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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!

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Purely in terms of describing whether there is a change that correlates with the time of treatment initiation your ideas (such as a test on the change from before to after or paired t-test) may be okay. However, the issue with any attempts at interpreting it more in terms of this having something to do with the start of treatment (and of course especially going anywhere near claiming that this improvement may be due to treatment), these approaches are unsuitable.

Amongst other problems there is likely to be regression to the mean, meaning that having an extreme value is likely to be followed by less extreme values (even if there is a general trend towards values moving in a certain direction, the fluctuation of values is in many real applications wider than the effect of the time-trend). At the same time I would guess that more extreme values are more likely to prompt a change in treatment so that one will typically tend to see a change in values correlating with initiation treatment in this type of situation - whether the treatment has any effect or not.

If you are aiming towards saying something about an effect of treatment, then I fear there is no really simple approach that will do and e.g. structural equation models would be one approach to read-up on.

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  • $\begingroup$ We are primarily trying to be descriptive about the means before and after and certainly have no intention of making causal statements of treatment on the score being higher or lower. The score on this assessment is unknown to everyone involved in decision making and has absolutely no impact on the choice of treatment (thought the two may be correlated). Only the research assistant and myself have seen the scores. WIth this in mind, it sounds like it may be okay to use a paired t-test with the participants' averages, but I'll look into the structural equation models as well. $\endgroup$ – Frederick1214 Feb 10 '16 at 21:02

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