Repeated measures ANOVA

Question

I have to apologise about my lack of experience but hopefully someone can clarify things for me.

I am interested in looking at change in psychosocial functioning over time and compare it between those with borderline personality disorder, another personality disorder and no personality disorder. My main focus is psychosocial functioning (PF) but I also want to show that full recovery (remission of symptoms plus improvement in functioning) is harder to attain than remission of symptoms alone.

So I was going to do a repeated measures ANOVA. My dataset is composed of the following variables:

• PF is measured at 4 time points (PF1, PF2, PF3 and P4);
• Symptoms are measured at 4 time points (S1, S2, S3, S4);
• I can then calculate another outcome variable at time 4 that is recovery (yes or no);
• And another outcome variable for remission (yes or no).

There are three groups: BPD, OPD and NPD.

To test my first hypothesis I was planning on doing repeated measures ANOVA to see if change in PF was less for the BPD group than the other groups. This seems simple enough.

However, it is my second aim as to where I get lost. I get stuck on how to test whether rates of recovery are less than rates of remission and compare the groups on this. I hypothesize that the BPD group will find it harder to achieve recovery than remission (i.e. the rates will be significantly different), while the NPD group will have similar recovery and remission rates, and the OPD will be somewhere in between.

I have no idea how to achieve this without using a mixed models approach. Unfortunately I cannot go down that route because of reasons that are out of my control (and in my supervisors control) but none the less I cannot. I have to keep the analysis as simple as I can.

Answer 1

I agree that the repeated measures ANOVA is appropriate for the first hypothesis. For the second hypothesis, I think it might be appropriate to view the outcomes as having binomial distributions, and that you are testing whether one proportion is greater than another.

In one case you want to show equivalence. So there you would specify a small delta and show that the difference in the proportions is less than delta. This however would not address the ordering of the proportions by group. So to deal with that another approach would be to fit a logistic regression or a loglinear model to show significant differences in proportion as a function of group (BPD vs OPD and NPG).

I would think that regarding the ordering you could set this up as a 2x3 contingency table with the 2 outcomes (remission vs no remission) vs 3 groups BPD, OPD and NPD). You can then apply the cochran-Armitage trend test. I would pick the sample size to be at least large enough to have good power to show that the difference between the "equivalent" groups is less than the prespecified delta that you choose.

I hope that the contingency table approach is simple enough to be acceptable to your boss. I can't think of anything simpler that would achieve your objectives.