# PharmPK Discussion - Bioavailability calculation - mean ratio

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• On 13 Mar 2014 at 10:47:07, Wie Vraa (wievraa.at.gmail.com) sent the message
`Question on bioavailibility calculationIn a cross-over design bioavailibility can be calculated as AUCpo /AUCiv (corrected for dose) for each subject. Then, take the (geo.)meanof the individual bioavailibilities (method1).Alternatively, one could take (geo.)mean-AUCpo / (geo.)mean-AUCiv(method2). Then, there is no cross-over design needed.In guidances (FDA: DDI, food-effect and bioequivalence) it reads thatone should report the ratio of the geometric mean AUC when comparingdose routes, food-effect or the influence of an interacting drug (i.e.method2).A mathematical characteristic of geometric mean is that the geometricmean of the ratio is the same as the ratio of two geometric means.With other words, when using geometric means, method1 gives exactlythe same geometric mean bioavailibility as method2.Question: Does this imply that, using geometric means, there is noadvantage of a cross-over design - because there is no difference-when compared to a parallel design?thanks for any comments on beforehand,Wie`
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• On 14 Mar 2014 at 10:48:25, Atish Salunke (atish_azad.-at-.yahoo.com) sent the message
`Dear Wie,Since PK parameter mainly Cmax and AUC follows log normal distribution, before statistical analysisthese PK parameter are log transformed. These are then back transformed to original scale.Exponential of the estimate of log tranformed data gives you geometric mean.No it does not imply that, using geometric means, there is noadvantage of a cross-over design - because there is no difference-when compared to a parallel design?Using cross-over design is always benificial provided your study/design should allow use ofcrossover.In cross-over design subject act as his on control, sample size required is small compared toparallel study.Parallel study is prefered when the drug has a large half life and it is difficult to conduct across-over study because duration of wash out period will very high and you may not be able toafford the same.Hope this helps.Regards,Atish`
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• On 14 Mar 2014 at 14:28:20, Xiao Quan Zhang (XiaoZ.aaa.amphastar.com) sent the message
`FDA has a definition of long half > 24hrs. You have to use parallel study. It needs to be approvedby FDA at pre-IND meeting.Kam`
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• On 14 Mar 2014 at 14:30:22, Garner Consulting (garner.consulting.-at-.btconnect.com) sent the message
`Absolute bioavailability is best measured when an IV microdose is given alongside an extravasculartherapeutic dose.  The microdose can be measured in plasma using various analytical technique but14C-labelled drug and accelerator mass spectrometry bioanalysis is recommended alongside LC/MS tomeasure cold drug (see Lappin G, Rowland M and Garner R C (2006)  The use of isotopes in thedetermination of absolute bioavailability of drugs in humans.  Expert Opin Drug Metab Toxicol, 2,419-427). This study design eliminates the variability associated with IV / oral cross-over studies.Professor Colin Garner BPharm PhD DSc FRCPathExploratory Clinical Development ConsultantGarner Consulting ServicesHonorary Clinical ProfessorHull York Medical School, University of York, UK`
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• On 18 Mar 2014 at 07:12:17, Fabrice Nollevaux (fabrice.nollevaux.-a-.arlenda.com) sent the message
`Dear Wie,The absolute bioavailability *can* indeed be estimated from a parallel design as well as fromcrossover study.<< Question: Does this imply that, using geometric means, there is no advantage of a cross-overdesign - because there is no difference -when compared to a parallel design? >>However, the absolute bioavailability will be more accurately estimated from a crossover design thanfrom a parallel design, since the crossover design allows to separate the inter-subject variabilityfrom the residual (sometimes called intra-subject) variability.  This is IMHO a non-negligibleadvantage!Kind regards,Fabrice--Fabrice NollevauxSenior Pharmacometrician – Senior StatisticianWebsite : www.arlenda.com`
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• On 18 Mar 2014 at 14:53:34, Angusmdmclean.-a-.aol.com sent the message
`Fabrice:  if you use a cross-over Latin Square design with 12 subjects  say A vs B, where B is an IVtreatment and A is an oral treatment of the same drug.Then the mean of the ratio of the individual  test Vs reference (A/B)  AUC values for each of the 12subjects is the absolute bioavailability.Or is it the geometric mean of the ratio  of individual ratios.( I think it is this).In statistical terms I think you are saying that using the cross-over design in the samesubject,where each subject acts as his or her control , then you can estimate the inter subjectvariance and the intra subject between treatment  variance from the design.It is scientifically  intuitive that using  the same subjects in a cross-over design will provide abetter result for the comparison.  I have difficulty putting it in statistical terms.  Please canyou expand a little on the statistical rationale and put it in simple language.Angus McLean`
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• On 20 Mar 2014 at 16:14:47, Fabrice Nollevaux (fabrice.nollevaux.aaa.arlenda.com) sent the message
`Dear Angus,<< Then the mean of the ratio of the individual  test Vs reference (A/B)  AUC values for each of the12 subjects is the absolute bioavailability.  Or is it the geometric mean of the ratio  ofindividual ratios.( I think it is this). >>It is the geometric mean, indeed.<< Please can you expand a little on the statistical rationale and put it in simple language. >>The precision on the estimates depends on the residual (i.e. unexplained) variability resulting fromyour statistical model.In a parallel design, both the intra-subject and the inter-subject components are counfounded withinthe residual variability .In a crossover design, you can identify the inter-subject component separately from the residualvariability. As the residual variability does only include the intra-subject component, it is lowerthan the residual variability of a parallel design. The actual gain depends on the relativeimportance of the intra- and inter-subject variability components.Fabrice--Fabrice NollevauxSenior Pharmacometrician – Senior Statistician`
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