Mixed-Effect Poisson Regression Model without count data

Question

I have gone in circles reading about this for days and still not quite understanding.

I have aggregated data at the state level and by year estimating breast cancer incidence rate per 100 k, mortality rate per 100 k, mortality-to-incidence ratio, and a number of aggregated socioeconomic predictors including number of hospitals, percent minority, and average income.

I would like to fit a mixed effect model where my outcome variable is the mortality-to-incidence ratio, which ranges from 0 to 1.

If my model meets poisson model assumptions, is this valid even though Im not using a count variable as my dependent?

Answer 1

If it were me I would fit a binomial glm with the response variable being the rate written with the cbind function. If you were to analyze the rates of breast cancers as well as the mortality rate for 100k, it would require that you have one column with number of breast cancers, then one column with number of non breast cancers. Both would then add up to 100k. The same for the mortality rate, you could express it as one column for the number of deaths, one column for the number of survivors. Then the model in R would look something like : glm~cbind(cancer,no_cancer)~number of hospitals + percent minority + average income, data=yourdata,family=binomial(“logit”) Or maybe you want to check for interactions, in which case you can replace the + by *.

Now in the case of the mortality to incidence ratio, I hope I picture it correctly : I imagine it being the number of death among the number of breast cancers. Then I suppose I would express it as one column being number of deaths, an other being number of survivors (number of breast cancers-number of deaths). Then I would build a similar glm : glm~cbind(deaths,survivors)~number of hospitals + percent minority + average income, data=yourdata,family=binomial(“logit”)