# Age Interactions in mixed models

We are using a mixed model to describe trends as subjects age. We have multiple measurements per subject of a continuous outcome. We also adjust for the age at entry into the study. It is of interest if early entry and long follow-up are associated with different outcomes than late entry and short follow-up (i.e. same current age, but entered study at different ages) and so we are including an interaction. So our model is of the form:

$y = current$ $age + baseline$ $age + current$ $age * baseline$ $age$

Are there any problems with estimation or prediction with a model of this form? I think that this is very similar to the standard age-period-cohort problem, but not sure if that means there are other considerations we need to have when modeling or interpretation.

• What about replacing the variable "current age" by the follow-up time (=current age minus baseline age)? This helps to prevent interpretation problems due to multicollinearity and it fits better to the original question. Let's say if the effect on mean response (higher = better) of "baseline age" is 1 per year and of "follow-up" 2 per year, then I don't even need an interaction term to see that late entry is bad. Commented Nov 18, 2013 at 20:15
• Yes, this was a consideration. However the outcome declines naturally with time/age, and so having a direct estimate of the effect of ones current age is of interest, e.g. does study population decline faster/slower than normal population. Additionally, the reasoning for the interaction with baseline age is that those that entered younger will decline faster as they age than those that entered older (or vice versa -- this is what we want to know). So without the interaction, the model forces all subjects to decline at the same rate over time, though we'd like to test if this is true. Commented Nov 20, 2013 at 14:22