Weber-Fechner law
When the Weber-Fechner equation is applied to the EMA-FDA data, there is
a highly significant association between the logarithm of treatment
effects and the likelihood that the regulators will not require further
testing in RCTs (Table 1). To illustrate the significance of this
finding, it is instructive to calculate differences in the change of
treatment effects (stimuli):
\begin{equation}
\text{logit}\left(p\right)=0.831\cdot TE_{10}+0.32\nonumber \\
\end{equation}which means that an increase of \(TE_{10}=\operatorname{}\text{OR}\)by 1 leads to an increase in the probability by\(\frac{e^{0.831}}{1+e^{0.831}}\approx 0.69\)
Consistent with Weber-Fechner law, we found that if\(\operatorname{}\text{OR}\) increases by one, the probability of not
requiring further RCTs increases by 69%, which, we contend, is very
large probability rarely observed in decision-making literature. Thus,
our analysis suggests that the difference between new treatments and
historical controls should be at least one logarithm of magnitude larger
to omit subsequent requests for RCTs. (Figure 1). Strictly speaking,
some would argue, evidentiary support in favor of this hypothesis is
moderately strong at p=0.007, but reaches the recently recommended
heuristic cut-off at p=0.005 24 when 5 observations of
treatment effects with empirically implausible large values
(OR>250) are removed from the analysis (not shown).