# PharmPK Discussion - Statistical method used in PK data analysis

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• On 22 Jul 2016 at 17:28:36, QRW (wxmwqr.-a-.163.com) sent the message
`Dear all，I have a problem about the statistical method used in PK data analysis.Total 4 subjects. Each of them did two PK studies(PK1 and PK2). PK1 served as self-control.Responses of PK1 are 204.9, 199.3, 225.6 and 256.10. Responses of PK2 are 341.5, 390.0, 330.6,368.9.Two statistical analysis methods were used on the SPSS.  Statistical power was calculated fromG*Power3.First, wilcoxon signed-rank test was used. The p value is 0.068, and statistical power is 0.966.Second, we use the paired-t test after log transformation. The p value is 0.016, and statisticalpower is 0.982.For these two methods, the p values show differences.  Consequently, the conclusions are opposite.My questions are:1) Is there something wrong in the above statistical analysis?2) Why the results of these two methods do not match?  (Usually if there is adequate statisticalpower, these two methods should draw same conclusion)3) Which method should be used in this case?4) In this study, 4 subjects get great statistical power. Is it necessary to increase the number ofsubject?Thanks in advance, :-)Xiaoming`
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• On 24 Jul 2016 at 10:50:50, Peter Bonate sent the message
`Given the number of subjects you have you should use a nonparametric test.  The results of your testare difference because they are different tests and are based on different assumptions about thedistribution of your data.  Given only 4 observations per group, the normality assumption for theT-test is hard to verify.I'm not sure I understand why you are looking at post-hoc power.  The power of a test is somethingto be considered before you do the experiment.Pete Bonate`
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• On 24 Jul 2016 at 11:01:48, Masaki Hiraoka (GCA02464.-at-.nifty.ne.jp) sent the message
`Hi, XiaomingFirstly, I'd like to confirm if the following my understanding is correct:1. You are comparing a PK parameter obtained in two conditions, 1 & 2, in the same subjects byone-way crossover design.2. You have a confidence of no sequence effects on the PK.3. The p-value you mentioned means alpha on the null hypothesis of PK1=PK2.4. The statistical power you mentioned means 1-beta, where beta stands for PK1PK2.5. You are thinking some doubts on the statistical analysis you made.I'm not a statistician and do not use SPSS but have some suggestions for your questions:1) The two methods calculate statistics in two different ways and usually differ from each other.2) Because the statistical methods stand different assumptions on the distribution of the values.3) It depends on what prior information you have on the distribution of the PK and on the studydesign.4) If you do not have a confidence on the distribution of the PK, you need more PK values to confirmthe assumption. This also means, if you need to estimate the degree of the difference in PK moreaccurately, you need more samples.Hope this helps,Masaki`
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• On 24 Jul 2016 at 11:09:09, zhigangjiang (zhigangjiang.at.gmail.com) sent the message
`	The statistical method is according to your data type. I dont understand why you choose wilcoxon?paired-t test would be better because you just had two group,and one of them used as self-control.`
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• On 25 Jul 2016 at 09:08:16, Atish Salunke (atish_azad.-at-.yahoo.com) sent the message
`	Dear Xiaoming,In my opinion the sample size is very less, power is post hoc analysis and depends on variation indata, lesser the variation less number of subjects required that does not mean you use foursubjects, the moment you are doing this there is good chance on either end to miss the truevariation of population.If the same subjects are used then paired T test is good choice.What is your objective/Hypothesis?Are you comparing PK1 Vs PK2?What values it represent when you say PK1 and PK2 are these Cmax, AUC, Tmax ....etcThere are statistical methods established for PK statistical analysis.Regards,Atish`
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• On 25 Jul 2016 at 11:05:06, Gordi, Toufigh (TGordi.aaa.nektar.com) sent the message
