# 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"?

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!

• I know the interpretation of the coefficients in the ordinary Poisson regression case. Some sources said that the random effect model and GEE answer subtly different scientific questions, and one should choose between these methods based on the scientific question. As I don't understand the difference, I wanted to make sure I'm doing correct conclusions. So in this case it should be OK to interpret it as I would an ordinary Poisson regression?
– Epi
Mar 19, 2015 at 21:36
• Yes, you are correct. There are subtle differences in GEE, but using the mixed model approach, your conclusions would be essentially the same as if you were performing regular old Poisson regression. Mar 19, 2015 at 21:59
• You may want to add a smooth function of year in addition to the year random effect; this won't improve the overall predictive capability much, but will decompose the yearly variation into trend + variation (and might improve the underlying Normality of the distribution of conditional modes by year) Mar 19, 2015 at 22:05
• The important thing to note, is that the interpretation is that the increase (or decrease) in your dependent variable is conditional on a particular subject's response (i.e. holding all other variables constant, INCLUDING, the random effects). Mar 19, 2015 at 22:06
• Ok, that makes all clear. Thank you very much StatsStudent and Ben!
– Epi
Mar 20, 2015 at 13:27