# PharmPK Discussion - Bioavailability statistics

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• On 29 Sep 2004 at 05:08:32, kanimozhi A (kani_bio01.-a-.yahoo.co.in) sent the message
`Sir/Madam,I have a doubt in interpretation of the bioequivalence results.In a bioequivalence trial if the 90% confidence interval and the  ratios are with in the acceptance limits of bioequivalence (80-125%).But in PROC GLM for all the three parameters i.e. Cmax AUC0-t and AUC  0-inf is significant by formulation wise, so can we conclude that the  two formulations are bioequivalent or not.Thanks and regards,kanimozhi.A`
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• On 29 Sep 2004 at 05:55:38, Priti Pandey (priti_pandey.-a-.yahoo.com) sent the message
`Dear Kanimozhi,Bioequivalence result depends only on 90% CI. If your definedregulatory (80%-125% for most regulatories) criteria meets then you canconclude bioequivalence. PROC GLM gives us "error" term to calculate90% CI.Hope this will be helpfull to you.RegardsPriti`
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• On 29 Sep 2004 at 13:48:32, Helmut_Schutz (helmut.schuetz.-at-.bebac.at) sent the message
`Dear kanimozhi A,don't worry about about significant results, we were testing themalmost more than two decades ago ;-)In BE assessment we are only interested in rejecting thenull-hypothesis of inequivalence by means of interval inclusion (given for bioavailability ratios):null hypothesis [=B5(test) and =B5(reference) are not equivalent]    H0:    =B5(test)/=B5(reference)theta2alternative hypothesis [=B5(test) and =B5(reference) are equivalent]    H1:    theta1<=B5(test)/=B5(reference)The interval [theta1,theta2] denotes the acceptance ranges for anygiven parameter, where a beta-risk of 0.2 leads to theta1(1-beta0.8)and theta21/theta11.25.Best regards,Helmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html`
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• On 30 Sep 2004 at 11:22:58, Helmut_Schutz (helmut.schuetz.aaa.bebac.at) sent the message
`Dear kanimozhi A,since yesterday's mail showed up in some strange coding, I will give it a second try:null hypothesis [mu(T) and mu(R) are not equivalent]   H0: mu(T)/mu(R)theta2alternative hypothesis [mu(T) and mu(R) are equivalent]   H1: theta1The interval [theta1,theta2] denotes the acceptance ranges for anygiven parameter, where a beta-risk of 0.2 leads to   theta1(1-beta)0.8,and   theta21/theta11.25.Best regards,Helmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html[Still looks strange to me but this is what arrived for distribution - db]`
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• On 30 Sep 2004 at 14:32:07, Angusmdmclean.at.aol.com sent the message
`September 30, 2004:Helmut; thank you for outlining the essence of statistical tests forbioequivalence and indeed bioinequivalence.  This is indeed usefulmaterial.  Pleasecould you add the definitions of all the symbols and  letters in theequations, since this will significantly aid  comprehension of theletters and symbolsin your presentation and eliminate  confusion.thank youAngus  McLean Ph.D.8125 Langport Terrace,Suite 100,Gaithersburg,MD  20877301-869-1009301-869-5737BioPharm  Global(http://home.comcast.net/~angusmdmclean/BGWEBSITE/home.html)`
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• On 1 Oct 2004 at 08:55:57, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message
`Dear Helmut Schutz,You wrote: > The interval [theta1,theta2] denotes the acceptance ranges for any > given parameter, where a beta-risk of 0.2 leads to >    theta1(1-beta)0.8, > and >    theta21/theta11.25.Perhaps I am wrong, but in my opinion, the values 0.8 and 1.25 aredefinedas the acceptable range for the AUC-ratio, with a probability of 95%(alpha 0.05  'consumers' risk'), and this has nothing to do with thebeta-risk('manufacturers' risk'). A beta of 0.2 implies that, given that the trueAUC-ratio is 1, the chance of concluding bioequivalence is 80%. Thesamplesize is chosen to achieve this.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.-at-.farm.rug.nl`
