If you don't use fancy words that the client has never heard before, how can you justify the huge consulting fee you charge?
Seriously, I always use the appropriate language and explain that it is similar to regression (or ANOVA depending on the context) but it better matches the correlated structure of the data set. I expect that this causes some short term confusion and consternation, but in the long run it puts them in a better position for future consultations and for reading the medical literature.
-------------------------------------------
Stephen Simon
Independent Statistical Consultant
P. Mean Consulting
-------------------------------------------