Bioequivalence and Bioavailability Forum

Dear SriRam!

❝ F = DNAUC po / DNAUC iv

❝ "N" stands for Dose "NORMALISED".

OK; in WinNonlin’s NCA module you get the following dose-normalized metrics:
Cmax_D, AUCINF_D_obs, and AUCINF_D_pred where “_D” stands for “divided by dose”. I would suggest to use the lin-up/log-down trapezoidal rule and AUCINF_pred (uncorrected) / AUCINF_D_pred (dose-corrected). Use these metrics as dependent variables in the BE wizard.

❝ ❝ If linear pharmacokinetics are applicable the equation of your image is correct.

❝ Can you explain other Corrections (apart from dose)…

I don’t know your study design. Was the iv dose the same for all subjects or individualized (like D/kg body weight, D/m², or D/1.73m²)? In the latter case you can use one of the “Normalization” options in WinNonlin’s NCA setup.

❝ … OR Normalisations as the image shows equations considering Clearance and T_1/2 for Calculating Bioavailabiliy in case of Nonlinear PK.

Forget it. The paper misquotes Wagner (1967)^[1] who suggested this method for across-study comparisons. The theoretical background for BA studies was derived by Koup & Gibaldi (1980)^[2] based on the assumption that the clearance, CL, is not necessarily constant in the same subject between treatments, but that the volume of distribution, V, is. The latter assumption is reasonable unless drastic physiologic changes are taking place during the course of the study, e.g. changes in protein concentration, adipose tissue fraction of body weight, hydration state, etc. Therefore,

(1) F = (CL_test·AUC_test)/(CL_ref·AUC_ref)·D_ref/D_test

Assuming V is constant and substituting V·k for clearance, where k is the terminal disposition rate constant, it follows that,

(2) F = (AUC_test·k_test)/(AUC_ref·k_ref)·D_ref/D_test

or,

(3) F = (AUC_test·t_½,ref)/(AUC_ref·t_½,test)·D_ref/D_test

Both (2) and (3) have been used in NDA BE studies. Abdallah (1998)^[3] gave an example where the CV was reduced from 35% to 18% (the CI shrank from 88–130% to 99–113%). He also performed simulations showing that the area correction reduced the CV only for drugs with highly variable clearance; if the variability resides in the volume of distribution and/or absorption the method worsened the situation. Gibaldi & Perrier (1982)⁴ suggested that

“It is probably reasonable to attempt the half-life correction in most bioavailability studies but to accept it only when it results in a substantial decrease in the standard deviation of the mean value of F or F_R.”

It was also noted by Koup & Gibaldi^[2] that area correction should be avoided when a systematic difference in k appears to exist between the test and reference treatments, as this most likely reflects a difference in absorption rather than variability in clearance. Note that the area correction was developed in the context of bioequivalence – not for absolute bioavailability studies. It might well be that different k values are not due to variable clearances but an artifact (you are not able to estimate them with the same precision). Personally I have not seen its application in BA.

❝ ❝ Administer equal doses and calculate f = AUC_po/AUC_iv or F = 100 × AUC_po/AUC_iv.

❝

❝ Monetary implications restrict the repeat of study, so any suggestions USING software simulation or applying corrections to arrive at the correct "F"

Do you have a study protocol? What does it say? On the other hand BA studies of NCEs are exploratory in nature – so you have some headspace. If doses where not too far apart (let’s say by a factor of two) it wouldn’t bother me too much. Don’t be tempted to use the area-correction. Keep it simple.

❝ Can you give me a practical implication of Calculating Bioavailability for a NONLINEAR PK data and its difference from LINEAR equation.

Sorry that’s not possible – unless you have data of at least three iv and po doses.

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1. JG Wagner
   Method of estimating relative absorption of a drug in a series of clinical studies in which blood levels are measured after single and/or multiple doses
   J Pharm Sci 56, 652–3 (1967)
   
2. Koup JR and M Gibaldi
   Some comments on the evaluation of bioavailability data
   Drug Intel Clin Pharm 14, 327–30 (1980)
   
3. HY Abdallah
   An Area Correction Method To Reduce Intrasubject Variability In Bioequivalence Studies
   J Pharm Pharmaceut Sci 1/2, 60–5 (1998)
   online
   
4. Gibaldi M and D Perrier
   Pharmacokinetics
   Marcel Dekker, New York, p171, 2^nd ed. 1982 (reprint: informa healthcare, New York, 2007)