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• On 1 Oct 2004 at 09:31:53, "Dowling, Thomas" (tdowling.at.rx.umaryland.edu) sent the message
`I was wondering if someone could share their experiences in terms ofcalculating sample size for BE studies? Since we rarely know theintra-subject variability of Cmax and AUC for either the reference ortest drug, what is the most common approach?Bests,Tom[Try searching athttp://www.boomer.org/cgi-bin/htsearch?method='and'&sort='score'&words=sample%20size&restrict=http://www.boomer.org/pkin/ - db]`
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• On 1 Oct 2004 at 10:43:45, "Lee, Jang-Ik" (LEEJANG.-at-.cder.fda.gov) sent the message
`Tom,Personally, I have used PASS in determining sample size for BE studies.Even though you do not know the variability, you can play around withassumptions (e.g., CV = 10%, 20%, 30%; and power = 0.8, 0.9....).  PASSgives you estimated sample size in each combination of assumption.I hope this helps.  Best regards.Ike.Jang-Ik Lee, Pharm.D., Ph.D.Clinical Pharmacology ReviewerOffice of Clinical Pharmacology and BiopharmaceuticsCenter for Drug Evaluation and ResearchU.S. Food and Drug Administration9201 Corporate Blvd, HFD-880, Rockville, MD 20850Phone: 301-827-2492  Fax: 301-827-2579[http://www.dataxiom.com/products/Pass/ orhttp://www.ncss.com/pass.html ? - db]`
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• On 1 Oct 2004 at 16:52:23, fabrice_nollevaux.aaa.sgs.com sent the message
`Dear Thomas,Unfortunately, you should have a previous estimation of theintra-subjectvariability to be able to calculate the required sample size.The compounds concerned by bioequivalence being generally quite "old",this information can be found or derived either from the litterature orfrom previous studies performed with the reference formulation.If this is not the case, I am afraid you need a pilot study with a fewsubjects in order to get this estimation.But then, be careful that the estimate of variability obtained wihtin alimited number of subjects will carry out a large uncertainty, so youwould have to use a conservative approach in further sample sizeestimation (e.g. based on the upper 95%CI of the estimated intra-CV).Hope this helps,FabriceFabrice Nollevaux,Senior BiostatisticianSGS Life Sciences - Wavre - Belgiumhttp://www.sgs.com/life_sciences`
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• On 1 Oct 2004 at 19:45:20, "Jadhav, Pravin *" (JadhavP.at.cder.fda.gov) sent the message
`Hi Hans and Helmut,I think, there are two issues here.1. BE limit: (0.8 - 1.25): In that sense, Helmut's logic makes sense.Thegiven logic >    theta1=(1-beta)=0.8, > and >    theta2=1/theta1=1.25.makes sure that the intervals are symmetric around 1 (20% on bothsides, theincrease from 100 TO 120 is only 16.67%). This limit is *recommended*by theagency. I don't see any relation with "consumers' risk" (alpha) or"manufacturers' risk" (beta). (or is it?) I see it as an expectationthat ifthe ratio of some relevant quantity (e.g. log transformed AUC) for twoproducts is within 20%, these two products will be equivalent.This was a result of Hatch-Waxman Act of 1984 where an assumption wasmadethatduplicates of pioneer drugs would be the same as the innovator's drug. Asecond assumption was that bioequivalence data was an effectivesurrogatefor safety and effectiveness. There is some controversy about theseassumptions, but this is what the law was about. Twenty percent wasconsidered as a fairly good margin, and many medical professionalsbelievedthat for drugs that have a wide therapeutic index, twenty percent is notimportant at all.Overview of Hatch-Waxman:http://www.oblon.com/Pub/display.php?hatchwax.html2. Confidence intervals: Now, we are going to have some variability intheestimate. So C.I.s are relied upon to get an idea of the uncertainty intheestimation. However, should it be 95% C.I. or 90% C.I.? is notmentioned inthe BA/BE guidance.In other words: if the C.I., a measure of uncertainty, falls within thesetBE limit(one could set it to 10%, 20% or 50%), it is reasonable toassumeequivalency. Also, it should be noted that these analyses are performedonlog-transformed data.Am I making sense here?PravinPS: Please note that these are my personal views and understanding ofthetopic.Pravin JadhavGraduate studentDepartment of PharmaceuticsMCV/VCU`
