- Joined
- Apr 3, 2019
- Messages
- 4,269
- Reaction score
- 9,961
I agree with your disagreements. And we really aren't disagreeing in our soul, only on paper. (And no one mentions that alpha beta is a "2nd order polynomial" line-fit thing but you're exactly right.) Interestingly, adding third or fourth (and so on) order components does increase the R^2 of the fit (a topic for another day). All your other points are valid too.I disagree.
My understanding is that α/β is really only the ratio of the coefficients of a 2nd order polynomial used to "fit" outcomes (most classic example is fractional cell kill in vitro) relative to dose fractionation. In the clinical setting, you can take retrospective data and come up with outcomes vs dose fraction curves that are always going to be a little bit bendy, are almost always going to seem monotonic and the data is always going to be fuzzy. This means that fitting these outcomes with a 2nd order polynomial is fine and the added value of a 3rd order term is meaningless in the real world. So you can have an α/β for cell kill, or early clinical outcomes (diarrhea) or late clinical outcomes (bleeding, late cystitis). My confidence in the particulars of these clinical curves is very low.
This α/β is not a model (I guess I heard some handwaving regarding 1 vs 2 photon interactions back in the day) it's just a fit. And by definition it is a fit regarding a single outcome. Most of our clinical and pre-clinical data does not control very well for time course of treatment (not explicitly included in α/β calculations), and the various relative contributions of "the 4Rs" as you shrink treatment time or course from 20-10-5-3-1 treatments is not well defined to my understanding. So you can claim that "cell kill for prostate cancer" demonstrates an α/β less than any pertinent competing toxicity risk, but still believe that single fraction or 3 fraction treatment is not prudent and is not the sweet spot in terms of therapeutic ratio.
But just from a PURIST P.O.V. re: this 2nd order polynomial line fit (on a log linear graph), the mathematical point stands regardless whether one "believe(s) that single fraction or 3 fraction treatment is not prudent and is not the sweet spot in terms of therapeutic ratio." Even given that this fitting comes from data that's "fuzzy" (you're right about that too), the implication e.g.:
Now whether one "believes" this is up for debate. But if one believes 60/20 e.g. is going to give better prostate cancer control, and maybe no more or worse late effects than 81/45 e.g., the reasoning behind that can logically follow to the conclusion in this pictograph: both thoughts are based on the same (mathematical) logic. You could look at this and be seduced that 16 Gy would give better local control than 81/45 with less late effects than 81/45. The seduction is real.
Last edited: