There is this split-mouth randomized clinical trial, in which one side of the mouth receives a particular treatment, and the other side receives another treatment (usually used as the control treatment); (we do this after randomization of the left/right sides of the mouth to treatments A and X [most likely X is a control treatment]).
This is a very good type of randomized clinical trial, because the two sides of the mouth are almost perfectly matched with each other in terms of almost every variable.
Now imagine that we combine three of these split-mouth clinical trials into one single study: We have three groups of subjects (randomly assigned to each group): In each person, one side of the mouth is assigned to the shared control treatment, and the other side is assigned to the experimental treatment. But we have 3 different experimental treatments in the three groups.
All of the three intervention groups have the same control treatment; but each of the 3 groups has a different experimental treatment.
Group 1: Side 1: Experimental treatment A -------- Side 2: Control treatment X Group 2: Side 1: Experimental treatment B -------- Side 2: Control treatment X Group 3: Side 1: Experimental treatment C -------- Side 2: Control treatment X
What will be the name of this strange and rare type of randomized clinical trial?
And by the way, subjects are randomly assigned to the groups 1, 2, and 3.