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• On 2 Oct 2004 at 12:15:10, helmut.schuetz.aaa.bebac.at sent the message
`Dear Angus, dear Hans,just another try:null hypothesis [mu(T) and mu(R) are not equivalent]    H0: mu(T)/mu(R)theta2alternative hypothesis [mu(T) and mu(R) are equivalent]    H1: theta1The interval [theta1,theta2] denotes the acceptance range for any givenparameter,where an acceptable deviation of 0.20 leads to    theta1 (1-AD) 0.80,and    theta21/theta11.25.H0    : null hypothesis (inequivalence)H1    : alternative hypothesis (equivalence)mu    : expected meanT     : test formulationR     : reference formulationtheta1: lower goalpost (acceptance limit)theta2: upper goalpost (acceptance limit)AD    : acceptable deviation of T from R         (generally 0.20, may be extended [e.g. to 0.25] in somelegislations         [EU,AUS,NZ,TR,MAL,RC; recommended by WHO] based onsafety/efficacy         of the drug)BE    : bioequivalenceBA    : bioavailabilitySince the expected (population) means mu(T) and mu(R) are unknown, theyareestimated from their sample means x_(T) and x_(R) by means of confidenceintervals.Two types of error must be observed:alpha : error type I, risk I         In BE patient's risk to be treated with an _inequivalent_         formulation, which was (erroneously) claimed to be equivalent.         Generally set to <0.05 (0.025 in Brazil for narrow therapeutic         range drugs).         Since a given patient can only show BA _either_ below _or_ above         the stated AD, the risk for the population becomes _2*alpha_(and         therefore we are building a >90% confidence interval)beta  : error type II, risk II         In BE producer's risk for an equivalent formulation[mu(T)/mu(R)1]         to be declared inequivalent (the chance to fail to show BE).Both errors are used in sample size estimation, where beta generally issetwithin 0.10-0.20 (power1-beta80%-90%). Sample sizes corresponding topower <70% or >90% will raise ethical issues (either unecessarytratment ofsubjects with a rather low chance to show BE, or probable cause for'forced' BE).Best regards,HelmutP.S.:   Thanks to Hans, who corrected my first sloppy mail.P.P.S.: .-at-.David:         Previous mails were produced as 'plain text' by Mozilla 1.7.1         This time I give it a trial with a web-mail application         SquirrelMail 1.2.10...--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html`
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• On 3 Oct 2004 at 13:46:18, =?ISO-8859-1?Q?Helmut_Schutz?= (helmut.schuetz.-at-.bebac.at) sent the message
`Hi Pravin, > However, should it be 95% C.I. or 90% C.I.? is not mentioned in theBA/BE guidance.Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];Guidance for Industry: Statistical Approaches to EstablishingBioequivalence.http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)states at B. Statistics:[...] average bioequivalence and involves the calculation of a 90%confidenceinterval for the ratio of the averages (population geometric means) ofthe measures for the T and are products. To establish BE, the calculatedconfidence interval should fall within a BE limit, usually 80-125% forthe ratio of the product averages.IMHO 90% CI is applied worldwide, with the exception of Brazil(ANVISA), where a 95% CI is required for BE of narrow therapeutic rangedrugs.Regards,Helmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html`
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• On 4 Oct 2004 at 03:14:41, vardhini kirthivas (vardhinikirthivas.-at-.yahoo.com) sent the message
`Hi.,Is it possible to estimate the sample size for Pivotal BE Studies from the results of Pilot BE studies.Can some one explain how?RegardsVardhini`
