "

"Strictly speaking, these are all proportions, but incidence rates or incidence density is a measurement of the frequency of a health outcome that is more like a true rate. ...Similar to computation of an average speed for an automobile, an incidence rate is computed by dividing the total number of health-related events that occurred by the total exposure time at risk for the group."

Below is an illustration of incidence rate taken from the above source. Here, the average rate at which the outcome occurred was 3/ 100 person-years of observed exposure time. That average rate can be expressed as a proportion.

Taking that into account, I fail to see why you cannot use a rate as covariate in a regression model, provided that the covariate is a meaningful predictor of your outcome, and that other issues such as potential attrition bias and endogeneity have been addressed.

For the case where the rate or proportion is the outcome variable, then I would recommend beta-regression.

So, my answer is yes.

enter image description here

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Yes, but you might want to apply feature scaling to the crude rate (other features as well) before using it to train your Poisson regression model.

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    $\begingroup$ Can you please explain why you think feature scaling is important? Without explanation this is more of a comment. $\endgroup$ – kjetil b halvorsen Nov 10 '18 at 13:36

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