## OT: Bias of AUCt, AUCall, pAUC [Regulatives / Guidelines]

Hi ElMaestro,

❝ […] it will not necessarily imply a bias on the BE conclusion unless someone can prove that E(ln(AUCall,T - ln(AUCall,R)) does not equal E(ln(AUCT) - ln(AUCR)), regardless of whether the latter is expressed as AUCinf or AUCt.

There will always be a bias in any AUC-approach if BQLs come into play and the true T/R-ratio is not  exactly  sufficiently close to unity. Exceptions: Comparison of (reliably) estimated AUC0–∞ or AUC0–t(common).

Since the bias will point away from unity, the T/R-ratio will get worse and regulators don’t care (wrong but conservative).

Example: I used the C1-column of this post as the reference (complete data). Then I generate three others (T) as R/2. Lin-up/log-down trapezoidal AUCs. The T/R-ratio should be 0.5.
1. Complete data
PK metric    T      R   T/R     %RE AUClast   1217.3 2434.6 0.500  ±0.00 AUCall    1217.3 2434.6 0.500  ±0.00 AUCcommon 1093.8 2187.5 0.500  ±0.00 AUC72     1217.3 2434.6 0.500  ±0.00 AUCinf    1298.4 2596.9 0.500  ±0.00
2. C72 of T missing
PK metric    T      R   T/R     %RE AUClast   1093.8 2434.6 0.449 –10.20 AUCall    1093.8 2434.6 0.449 –10.20 AUCcommon 1093.8 2187.5 0.500  ±0.00 AUC72     1216.6 2434.6 0.500  ±0.00 AUCinf    1297.2 2596.9 0.500  ±0.00
3. C72 of T set to zero
PK metric    T      R   T/R     %RE AUClast   1093.8 2434.6 0.449 –10.20 AUCall    1188.0 2434.6 0.488  –2.40 AUCcommon 1093.8 2187.5 0.500  ±0.00 AUC72     1188.0 2434.6 0.488  –2.40 AUCinf    1297.2 2596.9 0.500  ±0.00
As I wrote above, if we have missing(s) only AUC0–∞ and AUC0–t(common) are unbiased regardless the chosen method.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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