# Identifying below-average units in a Poisson model

I’m modelling tuberculosis (TB) case rates at the neighborhood level and trying to identify risk factors that are associated with higher rates. I would like to identify communities with below average case rates given their risk factor profile with the idea that these would be the best places for new case-finding. It’s a bit circular I realize to use the same units I’m identifying risk factors with to then identify areas with expected higher rates, but my thinking is that I could identify the communities which are at the lower end of the distribution for each risk factor.

My plan then would be to construct a Poisson model with significant risk factors, plug in each neighborhood and calculate the ‘expected rate’. Then calculate the difference by subtracting ‘observed’ from ‘expected’ rates, and then identify the communities with the highest difference.

Is this approach legitimate? Or is this using the model in a way it isn’t meant to be used?

• @Andre: Tuberculosis? Aug 26, 2013 at 15:19
• @Tom: I've not been able to figure out if your overall proposal is valid -- it seems like it is, but I can't prove or disprove it -- but when you say "rate", you do mean something like "3 per thousand per month" or something like that? Obviously different neighborhoods could have different populations, which would result in different rates per time period if you didn't also account for population. Aug 26, 2013 at 15:31
• If I understood you correctly, you want to look at the “residuals” of the model. Until someone provides an answer, this term might help you find some relevant information.
– Gala
Aug 26, 2013 at 15:38
• @AndreSilva, sorry yes tuberculosis (shows my health-centric view!). I'll change that in my question.
– Tom
Aug 28, 2013 at 0:03
• @Wayne: Yes, I'm comparing proportional rates (e.g. tuberculosis cases per 100 000 population per year).
– Tom
Aug 28, 2013 at 0:04