Bioequivalence and Bioavailability Forum

Dear all,

since I didn’t want to go too much off-topic in conversations I had with Franz and Detlew (see this post and followings) I prepared an example about analytical error. Calibration at six levels (replicates) compliant with the GL (CV ≤20% at the LLOQ, ≤15% above; back-calculated inaccuracy ≤±20/15%), linear model, weighting 1/σ².
  x   y       SDy    CV%
  1  0.032  0.0064  20.0
  2  0.062  0.0091  14.7
  4  0.128  0.0173  13.5
  8  0.280  0.0392  14.0
 16  0.520  0.0640  12.3
 32  1.020  0.1224  12.0
I got:
ayx -0.013642 ±0.0019957
byx  0.032667 ±0.000738
R2   0.099797
Not that bad. But what about variability? How reliable are concentrations obtained from the calibration? Imagine samples in the mid-range and close to the LLOQ. We have two measurements (y) each. Can we distinguish between estimated concentrations (x)?
                 y       x       95% CI
mid-range       0.40   12.3   11.7  – 13.0
                0.45   13.8   13.1  – 14.6
close to LLOQ   0.040   1.27   1.13 –  1.40
                0.045   1.42   1.29 –  1.55
Note the asymmetric confidence interval of estimated concentrations, which is caused by the hyperbolic CI of the regression.



We can reliably distinguish between two concentrations in the mid-range, but not close to the LLOQ since their CIs overlap. That’s not rocket since, but basic stuff.*
When we talk about excluding data points in the estimation of λ_z we should keep this issue in mind. We must not forget that PK data are not isolated pieces of information, but highly correlated. We should apply scientific judgment (an euphemism for common sense) on which data are included – and which not.

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• Miller JC, Miller JN. Statistics and Chemometrics for Analytical Chemistry. Upper Saddle River; 6^th ed 2010: Prentice Hall.