Forecasting monthly counts vs. rates for a population

[samp945]

Hello all,

I have count data (deaths and several other outcomes) for a large US state over a 10-year period. I am using Proc UCM to create plots showing actual vs. predicted count outcomes over this time and how the introduction of the pandemic in late 2019/early 2020 affected these various outcomes over the very short term (months or weeks) and the long-term.

I am trying to choose between forecasting counts  vs. rates. The examples I've come across for similar research use counts without mentioning how such forecasts would be affected by a growing population (i.e., certain count outcomes, such as vehicle collisions and crime, would be affected by a growing population).

It seems easy enough to use population data to create rates. The problem I see with this is population data are collected only once every 10 years (census). I can get state-level intercensal estimates for each year. But for a monthly time-series analysis, I need monthly population estimates. I can create these by linear interpolation, but the assumption of a linear population increase across yearly estimates is not a good one.

So it seems to me that forecasting population counts vs rates both involve known error. Is there a best practice for this sort of analysis? I welcome any thoughts on how to justify one approach vs. the other. Thanks for your consideration.