Hello!
I’ve recently been examining the statistical methods used in Morton et al.’s (2018) meta-analysis on protein supplementation and resistance training adaptations, particularly the segmented regression analysis that estimated a breakpoint around 1.6 g/kg/day:
I had a research colleague who suggested - the breakpoint analysis from this 2018 meta was somewhat “silly” on a conceptual level, at least in the way it’s been interpreted (beyond the basic fact that it wasn’t significant to begin with).
They performed a bisegmental regression with the slope of the second segment fixed at O, which essentially forces the conclusion they were trying to reach - it’s just asking whether a line with a slope of 0 past a certain point fits the data better than a line with a single linear slope. The answer to that question will always be “yes” for any relationship where the slope isn’t either linear or increasing over time. In other words, if the “true” relationship between protein intake and hypertrophy is, for instance, logarithmic, or a power law relationship with a scaling exponent of <1 (two common types of relationships that continually increase, but do so at increasingly slower rates), a bisegmental regression with a slope of 0 for the second segment will be capable of explaining more of the variance than a simple linear relationship (assuming the x-axis is bounded, which will always will be for this type of research).
However, that doesn’t mean there’s a “true” breakpoint - it just means that assuming there is a breakpoint allows you to explain more of the variance than assuming the relationship is strictly linear.
Basically, getting a better fit with bisegmental regression (with a fixed slope of 0 for your second segment) doesn’t actually tell you there’s a ceiling. It just tells you the scaling factor for your trend is sublinear (i.e., it tells you the slope decreases over time, but it doesn’t necessarily imply that the actual slope reaches O at the “breakpoint.” In fact, it doesn’t necessarily imply that the slope ever actually reaches 0).
I wanted to know if this criticism statistically justified?Specifically, does fixing the second slope at zero limit our ability to distinguish a genuine plateau from a continuously increasing relationship with diminishing returns?
The researcher also argued that a segmented regression with a flat second segment will always fit a diminishing-returns relationship better than a simple linear regression, assuming the predictor is bounded. Is this necessarily true?
I’m particularly interested in whether the estimated breakpoint can be interpreted as evidence of a physiological ceiling or whether it should be understood as a parameter estimated under a specific model assumption.
Thank you in advance for your time,
Juan. S