# PharmPK Discussion - Calculation of F and PK/PD Modeling

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• On 5 Sep 1997 at 10:54:12, Tony Lee (p2149z.aaa.hotmail.com) sent the message
`Dear Readers:I would like to get your opinions on the followingquestions.First one is on the calculation of relative bioavailability.To calculate the relative bioavailability of a oralformulationin individual subject, we can use (1) the ratio ofindividualAUC from oral dosing to average AUC from IV dosing toa group of subjects or (2) the ratio of individual AUC fromoral dosing to individual AUC from IV dosing. I call secondmethod self-comparison method. I would like to know whichmethod is more accurate? Any statistical or physiologicaljustification?Second question is on PK/PD correlation.I would to know how to deal with PK/PDcorrelation problems in the situations such asplasma concentration measurement and efficacydetermination on different time intervals (PK inhours and PD in days) or different dosage regimenfor PK and PD (PK-single dosing and PD-multipledosing). Your answers or suggestions for referenceswill be greatly appreciated.Tony LeeMailto:p2149z.aaa.hotmail.com`
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• On 8 Sep 1997 at 10:20:45, Hans Proost (J.H.Proost.aaa.farm.rug.nl) sent the message
`The topic is more complicated than is suggested in this question.There can be hardly any debate about the question which method shouldbe used to calculate the relative (or absolute) bioavailability FORAN INDIVIDUAL: method (2). The reason is simple: AUC comparison isbased on the assumption that clearance is constant. Since clearanceis, in general, a pharmacokinetic parameter with relatively highinterindividual variability, it is essential that AUC of the sameindividual are compared.However, the question is more complicated if you are interested inthe 'best' (unbiased) estimate of 'average' bioavailability of a groupof subjects (or, in terms of population PK, a typical value ofbioavailability of the population), and its variance.In this case, some assumption on the statistical distribution arenecessary. In my opinion, it is both realistic and practical toassume a log normal distribution of the pharmacokinetic parameters.The calculation is easy: (a) calculate the bioavailability of eachindividual subject (ratio of dose-adjusted individual AUCs)(b) calculate the mean and sd of the log(base e)-transformed ratio's(c) mean bioavailability is inversed of log-mean(d) coefficient of variation (CV, expressed as fraction) is the sd ofthe log(base e)-transformed ratio's(e) sd of bioavailability is product of mean bioavailability and CV.If AUCs from the same individual are not available, theaforementioned procedures don't work correctly! In this case adifferent approach is necessary.Johannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyGroningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.-a-.farm.rug.nl`
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• On 9 Sep 1997 at 10:46:11, "Gentry, Tom" (TGENTRY.-a-.willco.niaaa.nih.gov) sent the message
`To: Tony LeeRe: Calculation of Bioavailability.	What you refer to as the "self-comparison method" is the betterway to assess the bioavailability (F) of a drug in an "individualsubject".  The ratio of  AUCpo / AUCiv both obtained from the sameindividual (under all the same conditions, other that route ofadministration) would control for between-subject sources of variancewhich would have an equivalent influence on the AUCs regardless of theroute of administration.  Such sources of variance would include forexample, the apparent distribution volume of the drug and it's rate ofclearance.	The only instance this might not be true is when the error ofmeasurement is much greater than individual differences in thepost-absorptive determinants of AUC.  But if that were true, the wholequestion of "the relative bioavailability of a oral formulation inindividual subject" would be compromised.  If it's not already obvious,the best method is to assess the AUCpo / AUCiv for each individual in agroup of subjects and then describe bioavailability by descriptivestatistics.	By the way, there is at least one important drug for which thecomparison of AUCpo / AUCiv is not appropriate for assessment of itsbioavailability.  (hint: it accounts for > 5% of the total Americancaloric intake).Tom Gentry ================================================== R. Thomas Gentry, Ph.D. Office of Collaborative Research Activities National Institute on Alcohol Abuse and Alcoholism Willco Bldg., Suite 400, 6000 Executive Blvd. Bethesda, MD, 20892-7003 tel. 301-443-6009   fax. 301-443-7043 Email: tgentry.-at-.willco.niaaa.nih.gov ================================================------------------------------Date: Wed, 10 Sep 1997 10:47:20 -0500From: Ofer Spiegelstein Subject: Grapefruit juice-drug interaction warningsDear Fellows,Should drugs that have or are suspected of having possible clinicallysignificant interaction with grapefruit juice, have warnings against it inpatient=EDs inserts and/or doctor=EDs data sheets?I am asking this because of the replies to my question (ANCHODD andPharmCare) regarding the existence of such warnings. As you may have seenthere are warnings for terfenadine in the UK, felodipine in Australia andindinavir and saquinavir as well.Both felodipine and terfenadine have proven interaction with grapefruitjuice. On the other hand neither indinavir nor saquinavir have been shownto interact with grapefruit juice. Yet they both have the potential of suchan interaction as they have low bioavailability  and major CYP 3A4 metabolism.What about cyclosporin and nisoldipine, both having documented interactionswith grapefruit juice?Should cisapride have a warning as well?Sincerely,Ofer Spiegelstein*********************************************************************Ofer SpiegelsteinDepartment of PharmacyThe Hebrew University of JerusalemP.O.Box 12065, Jerusalem 91120Israelofersp.-at-.cc.huji.ac.il**********************************************************************`
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• On 15 Sep 1997 at 15:12:58, Hans Proost (J.H.Proost.-a-.farm.rug.nl) sent the message
`Again, the situation is more complicated than in my first answer!My first answer to the PK/Pharm group was an approximation,which will be sufficiently accurate in most cases.Here is a more complete answer, with the exact solution.The only, almost complete reference to log normal distributions canbe found in:Biostatistics in Pharmacology (volume I, pp. 544- )by AL Delaunois, LJ Martin, E Olbrich, AA WeberPergamon Press - Oxford 1973 (ISBN 0 08 016556 7)(series 'International encyclopedia of pharmacology and therapeutics)According to this reference, the relationship mentioned in my note tothe PK/Pharm group is only valid for the case CV is small.For variance, the following relationship is given in theaforementioned reference (symbols modified to text):var = s^2 = ln(1+CV^2)where var is the variance of the ln-transformed data,s is the standard deviation of the ln-transformed data, andCV is the coefficient of variation (^2 = square)If CV is small, var is almost equal to CV^2.E.g., if s = 0.1, it follows that CV = 0.10025,if s = 0.25, then CV = 0.25396if s = 0.4 (rather large!), CV = 0.41655Note: always use 'ln', natural logarithm, base e(using logarithms with base 10 requires co factors; I don'tlike them, and they should be banned from the whole field ofpharmacokinetics).Johannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyGroningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.aaa.farm.rug.nl`
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• On 17 Sep 1997 at 10:57:56, Roger Jelliffe (jelliffe.-a-.hsc.usc.edu) sent the message
`About bioavalaibility. The fraction absorbed can also be computed directlyfrom a mixed dosage regimen containing both IV and PO dosage in individualpatient regimens. This can be done in both parametric and nonparametricpopulation models, using iterative Bayesian and nonparametric EM softwarefor such modeling. This avoids comparison of AUC's, obtained possibly underdiffereing clinical circumstances, and permits it to be done in thepatients of interest, in their often changing clinical circumstances. Ifone would like more info, call me at (213)342-1300, or check our web sitefor more info.Sincerely,Roger Jelliffe************************************************Roger W. Jelliffe, M.D.USC Lab of Applied PharmacokineticsCSC 134-B, 2250 Alcazar St, Los Angeles CA 90033Phone (213)342-1300, Fax (213)342-1302email=jelliffe.aaa.hsc.usc.edu************************************************Take a look at our Web page for announcements ofnew software and upcoming workshops and events!!It is    http://www.usc.edu/hsc/lab_apk/************************************************`
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