How to deal with participants that don't last through a treatment?

Question

My study involves repeated measures to compare the effectiveness of two distinct drug formulations at reducing the volume of an abscess, measured at three time-points (one baseline and two follow-ups), with participants in 5 groups (two treatments, Two positive controls [or placebo] and one negative control).

In some individuals (in all groups studied, but mostly in control groups, especially in follow-ups), abscesses have been "ruptured" suddenly due to increasing volume and/or decreasing wall thickness. On the other hand, complete treatment occurs when the abscess volume reaches a conventional zero (and not necessarily "real zero").

The question is that for data analysis, for example by the ANCOVA-Change method, should the cases leading to the rupture be removed or kept? If these cases are to be kept in the study and categorization based on Outcome measures (due to concerns about reduced power of the analysis) should be avoided, what measures should be considered?

Answer 1

You somehow need to include the ruptures in your data.

One simple solution could be to have rupture, complete treatment, and unresolved as 3 separate categorical outcomes. Even simpler if you don't really care whether this represents outcomes at the first or second follow up and you don't need to take covariates into account--then standard contingency table analysis of final abscess status would provide your results.

If you do care about whether these categories exist at the two different follow-up visits or need to correct for covariates, then a multinomial (logistic) regression with those three outcomes could provide a solution. The follow-up time would be included as a predictor. The starting abscess volume and other relevant covariates could also be used as predictors with such a regression.

I've struggled with finding a good way to measure the rate of volume change, which I inferred to be what you would really like. A reduction to 0 volume by rupture is clearly not the same thing as reaching that place through treatment. I suppose you could restrict that analysis of volume-reduction rate to cases that didn't rupture, provided that you also provided information about rupture rates under each of the treatments.