## Threshold of % change? [General Sta­tis­tics]

Hi Ben,

» So you are essentially saying statistical relevance is not the right tool here. Agreed.

I was talking about statistical significance.
When it comes to a test, see the end of Section 1 in this post (EUFEPS workshop, Bonn, June 2013).

» Instead of relying on visual inspection & gut feeling (= common sense? ) …

Well, we are using visual inspection in other areas as well. Automatic algos for selecting time points in estimating $$\small{\hat\lambda_z}$$ (e.g., $$\small{R_{\textrm{adj,max}}^{2}}$$, $$\small{AIC_\textrm{min}}$$, $$\small{\text{TTT}}$$) quite often fail for ‘flat’ profiles (MR) or multiphasic profiles. I’m fine with selecting time points ‘manually’. Never had any problems with acceptance.

» … can we define pharmacological relevance?

That’s actually the idea behind assessing the slope. Either we are still in the saturation phase (slope >0) or reasonably close to true steady state (slope ≈0).

» Is there a way to define quantitative thresholds based on the PK (or even PD?) of the compound (i.e. concentration should not change by more than x%)?

But how could we do that? We design the study based on τ and t½. Hopefully we don’t use an average t½ – from the literature – but a worst case (i.e., a longer one).
$$C_\tau$$$$\small{ \begin{array}{crr} \hline \text{Dose} & \text{% of steady state} & \text{% Change} \\ \hline 1 & 50.00000 & - \\ 2 & 75.00000 & 50.000000 \\ 3 & 87.50000 & 16.666667 \\ 4 & 93.75000 & 7.142857 \\ 5 & 96.87500 & 3.333333 \\ 6 & 98.43750 & 1.612903 \\ 7 & 99.21875 & 0.793651 \\ \hline \end{array}}$$Looks nice on paper. However, I see a problem here (maybe I’m wrong). In the regression we assess the last three pre-dose concentrations, which – to some extent – takes the inter-occasion variability into account. Of course, we may fall into the trap mentioned previously.
When we set a threshold of $$\small{x\%}$$, we are essentially believing that the last two pre-dose concentrations are the true ones, right? Of course, that’s another trap.

Dif-tor heh smusma 🖖
Helmut Schütz

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