I am trying to model incidence rates (number of malaria cases per 1000 people per month) over time. I only have the data in the form of rates per 1000 people per month, i.e. I do not know the total population size each month. i.e. in January, there were 3.3 cases per 1000 individuals, in February, there were 5.6 cases per 1000 individuals etc. etc.
What I am unsure about is whether I can use a Poisson regression model to model the rates i.e 5.6 and 3.3, without using an offset, or weighted Poisson regression? I haven't done either of these things as the population would always be 1000 so I don't think using an offset or a weighted Poisson regression approach would achieve anything.
I am just not sure whether my approach is valid when the "count data" aren't the actual number of events, and indeed aren't count data as they are not integers.