An Extension of Beta Regression to Handle Scores at Boundaries

Over the course of the last decade, a variety of methods have been proposed for fitting pharmacometric models to outcomes with constrained pharmacodynamic scales. One approach is to model the residual distribution as a Beta distribution (methods that employ this strategy are referred to broadly as "Beta regression" methods.) There are several reasons why one might choose to NOT use Beta regression in pharmacometrics: 

1. It is not clear how to handle the technical implementation in NONMEM. 
2. The Beta distribution doesn't accommodate scenarios when a substantial portion of the data is exactly at the lower (or upper) boundary value. 
3. Reasons related to the realism of the model (e.g. real observable scores are discretized, perhaps to the point where using a continuous distribution is not appropriate) or to statistical operating characteristics ("My simulation study shows that I can better estimate the effect of exposure when I use method x instead of using Beta regression".)

The attached slides are meant to illustrate that reasons 1 and 2 are not good reasons to avoid Beta regression. As these slides show, technical implementation is not that difficult, and values exactly at the boundary can be accommodated by using an "augmented" Beta distribution. 

OK, but what about reason 3? Why do you use or not use Beta regression when dealing with constrained scales? What alternative methods (if any) do you prefer, and why? Let us know your thoughts.

Download the slides here (PDF): https://www.metrumrg.com/wp-content/uploads/2021/06/BetaRegression-MetrumRG-Rogers-French.pdf