A curious design - What is the type / name of this rare design?

#1
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 design, 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 the groups): In each person, one side of the mouth is assigned to the 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. Note that each group has two sides of the mouth; so each group is under 2 different treatments.

Like this:

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 design?
 
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Dason

Ambassador to the humans
#2
I don't see why it wouldn't also be called the same thing. We don't typically change the name when the only difference is that there are multiple treatments.
 
#3
Thanks Dason. You know, in the conventional split-mouth randomized clinical trial, there is only this comparison between the (perfectly matched) experimental versus control groups. But in this special scenario, there is also the comparison between effects of the treatments A, B, and C (each being normalized/adjusted with its control treatment). I want to account for this second kind of comparison too, in the title.

Until now, I have called it "A combination of 3 split-mouth randomized clinical trials".
 

Dason

Ambassador to the humans
#4
Actually now that I think about it what I said would more accurately apply if all of the treatments were applied in the same mouth. Let me think about it a bit.
 

hlsmith

Less is more. Stay pure. Stay poor.
#7
If you are conducting the studies, it would just be interesting. But if you have secondary data, it is a way to compare treatments that have not been directly compared but have been compared to a comparable control.

I would simulate some data, and play around with if they is a nice clever way to do post hoc comparisons!

P.S., good to see you around!!!
 
#8
Thanks :) Glad to be here too!!! :)

Yes we have conducted it. And I want to decide on the title of the article, hence my struggle with the type of the randomized clinical trial.

Treatments can be compared with each other (as between-subject factors) in a mixed regression/repeated-measures ANOVA framework, accounting for the repeated-measurements between the treatment and control sides of the mouth.

Also, I have subtracted the outcome on the control side from the outcome on the experimental side, as the "delta" outcome, showing the effect of each experiment compared to control. And then simple one-way ANOVAs can be used for comparing these delta values among the three intervention groups.

Post hoc comparisons were simple too.

The only difficulty is the title of the article with the type of the RCT!
 
#9
In my understanding, what you call a split mouth clinical trial is in statistics usually called a split plot design. The sub plot is each mouth and the main plot are the individuals. Of course the sub plots estimated effects will be quite precise and the main plot effects will not be so precise, since they vary between individuals (and I take it for granted that the individuals can be quite different).

So the testing of the effects between main effect treatment A versus main effects treatment B will not be so precise.

So I would call this design a "split plot design" or a "mixed model design".
 
#10
Thanks Greta, nice suggestions.

My thoughts: The conventional split mouth (or split plot) design is already a mixed model design.

Our study has three of these mixed models together. Then maybe, it might be something like a hierarchical mixed model design, right?
 
#11
My thoughts: The conventional split mouth (or split plot) design is already a mixed model design.
yes.

Our study has three of these mixed models together. Then maybe, it might be something like a hierarchical mixed model design, right?
Well yes. A popular model can have many names. A mixed model can also be called a multilevel model or a hierarchical model. But since (I believe that it was @Jake that pointed out) that a mixed model can have crossed terms, then it will not be a multilevel model. So I think that the expression "mixed model" is a better and more general term.

I would call your model a split plot model or a mixed model.

But as you say, if you just take the difference: treatment X minus the control, you will get a one way anova.

If you are mostly interested in A vs control, B vs control etc the design seems good.

But if you are mainly interested in in comparing: A vs B, A vs C and B vs C, then people might ask: "Why didn't you run a split mouth wit A on one side and B on the other side etc?"
 
#12
If you are mostly interested in A vs control, B vs control etc the design seems good."
I am interested in both the within-subject difference between the Intervention (being A or B or C combined) versus the Control (being X), and at the same time the between-subject differences among the three levels of the Intervention (A versus B versus C).

But if you are mainly interested in in comparing: A vs B, A vs C and B vs C, then people might ask: "Why didn't you run a split mouth wit A on one side and B on the other side etc?
There are some important reasons to put the Intervention levels (the experimental treatments A, B, or C) as a between-subject factor, rather than a within-subject factor:

1. Unlike a split-plot design that can have more than 2 levels of within-subject factors (for example, a plot can be split into 3 or 7 subplots), a split-mouth design can only have 2 sides of the mouth (only 2 subplots per plot). So any within-subject factors in a split-mouth design can only have 2 levels. My current Intervention factor has 3 levels, or assuming the control treatment X as another intervention, I should say it has 4 levels.

It is impossible to put my current Intervention factor as a within-subject repeated-measures factor, and to split the mouth into 3 or 4 subplots to compare the interventions A with B with C (also with the control X). Therefore, the only way to be able to compare these 3 treatments seems to be to put them as a between-subject factor.

2. If we had 2 experimental treatments A and B, technically we could use one side of the mouth for A and the other side for B (treating the Intervention factor as a within-subject factor). This is quite possible with two treatments; and many studies do so.

But even in that case, we would have missed the opportunity to know if effects of the interventions A or B are any larger and better than a placebo / control treatment X. Maybe the effects of A or B or both of them be no more better than placebo.

In such a scenario, we would be forced to include the control treatment X in a new group of patients, again introducing some "between-factor-ness" to the design. I haven't seen any such a design with placebo being set to a whole new group. They usually put placebo in the same mouth, or if they want to compare A with B in the same mouth, they remove the placebo altogether.

And remember that this whole was possible only with 2 interventions A and B. With 3 intervention levels A and B and C (plus an extra intervention Placebo X), the best way seems to recruit 3 groups of patients the way we did it.

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A question to ponder shortly (maybe I should start a new thread for it):

What if we hypothetically recruited only 2 groups of patients (giving us a total of 4 sides of mouths). We could hypothetically randomize the 4 treatments A, B, C, and X into the 4 sides of the mouths. Such a messy design. But still, it would be possible. Some comparisons between say A and B would be within-subject (when A and B happened to randomly land in the same mouth), and some other comparisons between A and B would be between-subject (when A and B where in two different mouths).

The same would happen for other pairs of intervention levels (A - C, A - X, B - C, B - X, C - X).

What do you think of such a messy but possible design?
 
#13
And Greta, give it some more thought. I still think when we have 3 parallel arms of split-mouth randomized trials together, we can still name it a hierarchical split-mouth randomized clinical trial. Right?
 
#14
we can still name it a hierarchical split-mouth randomized clinical trial. Right?
You can use the expression you prefer. I don't think the nomenclature is so fixed.

But I would call it a split plot.

About using: A vs B, A vs C, A vs X, B vs C, B vs X, C vs X, I think it is possible. Maybe it would be similar to a balanced incomplete block design?