You’re right. There is no direct safety margin factor in the formula. I thought there was one based on memory, but there wasn’t. However, the safety margin is still in the formula in a less obvious way. I know it doesn’t look like it, but a safety margin is actually hidden in the formula.
Yes, that’s the formula the FDA uses to get their scaling factors. This formula is somewhat misleading in that it makes it look like there is no safety factor. But fact is, the use of the exponent 0.33 in the equation, is the safety margin. The more correct exponent is actually 0.25. The 0.33 exponent is derived from the exponent for body surface area of 0.67 while the 0.25 is derived from the exponent for body surface area of 0.75. The latter is more accurate when scaling doses between humans and other animals. The former however is used, despite being less accurate, because it leads to estimations of lower doses for humans, which is safer.
Here is a quote from a study (To scale or not to scale: the principles of dose extrapolation - PubMed) on this:
" The FDA approach uses the exponent for body surface area, 0.67, to scale doses between species. This practice was traditionally rationalized as a means of accounting for differences in metabolic rate. The link between body surface area and metabolic rate, as discussed above, is the evolutionary adaptation of animals to their size, so body surface area is an indirect and imperfect correlate of metabolic rate. There has been debate in the literature about whether the exponent 0.75 would be more appropriate to account for metabolic rate/physiological time (0.75 is the exponent used in veterinary practice). Indeed, better scaling of doses has been demonstrated with the use of the 0.75 exponent (Rennen et al., 2001). On a conceptual level it is more logical to use the exponent that directly accounts for differences in physiological time, rather than an imperfect correlate of metabolic rate, and the proposed fractal origin of the scaling relationship also supports 0.75 as the proper exponent to use (West and Brown, 2005). The justification for using 0.67 is safety related; it provides a more conservative dose estimate."