Bioequivalence and Bioavailability Forum

Dear Detlew!

❝ In this post I had claimed "I never have seen deficiency questions concerning the fit of the terminal phase of concentration time courses in my ~30 years career. Even if the 'fit' was done with only 2 points".

I remember this post very well. So far I received only one request myself (by the sponsor, not an agency) why I have selected specific time points and not others. I answered by “visual inspection of the fit” (aka eye-ball PK) as recommended in the literature. BTW, I don’t know a single reference suggesting maximum R²_adj or a statement about exclusion.

❝ Say never never.

❝ Quite recently I got: … The applicant should justify the calculation of the terminal rate constant for patient #xxx, reference/r.1, patient #yyy, test/r.2 … […].

❝ The questioned cases had in common that the last measured concentration was increasing compared to the preceding ones and doesn't fit into the linear part for the log-linear regression. To not grossly overestimate the terminal half-life in such situations it is my standard operation to act according to Helmut's first option above.

Oh no! What will you answer? Maybe this post helps. Seems that (some) regulators are not aware about the consequences of (acceptable!) limitations of analytical methods (20% inaccuracy, 20% imprecision at the LLOQ) and take results as set in stone. As a finger exercise we once solved the confidence bands of weighted inverse regression (aka calibration) – which required some nasty algebra (partial derivatives, etc.).* Then you can come up not only with estimated concentrations but also their confidence intervals (asymmetric – since the CI of a linear function are two hyperbolas). If the CIs of two concentrations overlap, they are not significantly different…

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• If one doesn’t have the knowledge and stamina to step into algebra here is an alternative: Calculate the CI of the regression (available in all statistical packages). To get the lower CL of the estimated concentration (x₀|y₀) use the bisection algo with starting values of x_low=0 and x_hi=x₀ and the estimated upper CL at these values. To get the lower CL run the algo within x₀ and the ULOQ.