I have a research design with three treatment groups (10, 20, and 30 exposures to a certain phenomenon) plus one control group (no exposure to the phenomenon). In order to measure the preferences of the members of each group and compare them for the different treatments, I plan to conduct a CBC HB analysis. I know that HB assumes one underlying population-wide distribution and only "adjusts" this distribution to get individual-level estimates. A clean study design would therefore include three CBCs (four including the control group), that look alike but are estimated separately. This in turn requires a high number of respondents because I have to run multiple analyses.
My problem is that it will get very hard to get enough respondents for the specific matter that I am interested in. My idea was to conduct only one analysis including all four groups at once, save 75% of respondents and enter the number of exposures to the phenomenon (my treatment groups) as a metric covariate. As far as I know, this will produce estimates that do not come from one underlying distribution but from several, which would be pretty much the same as having different treatment groups. Is this an acceptable workaround or is there a flaw in this argumentation?
Thanks a lot!