My data consists of people who chose either no treatment or treatment and were given a specific assessment at time 0, 1, 2, 3, 4, 5,... . Participants may miss an assessment but will still be followed and given future assessments. Those who chose no treatment may elect or be referred, at any time, to receive the treatment. At that point they will become part of the treatment group and continue to receive the assessment.
We would like to perform a subgroup analysis of only those participants who crossed over from no treatment to treatment. We want to test whether the average assessment score of participants is higher after crossing over to treatment.
Ultimately, I'd like to find the simplest solution to answer our question. My thoughts so far have been to find the individual participants' averages within no treatment and treatment groups and use a paired t-test. This would obviously lead to a loss of information about scores over time within groups, but that is not really something that we are interested in assessing. Another option might be GEE to account for the correlation between observations, but is that really the simplest option?
Thanks in advance for any discussion to lead me in the right direction!