Investigate change in mean levels of risk within a service- alternative to unbalanced repeated measures ANOVA

Not sure if this is as complicated as it's ended up in my head, here goes.

I have a series of measurements which measure how risk-prone psychiatric patients are (hereafter referred to as HCR and it's an interval, normally distributed outcome). These measurements come from five different locations within the hospital and are measured at different times on a varying number of occasions (I have the exact date of each measurement for each patient).

It's very simple to model the change in this variable for patients using my old friend lme4- the model looks like this:

HCRmodel=lmer(HCR~Day+Location+(1|patient), data=mydata)


[in English, the HCR score depends on the day (counting from 1 for each patient) plus an effect for where they are in the hospital and these measurements are clustered in patients]

So far, so good. The problem I'm having is that I would also like to model changes in locations over time. The theory is that each location may have changed over the 5 years of data, say, service A is dealing with riskier and riskier patients, service B with less and less risky, something like that.

Clearly this kind of analysis lends itself to ANOVA, except that the measures are repeated and it's completely unbalanced.

I can't even post where I've got to so far because I haven't really got anywhere- I'm thinking along the lines of calculating the mean levels of risk in each service for each day over the whole study and putting this into a balanced ANOVA design. But I'm a little unsure whether I'd just be munging the data to appear balanced, or whether it really would be balanced.