Bioequivalence and Bioavailability Forum

Dear Ratnakar!

❝ [...] how the data has to be considered while performing PK & Statistical analysis in the following cases?

❝

❝ - If the concentration is reported as Not Detectable

❝ - If the concentration is reported as not reportable due to poor

❝   chromatography

Terminology:

• LOD (Limit of Detection) is of no importance according to guidelines, because both accuracy and precision are not determined at this level. Many approaches are used in the analytical literature, but most of them rely on statistical assessments of the variance at C=0 (the intercept in linear regression) and/or the signal-to-noise ratio.
  
• LLOQ (Lower Limit of Quantitation) is the lowest concentration with validated accuracy and precision. Limits generally are ±20%/20% and ±25%/25% for ligand binding assays – but may be higher, if justified.
  
• Zero doesn’t exist in bioanalytics.

If a value fails due to poor chromatography, it should be reanalysed. Only if you get again a ‘strange’ result again, the value should be set to ‘not reportable’.

❝ In both the cases, should we consider as 'Zero or Missing' during PK and Statistical analysis?

I guess you mean ‘BQL’ (Below Limit of Quantitation) in the first instance? Some analytical labs report values between the LOD and LLOQ, but mark these values clearly. These values may be useful for PK-modeling (unlike in NCA pharmacokineticists will be able to include the error in the model). However, in BE these values are (mandatorily) not used.
As said above, Zero doesn’t exist - so values below the LLOQ should be given as ‘BQL’. ‘Missing’ should be reserved for true missing values (e.g. sample vial broken in centrifugation), or values which are not reportable (e.g. poor chromatography). How you treat these values in NCA-PK is another story. You should have an SOP in place describing your method (and I would recommend to state it in the protocol as well). For instance in Phoenix/WinNonlin there’s a ‘Status Code Tool’ supporting you to set up rules (see this thread and linked posts). Most people treat both ‘BQL’ and ‘Missing’ values after a single dose within the time of administration and t_max as zero. Some people use a rule to set the first ‘BQL’-value after C_max to LLOQ/2, but I would not recommend that.
If you have a ‘Missing’ value within the profile (i.e., neighbouring values are >LLOQ) I use an estimate - of course as stated in the protocol. If you follow this approach, it’s important not to use this value in estimating lambda_z. WinNonlin always interpolates linear between such values - which may give a positive bias in the elimination phase (see this thread), whereas Kinetica interpolates log/linear. There’s a workaround in WinNonlin based on partial AUCs - but it’s pretty complicated and not documented anywhere. I would recommend to perfom the estimation somewhere else (in R - or even by means of a pocket calculator).

b  = (ln C1 - ln C2) / (t1 - t2)
C0  = ln C1 - (b × t1)
Ce  = exp(C0 + b × te)
where C1,2 are the neighbouring concentrations at time points t1,2, te is the time point of the missing concentration, and Ce is the estimated concentration.

Example: C₁=6.25, C₂=3.125, t₁=8, t₂=10, t_e=9, C_e=4.420. Linear interpolation (WinNonlin’s default) would give you 4.690 (bias +6.11%).