# PharmPK Discussion - Calculating dose normalized AUC

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• On 25 Mar 2014 at 09:35:47, AnnaLog (trulala86.aaa.gmail.com) sent the message
`Dear all,maybe someone can help me with this problem:I need to analyze dose normalized AUC (dAUC) for two different formulations (Form. A molecularweight: 100g/mol and formulation B (reference drug): 250g/mol) with 2 dosing steps. Molecular weightof the actual drug is 150g/mol.Dosing steps  for formulation A: 390mg and 780mg + formulation B: 500mg and 1000mg.Bioequivalence has already been proven. That’s why I calculated dose normalized AUC for bothformulations by dividing the AUC through Dose(Reference). But I am not sure if this is the rightapproach.For example: dose normalized AUC(Formulation A): AUC(Formulation A)/Dose(Formulation B)Isn’t it better to adjust all dosing steps and formulations to eqimolar weight of the actual drug?Here is one example how I calculated dose normalized AUC by normalizing to equimolar doses of thedrug:780mg * 100g/mol= x *150g/molX= (780mg*100g/mol)/150g/molDose normalized AUC= AUC/xPerforming LMEM (and bioequivalence testing) revealed a signficant difference between bothformulation (which is not possible) even if I split the analysis into  the different dosing steps…Can anyone tell me if this is the right approach?Thanks in advance!`
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• On 25 Mar 2014 at 10:28:06, Wagner, Thomas (Thomas.Wagner.aaa.takeda.com) sent the message
`I assume the formulation are different salt forms of your drug and I also assume you do not measuresalts in your PK assay. If so, you should use the molecular mass of actual drug and not of thedifferent salt derivativesBestThomas`
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• On 25 Mar 2014 at 11:45:50, AnnaLog (trulala86.at.gmail.com) sent the message
`Ah I am so sorry. I meant molecular mass... I wrote it very confussing.Formulation 1 is a prodrug, MW: 250 Dose1: 500mg Dose2: 1000mgFormulaton 2 is the salt of the active drug, MW: 150 Dose 1: 390mg, Dose2: 780mgDose 1 of formulation 1 is equivalent to dose 1 of formulation 2.Dose 2 of formulation 1 is equivalent to dose 2 of formulation 2.MW of active drug: 100.Formulation 1 is the reference drug.I have to analyze a 4x4 crossover interaction study. I tried to calculate the correspondingequivalent dose of the active drug but something is wrong. When performing bioequivalence analysisor LMEM it tells me both formulations are not equivalent or there is a signficant difference betweenthem respectively.`
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• On 25 Mar 2014 at 13:56:38, Nathan Teuscher (nathan.aaa.learnpkpd.com) sent the message
`Thanks for the clarification. This makes more sense.I would convert the doses to common units. For example, Formulation 1 doses could be expressed as390 mg eq and 780 mg eq for the 500 mg and 1000 mg doses of prodrug, respectively. Now everythinghas the same dose "unit" and you can dose normalize by dividing the exposure parameters by theappropriate dose. I would write the doses this way for your calculations.Formulation 1:Dose 1 = 390 mg eq active = 500 mg prodrugDose 2 = 780 mg eq active = 1000 mg prodrugFormulation 2Dose 1 = 390 mg activeDose 2 = 780 mg activeNathan--Nathan S. Teuscher, PhDFounder and President, PK/PD Associates`
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• On 25 Mar 2014 at 15:43:13, Simon Davis (Simon.Davis.-a-.certara.com) sent the message
`AnnaLog,When you say " both formulations are not equivalent or there is a signficant difference between themrespectively." Which do you mean?Note it IS possible for forms to be bioequivalent yet significantly different from each other.If you are perfroming your analysis in Phoenix WinNonlin you could try posting the project to thediscussion forum www.pharsight.com/extranet so we can see your actual data and analysis steps andadvise better.                         Simon.[Or you could post some example data here (avoiding tabs if possible) - db ;-]`
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• On 26 Mar 2014 at 09:04:14, David Bourne (david.-a-.BOOMER.ORG) sent the message
`Dear AnnaLog,I agree with Thomas' analogy. Since the bioassay quantifies only the active, you need to divide theAUC of each formulation by the Mwt of the active drug (i.e. 100mg) for AUC/D.Best regards,Magnus Atemnkengmagnusajong.at.yahoo.com --Reply to Nathan:This is what I also assumed.Is it ok to calculate dose normalized AUC this way:Dose 1 = 500mg eq active (formulation 2) = 390mg (formulation 1)dose normalized AUC (formulation 2) = AUC/(dose of formulation 1)If I do it this way I do not have any problems with further analysis.My reference is formulation 1 (prodrug).I am not sure if this is the right approach.AnnaLog --Dear Simon,I do have bioequivalence when looking at both formulations at eachdosing step using the acutal AUC. Using dose normalized AUC ascalculated aboth I also get the same results for each dosing step.But I need to compare all dosing steps together for both formulation.Trying to analyse the data with dose-normalized AUC mentioned above:dose normalized AUC (formulation 2) = AUC/(dose of formulation 1)I also have bioequivalence.Trying to calcuate the corresponding dose of the active drug I do nothave bioequivalence. In my first post I showed the calculation steps.What data do you need? Descriptives? Bioequivalence results?Thanks in advance!AnnaLog `
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• On 18 May 2014 at 22:36:33, AnnaLog (trulala86.aaa.gmail.com) sent the message
`Dear all,because I do not want to start a new topic I would like to ask you for help with another questionconcerning dose normalized AUC/Cmax.There are two different formulations and also different dosing steps (same drug as mentioned above) I tried to calculate dose normalized PK parameters for the metabolites using equimalor doses of theactive drug. Also I tried to calculate AUC/Cmax by calculating equimolar doses in relation to themolecular weight of the metabolites.When splitting up in different dosing steps I receive totally different results in stat. analysisfor dosenormalized AUC/CMax than for not dosenormalized parameters. Is this possible? I would assumeresults should be similar? Do I really have to calculate dose normalized PK parameters formetabolites?Hopefully someone can help me.P.S.: If you know any literature on this subject please let me know.`
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