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• On 4 Oct 2004 at 09:47:29, "Kurnik, Daniel" (daniel.kurnik.-at-.Vanderbilt.Edu) sent the message
`Hi Helmut,can I ask: why istheta2 = 1/theta1,and nottheta2= (1+AD) = 1.2 ?Daniel`
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• On 5 Oct 2004 at 09:14:31, "Mitesh Gandhi" (miteshgandhi.aaa.alembic.co.in) sent the message
`Dear vardhiniOne of the objective of carrying our pilot BE study is to get idea ofsamplesize for pivotal trial.  From pilot study, you will get intra CV%, T/Rratio.  and from this you can have estimate of sample size to generate80%power.For detail, you can refer Pharamceutical statistics by Bolton.Hope, this will help you at somewhat extent.RegardsMitesh`
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• On 6 Oct 2004 at 12:13:55, Helmut_Schutz (helmut.schuetz.-a-.bebac.at) sent the message
`Dear Daniel,you wrote:why istheta2 = 1/theta1,and nottheta2= (1+AD) = 1.2 ?The statistical model for AUC and Cmax is multiplicative, not additive.If we assume no carryover (sufficient washout period, verified by takinga predose sample in each treatment period) it is given with:X(ijk) = mu * pi(k) * Phi(l) *s(ik) * e(ijk)whereXijk: log-transformed response of j-th subject [j=1,_,n(i)] in i-thsequence [i=1,2] and k-th period [k=1,2]mu: global mean, mu(l): expected formulation means [l=1,2:mu(1)=mu(test), mu(2)=mu(ref.),pi(k): fixed period effects,Phi(l): fixed formulation effects [l=1,2: Phi(1)=Phi(test),Phi(2)=Phi(ref.)]s(ik): random subject effect,e(ijk): random error.Main Assumptions:a) All ln{s(ik)} and ln{e(ijk)} are independently and normallydistributed about unity with variances sigma(Z)(s) and sigma(Z)(e).b) All observations made on different subjects are independent.The assumption of a multiplicative model is based on:1) pharmacokinetic groundsfrom[F(test) * AUC(test)] / [D(test) * CL(test)] , [F(ref.) * AUC(ref.)] /[D(ref.) * CL(ref.)]assumingc) D(test) = D(ref.) andd) CL(test) = CL(ref.)we are apble to calculateF(rel.) = BA = AUC(test.) / AUC (ref.)2) analytical groundsSerial dilutions used in the preparation of calibration curves leadaccording to the law of error propagation to a multiplicative errormodelTherefore we log-transform AUC and Cmax. In the logarithmic scaleequidistance is given by [x,1/x] --> [0.9/1.11], [0.80/1.25],[0.75/1.33]...Some remarks on assumptions:ad a) According to Good Statistical Practice this can (and should) betested (1). If rejected, one should opt for a nonparametric method.Funny enough FDA is against this procedure (2).ad b) Speaks aginst the inclusion of twins in BE-studies ;-)ad c) Dose correction according to actual content may be reasonable(also recommended in some guidelines [Canada, WHO])ad d) In a 2x2 crossover it is impossible to separate inter-occassionvariability from inter-treatment variability, therefore we rely on thisassumption. A replicate design would be needed to separate theseeffects. For highly variable drugs/drug products the use of AUC*k(el)instead of AUC _may_ help (3).(1) Jones, B. and M.G. Kenward;Design and Analysis of Cross-Over Trials.2nd Edition, Chapman & Hall, Boca Raton, London, New York, Washington,D.C. (2003)"No analysis is complete until the assumptions that have been made inthe modeling have been checked. Among the assumptions are that therepeated measurements on each subject are independent, normallydistributed random variables with equal variances. Perhaps the mostimportant advantage of formally fitting a linear model is thatdiagnostic information on the validity of the assumed model can beobtained. These assumptions can be most easily checked by analyzing theresiduals."(2) Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];Guidance for Industry: Statistical Approaches to EstablishingBioequivalence.http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)"The limited sample size in a typical BE study precludes a reliabledetermination of the distribution of the data set. Sponsors and/orapplicants are not encouraged to test for normality of errordistribution after log-transformation [...].(3) H.Y. Abdalah;An Area Correction Method To Reduce Intrasubject Variability InBioequivalence Studies.J Pharm Pharmaceut Sci 1 (2), 60-65 (1998)Best RegardsHelmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html`
