# PharmPK Discussion - Posed Stat Question about a Phase I - 3-way cross

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• On 11 Aug 2000 at 14:28:04, "Jack Jenkins" (jack.jenkins.at.Covance.Com) sent the message
`We have a 3-period, 3-sequence cross over design in which we would liketo analyze for food effects.  The study design:Sequence 1: A B CSequence 2: B C ASequence 3: C A Bwhere:  A is fasted             B is low-fat meal             C is high-fat meal7 people are assigned to each sequence.  For period 1, 12 people (4 persequence) will be dosed on day W and 9 people (3 per sequence) will bedosed on day X.  All 21 people will be dosed for period 2 on day Y andall 21 people will be dosed for period 3 on day Z.Normally we would use the following model in which period has 3levels:y = sequence + subject(sequence) + period + treatmentFor the above study, we are considering using the same model in whichperiod has 4 levels.  Do you think this will work or do you have anyother suggestions?Thank you for your time.Jack Jenkins`
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• On 12 Aug 2000 at 17:33:02, ml11439.-at-.goodnet.com sent the message
`Dr.Jenkins,    One possible statistical model is repeated-measures analysisof variance. In this case the sequences would be the differenttreatments, and the differences in bioavailability would be thetreatment effects. If the measured treatment effect (F) does nothave a normal distribution, then a nonparametric approach in theform of a Friedman Statistic could be applied.     Recent statistic books such as Daniel's Biostatistics or Glantz'sPrimer of Biostatistics have chapters on repeated-measures analysisof variance and the use of the Friedman statistic in the nonpara-metric case.     If there is covariate affecting bioavailability in addition tothe treatment (diet sequence), then an analysis of covariance studydesign could be used. This is found in more advanced statistic bookssuch as Dowdy's Statistics for Research.                           Mike Leibold, PharmD, RPh                           ML11439.aaa.goodnet.com`
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• On 14 Aug 2000 at 19:49:27, wang.yamei.-at-.kendle.com sent the message
`I think as soon as we have enough wash-out period between day X and day Yor day  W and day Y, we don't need treat that model as 4-level. Otherwisethe whole cross over design and model will be ruined.Yamei WangStatistical Programmer/BiostatisticianKendle International Inc.`
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• On 16 Aug 2000 at 12:09:29, "Carol Roby" (croby.-at-.stagnes.org) sent the message
`A good site for stats info and online calculator scripts is:http://member.aol.com/johnp71/javastat.htmlCarol A. Roby, PharmD, MSClinical PharmacistSt. Agnes Hospital900 Caton AvenueBaltimore, MD 21229410-368-3109`
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• On 16 Aug 2000 at 12:11:10, "R.A. Fisher" (ra_fisher.aaa.hotmail.com) sent the message
`Hi Jack/All,I thought I would hopefully be able give you some guidance regardingyour query.  My thoughts are split into two parts.  Firstly, somepersonal thoughts on why you should look for a period effect ingeneral, and the second part I hope is the analysis I think youshould undertake.Why look for period effect--------------------------There is often no good reason to suspect a period (or centre) effectin a PK or biomarker study.  These effects shouldn't, in theory,exist.  There is often no true physiological reason for thesedifferences.  Unfortunately, in the real world these differencesfrequently exist in the data derived from multi-centre or multipleperiod studies, and the magnitude of these effects can be very large.The obvious suspects are differences in the aquisition, storage,transfer and analysis of the samples.  This potential additionalvariability/bias has to be considered.  If my biomarker has a CV of20% based on 50 subjects from a one centre study, will it be 20% if Ihad recruited just one subject from each of 50 centres ?   In theory,perhaps yes, in practice, perhaps no.Analysis--------This I hope is a fair re-ordering of your data, which may clarifysome of my comments.  I referred to the two occasions for the firstperiod as w and x, as per your email.  The first 12 subjects ascohort 1, and subjects 13-21 as cohort 2.   For simplicity, I havecalled the first 4 subjects 1-4, although I know you would haverandomised the subjects within cohorts.Data        per1   per2   per3       Occ  w  x   y      zsub 1-4     a  .   b      csub 5-8     b  .   c      asub 9-12    c  .   a      bsub 13-15   .  a   b      csub 16-18   .  b   c      asub 19-21   .  c   a      bMy opinion is that w and x should be linked under the per 1 banner,as two levels under per 1.  These two levels are intrinsically moresimilar to each other than per 2 and per 3 (the first time thesubjects enter the study).  This "w versus x" contrast is of interestin the preliminary analysis.Some things become more obvious with this layouti) differences between 'w' and 'x' is a between subject comparison.ii) differences between sequence is a between subject comparison.iii) differences between period is a within-subject comparison.iv) differences between tmt's is a within-subject comparison.Thus the 'technical' ANOVA (and degrees of freedom) can be written as:            d.f.w versus x   1    (compare to subject error)sequence     2    (compare to subject error)Subject      17tmt          2    (compare to residual error)per          2    (compare to residual error)total        24Residual (+ everything else(e.g. interactions)) = 2 d.f. for eachwithin comparison for each subject less 2 for period, less 2 for tmt.Hence 2 * 21 - 2 - 2 = 38.  Hence the good news is the d.f. add up,and we have N-1 (63-1) total d.f. = 62 (24 from above, and 38residual).Our 'weak' between subject contrast of the 'w versus x' to thesubject to subject error, will guide us to the appropriateness ofinvestigating period effects at the within-subject level.  Thesequence effect should (I haven't checked) be orthogonal to the 'wversus x' comparison.The reason I wrote 'technical' above the ANOVA table is that I'm notcompletely sold on this analysis.  The confounding with cohort,combined with the low power of this contrast, doesn't seem great.Similarly, I do not like a 'sequence' effect, because I think thepresence or absence of this effect has more to do with whether 7subjects happen to be giving a higher response than 7 others, ratherthan anything to do with the sequence of treatments they actuallyreceived.  However, I think your consideration and definition of thisproblem was wholly merited.I hope this helps,good luckRA Fisherp.s.I would use the reverse williams square for subjects 13-21. That is,sequences "a c b", "c b a", and "b a c".  This ensures that anypotential differencial carry-over is minimised.`
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