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I often used Poisson regression models to estimate prevalence ratios. However, in these cases my data contained information on the whole population, including events (1) and non events (0). Unfortunately, In this new scenario I would only have information on events extrapolated from my population (and covariates for those with the event as well). I was wondering whether it is still correct to employ a Poisson regression model in this case. My dataset looks like this:

+--------+-----+-----+-------------+----------+
| events | sex | age | denominator | district |
+--------+-----+-----+-------------+----------+
|      1 |   1 |  60 |        1000 |        1 |
|      1 |   2 |  58 |        1000 |        1 |
|      1 |   1 |  48 |         840 |        2 |
|      1 |   2 |  50 |         840 |        2 |
|      1 |   2 |  60 |         700 |        3 |
|      1 |   2 |  62 |         700 |        3 |
|      1 |   1 |  60 |         700 |        3 |
+--------+-----+-----+-------------+----------+

In this case my main variable of interest would be the district as I would be interested in modelling prevalence ratios between districts adjusting for proportion of females and mean age. My offset would be the district size (denominator).

I am worried because I have always used this approach when I had data on the whole population (those with and without the event), therefore, I was wondering whether this is the best approach in this case.

Alternatively, I might average everything at district level, calculate the rates and fit a linear regression model to assess the association between district and calculated rates. However, I would lose power doing that.

Is it correct to use Poisson in this case? Alternatively, is there any other clever way to do so? I suspect Bayesian estimation might be an option if I move away from frequentist approaches but I only have basic knowledge of that.

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