# Analyzing binomial distributed variables

I have the following situation. A subject comes to the clinic at day 1 and is evaluated using a 10 item checklist. The sum of those 10 items is the subjects score. A intervention is performed. The subject then comes back to the clinic at day 10 and is evaluated with the same 10 item checklist. Each of the questions on the checklist is Yes/No with probability p, so I know that the sum of the 10 Bernoulli(p) is Binomial(10,p). I perform this experiment on 30 people and my objective is to determine if there is any difference before and after intervention. My sample data table looks like:

id day score
1    1     3
2    1     6
3    1     1
4    1     2
5    1     0
1   10     5
2   10     2
3   10    10
4   10     7
5   10     4


A naive method that comes to mind is to do a paired t-test on the scores but I'm not so sure that comparing the means of Binomial rv's is valid in this case.

Does anyone have any other suggestions on how to analyze this data? One idea that comes to mind is to do a GEE with binomial family see here but I'm not sure how to implement that in R. My best guess would be:

geeglm(cbind(score,10-score)~factor(day), family=binomial(link="logit"),
id=id, corstr = "independence", std.err="san.se")


Is this a valid analysis or are their other ways as well?

Thanks