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• On 6 Oct 2004 at 12:13:55, Helmut_Schutz (helmut.schuetz.aaa.bebac.at) sent the message
`Dear Daniel,you wrote:why istheta2 = 1/theta1,and nottheta2= (1+AD) = 1.2 ?The statistical model for AUC and Cmax is multiplicative, not additive.If we assume no carryover (sufficient washout period, verified by takinga predose sample in each treatment period) it is given with:X(ijk) = mu * pi(k) * Phi(l) *s(ik) * e(ijk)whereXijk: log-transformed response of j-th subject [j=1,...,n(i)] in i-thsequence [i=1,2] and k-th period [k=1,2]mu: global mean, mu(l): expected formulation means [l=1,2:mu(1)=mu(test), mu(2)=mu(ref.),pi(k): fixed period effects,Phi(l): fixed formulation effects [l=1,2: Phi(1)=Phi(test),Phi(2)=Phi(ref.)]s(ik): random subject effect,e(ijk): random error.Main Assumptions:a) All ln{s(ik)} and ln{e(ijk)} are independently and normallydistributed about unity with variances sigma^2(s) and sigma^2(e).b) All observations made on different subjects are independent.The assumption of a multiplicative model is based on:1) pharmacokinetic groundsfrom[F(test) * AUC(test)] / [D(test) * CL(test)] , [F(ref.) * AUC(ref.)] /[D(ref.) * CL(ref.)]assumingc) D(test) = D(ref.) andd) CL(test) = CL(ref.)we are apble to calculateF(rel.) = BA = AUC(test.) / AUC (ref.)2) analytical groundsSerial dilutions used in the preparation of calibration curves leadaccording to the law of error propagation to a multiplicative errormodelTherefore we log-transform AUC and Cmax. In the logarithmic scaleequidistance is given by [x,1/x] --> [0.9/1.11], [0.80/1.25],[0.75/1.33]...Some remarks on assumptions:ad a) According to Good Statistical Practice this can (and should) betested (1). If rejected, one should opt for a nonparametric method.Funny enough FDA is against this procedure (2).ad b) Speaks aginst the inclusion of twins in BE-studies ;-)ad c) Dose correction according to actual content may be reasonable(also recommended in some guidelines [Canada, WHO])ad d) In a 2x2 crossover it is impossible to separate inter-occassionvariability from inter-treatment variability, therefore we rely on thisassumption. A replicate design would be needed to separate theseeffects. For highly variable drugs/drug products the use of AUC*k(el)instead of AUC _may_ help (3).(1) Jones, B. and M.G. Kenward;Design and Analysis of Cross-Over Trials.2nd Edition, Chapman & Hall, Boca Raton, London, New York, Washington,D.C. (2003)"No analysis is complete until the assumptions that have been made inthe modeling have been checked. Among the assumptions are that therepeated measurements on each subject are independent, normallydistributed random variables with equal variances. Perhaps the mostimportant advantage of formally fitting a linear model is thatdiagnostic information on the validity of the assumed model can beobtained. These assumptions can be most easily checked by analyzing theresiduals."(2) Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];Guidance for Industry: Statistical Approaches to EstablishingBioequivalence.http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)"The limited sample size in a typical BE study precludes a reliabledetermination of the distribution of the data set. Sponsors and/orapplicants are not encouraged to test for normality of errordistribution after log-transformation [...].(3) H.Y. Abdalah;An Area Correction Method To Reduce Intrasubject Variability InBioequivalence Studies.J Pharm Pharmaceut Sci 1 (2), 60-65 (1998)Best RegardsHelmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at http://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html[Sorry, I caused a couple of errors in the first version - db]`
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