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).