# PharmPK Discussion - Sample Size Calculation and Washout Period

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• On 8 Aug 2005 at 17:29:32, "Letendre, Laura" (Laura.Letendre.at.Merial.com) sent the message
`I am working on a sample size calculation for a two period cross-overdesign using nQuery Advisor.  The program asks for the CV.  The CV Iwant is the within subject CV which can be estimated from a crossoverpilot study.  This is calculated using the residual (within-subjectvariance) from proc Mixed in SAS on Ln transformed data.  I=92m toldthat the CV should be calculated by dividing the residual variance bythe square root of two.  Does anyone know if this is correct?  If sowhere does the square root of 2 come from?  Does anyone know any goodreferences for this - I already have the papers with tables but I amtrying to understand the procedure used here.Also, an easier question:I am designing a BE study with a two period crossover design.  Thehalf-life of the drug is 3 days and the Tmax is 2 days.  The washoutperiod I want is 10x the terminal half-life or 30 days.  Would I givethe second period dose on day 32, 30 days after Cmax?  My question iswhen does the washout period begin - at Cmax, at t=0?Thanks!Laura`
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• On 9 Aug 2005 at 09:06:50, "Vinay Hk" (vinay.hk.at.ranbaxy.com) sent the message
`The following message was posted to: PharmPKDear LauraThe formula for calculating the sample size is sqrt(exp(residualvariance)-1).  This is the formula that I use, proposed by Diletti etal 1991.  Ref- Sample size determination for bioequivalenceassessment by means of CI. Int Journal of Clinical Pharmacology,Therapy and Tox, 29; No.1 1991 (1-8).  This paper may clarify allyour doubts.Washout :  It does not start from Tmax.  It starts from t=0.With regardsVinay`
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• On 9 Aug 2005 at 09:56:52, mallikarjunard.-a-.drreddys.com sent the message
`Dear LauraMy answer to your question on washout period.Washout period ideally considered as period between the dosingtimings in two periods.  If you are dosing on Day 1 in period I anddosing in period II can be on Day 31 keeping 30 days washout period.ThanksD Mallikarjuna Rao[I updated the PharmPK archive (and CD) over the weekend - db]`
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• On 9 Aug 2005 at 17:55:06, radhakrishnav.at.drreddys.com sent the message
`Dear Laura Letendre,1. The intrasubject variability is the square root of the mean squarederror from the crossover ANOVA computed using the natural log scale.2. The washout period of a drug is calculated from the half-life, youcandose second period on day 30.With Regards,V.RadhakrishnaClinical Pharmacology and Pharmacokinetics`
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• On 9 Aug 2005 at 09:32:57, DDubins.at.allied-research.com sent the message
`Hey Laura, the reality is that by 10 half-lives there will be lessthan 0.1% of the drug left, so a few days probably won't end upmaking any difference. However, if we can envision a modified releasedrug with a Tmax of 1 day with a flat profile but a half-life of 2hours, we would run into difficulties if we start the washout clockat t=0. In this case, 10 half-lives after t=0 gets you to 20 hours,not even passing the Tmax. So in principle, I would start the washoutclock at Tmax to be conservative (realizing that in most cases itshouldn't make much of a difference considering the inter-individualvariability of PK parameters). One more comment about washout, it isusually preferable to run each period on the same day of the week andthe same time of day to normalize for circadian effects, so if you'redebating between 30 and 32 days washout, perhaps you could considereither 28 days or 35 days after t=0.-Dave`
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• On 9 Aug 2005 at 12:42:21, "Edmond B. Edwards, Ph.D." (editr.at.sympatico.ca) sent the message
`Hello Laura,By now you've heard about all you want to hear - and here's somemore:  if you're designing your washout period for the RegulatoryAgencies, please note that 5 half-lives are usually sufficient toreach the limit of quantitation (LOQ) of most analytical methods, soyou might want to estimate if (15 +2) days will result in samplesthat are below the LOQ.  Also, the last time I checked, the FDA willallow a carry-over if it is less than 5% of the Cmax in the nextperiod.  Hope this encourages you to select a shorter washout time,since one of the concepts behind the cross-over design is a similarpopulation between periods and 30 days might just compromise thisimplicit assumption.Good Luck.Edmond B. Edwards, Ph.D.EDIT Research`
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• On 9 Aug 2005 at 13:52:07, "Nageshwar R. Thudi" (nageshwar.thudi.-at-.ranbaxy.com) sent the message
`The following message was posted to: PharmPKHI Laura,I do agree with what Dr Edmonds says, if you really want to shorten thewashout period.  But if you don't want to invite any risks regardingcarryover in predose samples of next period I suggest you to go for morethan 5 half life's but less than 4 weeks.Hope this will help you,Nageshwar`
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• On 10 Aug 2005 at 10:08:24, "Mitesh Gandhi" (miteshgandhi.at.alembic.co.in) sent the message
`Dear LauraUseful articles for sample size calculations:1. International Journal of Clinical Pharmacology, Therapy andToxicology:Vol 30, Suppl No. 1-1992(ppS51-58).2. Statistics in Medicine, 2004; 23: 1921-1986 'Tutorial inbiostatistics -Sample sizes for clinical trials with normal data'Washout period :Washout period is a gap in between two dosing.  Starts at t = 0.RegardsMitesh Gandhi`
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• On 10 Aug 2005 at 19:06:06, "Heuvel, M.W. van den (Michiel)" (michiel.vandenheuvel.-at-.organon.com) sent the message
`The following message was posted to: PharmPKDear Laura,I guess you are using the older version of nQuery (e.g. V3.0), whereprograms MTE0 and MTE1 can be used for sample size calculations inequivalence settings both for two-group (i.e. parallel) designs and forcross-over designs. In both cases the same formulae are used without theprogram knowing which situation it is dealing with.In case of a two-group parallel test the number of subjects per parallelgroup (n) is calculated and assuming equal n's the total sample sizewill be 2n. The variance of difference in treatment means will be:VAR(diff) = VARe * (1/n + 1/n) = VARe * 2/n.In case of a two-way cross-over design the number of subjects persequence group (n) is calculated and the total number of subjects willalso be 2n. The variance of difference in treatment means will be here:VAR(diff) = VARe * 1/4 * (2/n + 2/n) = VARe * 1/n (using a cross-overmodel).So the variance for the cross-over situation should be a factor twolower than in the two-group situation. This factor 2 difference invariance corresponds to a factor square root of two in standarddeviation (or CV).In the newest version V5.0 you now have separate programs for thetwo-group tests and the cross-over tests, which makes life somewhateasier.Hope this helps you.Michiel van den Heuvel`
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