Let’s say we have an experiment where we want to apply some treatment to some group to test whether the treatment “works”. But the treatment is such that the act of applying the treatment to some people within the group and not others actually undermines the treatment; in other words, in order for the treatment to work “properly” / to “full effectiveness”, the treatment must be applied to the entire group. In the world of experimental design, what is this phenomenon called? It seems to me like it might be considered some kind of “interaction” or dependency effect? Is there an area of experimental design that deals with this sort of stuff? Is this a case where so-called “observational studies” or “observational experimental design” are more suitable than the so-called “controlled trial” / “randomised controlled trial” sort of experimental design?
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1$\begingroup$ I’d call it group effects. E.g.: exterminators are more effective when they can apply their treatment to every unit in a building. $\endgroup$– user225256Commented Feb 10 at 2:34
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1$\begingroup$ @MattF. As per Demetri Pananos's answer, it seems to be "interference" from the "non-interference assumption". From Design of Observational Studies, second edition, by Paul R. Rosenbaum: "The notation for treatment effects appears innocuous, but it actually entails a fairly strong assumption, called “no interference between units” by David Cox [12, §2.4], namely “that the observation on one unit should be unaffected by particular assignment of treatments to other units.”" [...] $\endgroup$– The PointerCommented Feb 10 at 3:47
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1$\begingroup$ [...] In our case, assignment of control to one unit diminishes the effectiveness of the (actual) treatment to those units that are assigned it. $\endgroup$– The PointerCommented Feb 10 at 3:51
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1$\begingroup$ For RCT's the natural units are often geographic units, e.g. everyone in a particular village is assigned either to treatment or to control, or all the patients at a particular primary care clinic, or all the students in a particular classroom, etc. Do you have natural clustering like this? $\endgroup$– num_39Commented Feb 11 at 12:00
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2$\begingroup$ Yes. For more on this, look at the literature on clustered RCT's. $\endgroup$– num_39Commented Feb 11 at 20:34
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A term you might be interested in is "Stable unit treatment value assumption (SUTVA)". The scenario you describe is a violation of SUTVA and hence makes causal inference much more difficult.
Roughly, SUTVA is the assumption that potential outcomes are independent of the treatment status of other participants. That is to say, whatever happens to me under treatment/control is independent of what group you are assigned to. From your description, this seems to be the case since the treatment "effectiveness" (and hence I would argue the potential outcomes of the participants) are effected by the size of the treatment group.
answered Feb 10 at 0:41
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1$\begingroup$ Ahh, yes. This seems to be related to the “non-interference assumption” and kind of the opposite of “spillover”? $\endgroup$ Commented Feb 10 at 1:52