Using subject-specific random intercept to account for repeated measures over time 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"?
 A: What you have described so far with the information you have provided seems appropriate to me -- you could use mixed models or the GEE approach as you've indicated, since it doesn't sounds like you need to make individual-level inferences (if you do, you shouldn't even consider learning GEE as you can't obtain subject-level estimates with this method).  You could add the year into the model as either a fixed or random effect. If the years were specifically selected and cannot be considered to be generalizable, put the variable for year into the model as a fixed effect.  Otherwise, consider it random.  You may need to explore interactions with the year variable to determine if there are any moderating or confounding effects and the need to include these terms in your model.
The coefficients can be interpreted as the percent change in the incident rate of your dependent variable for every unit increase in the independent/coefficient variable.  So for example, 1.07 on the year variable (assuming no interaction) would be interpreted as a 7% increase in in the incident rate of your dependent variable, given a one-year increase.  The interpretations for the the mixed model are generally the same as the fixed effects model.  See the following course notes for a more detailed discussion of coefficient interpretation.
Best of luck to you!
