I have an epidemiologic study on subjects with yearly repeated measures on a count variable as an outcome and various yearly measured predictors. The study population changes every year somewhat, so that some new subjects are introduced and some old subjects drop out. I'm interested in the effects of the predictors on the dependent variable, while taking into account the repeated measurements by subject. I'm not interested in any changes over time or other time effects.
What I have done so far is to have a (quasi)Poisson random effect model, treating the predictors as fixed effects and including a subject-specific random intercept to account for the repeated measurements. Is this approach correct?
Should I somehow add the measurement year to the model to account for periodic fluctuations in my dependent variable or predictors, or their correlation over time?
I'd rather use the random effect approach and not learn a new method such as GEE unless my current method is obviously incorrect.
A related question: it seems the distinction of population average and subject-specific estimates may be relevant to the interpretation of the estimates, but I'm not sure I understand the difference. Is it correct to interpret my coefficients from the random intercept model as "increase in the covariate for an individual increases their dependent variable by X"?