`Hi Xiaoming,The purpose of any significance test is to investigate whether there are differences between twopopulations with regards to a specific outcome. To do so, we sample a number of subjects from onepopulation and then compare the outcome of interest to another sample with a number of subjects frompresumably another population. The idea is that the observed differences are so far away from beingcaused by mere chance that we can conclude it is unlikely that the two populations (from which wehave sampled) are the same. A major factor in this analysis is that subjects in our sample arerepresentative of the broader population so any conclusions made based on comparing samples arevalid for the larger population. So I'd like to answer your question by asking you this: Do youreally believe that 4 subjects truly are representative of the larger population? If not, there isno reason for you to do any significance test.In more general terms, what is the goal of the project at an early stage of development? People gettoo focused on significance testing based on extremely small number of subjects and at very earlystages of the development. In my opinion, instead of looking for differences based on limited datafrom small samples one should focus on learning the system under investigation and use that to planfuture studies to learn even more until there are compelling evidence that there is enough knowledgeto move ahead and have a proper head-to-head comparison. I am a little biased so by learning I referto developing mathematical models that relates various factors of a study (e.g., dose,concentration, ...) to an outcome. Once the relationship between those factors and the outcome isestablished, one will have more confidence in designing and performing studies that test asignificant difference between various populations. In fact, one can look at the number of subjectsnecessary, type of subjects, probability of success with each study design, and more using thesemodels.Toufigh`
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• On 25 Jul 2016 at 11:08:22, Roger Jelliffe (r.jelliffe.aaa.usc.edu) sent the message
`	Dear All:	This is not on the current subject, but if you are interested in doing things optimally, in away that leads to maximally precise dosage regimens for patient care, which I  would suggest is whywe are all doing this, then I would strongly urge you to use nonparametric (NP) methods forpopulation PK/PD analysis. They are not bound by the constraints of assuming the shape of theparameter distributions, and because of this, they get results which have truly maximum likelihoods,which are not limited by the constraining assumptions of normal, lognormal, bimodal, etc.  They alsodo better ar perceiving unsuspected subpopulations and outliers. The distributions simply are whatthey are.	I am attaching 3 papers for you all to consider [Sorry didn't see the papers and no attachmentsanyway - db ]. The real problem is that when you  use parametric procedures like so many seem towant to do (perhaps because the drug industry is not really interested in any form of dosage exceptone size fits all), they can never perceive the issue of precise dosage, as there is only one doseto consider, and one simply assumes it will hit the desired target exactly, and we all know that isnever so, simply because of the diversity among the subjects in the population.	Using NP models, one can also use multiple model (MM) dosage design to develop a dosage regimenthat specifically hits a clinically desired target goal with maximum precision (minimum expectedweighted squared error).Very best  regards to all,Roger JelliffeRoger Jelliffe MDProfessor of Medicine Emeritus, Founder and Director Emeritus,Laboratory of Applied Pharmacokinetics and Bioinformatics, USC School of Medicine,Consultant in Infectious Diseases, Children’s Hospital of Los Angeles`
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• On 25 Jul 2016 at 17:44:41, Nadeem Irfan Bukhari (nadeem_irfan.aaa.HOTMAIL.COM) sent the message
`Dear XiaomingIn the case under discussion, the number of subjects is very small, same population has been usedand distribution of data with this much lesser number of subjects is not verifiable thus,non-parametric paired test, i.e., Wilcoxon test is appropriate. However, the number of subject istoo small to get a validated outcome and generalizable inference. To avoid biasnss, the statisticaltest is considered before experimentation.Regards.Truly yours--Prof. Dr. Nadeem Irfan BukhariUniversity College of Pharmacy,University of the Punjab,Allama Iqbal Campus, Lahore-54000Pakistan`
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• On 26 Jul 2016 at 09:57:39, Stan Alekman (stanley110.at.aol.com) sent the message
`Dr. Jelliffe,Can you post the three papers you mention? [Maybe just the citations - db ]Thank you.Stan AlekmanStanley L. Alekman, PhDPharmaceutical ConsultantsS.L. Alekman Associates Inc.Stanley110.-at-.aol.com`
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• On 27 Jul 2016 at 23:02:49, Roger Jelliffe (r.jelliffe.-a-.usc.edu) sent the message
`	Dear Stan:        You bet. They areBustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and NonparametricPopulation Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two MonteCarlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers andSubpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and SimulationPackage for R. Therap. Drug Monit. 34: 467-476, 2012.Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function, without aUrine Specimen. Am. J. Nephrology, 22: 320-324, 2002.Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals mostPrecisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.Therap. Drug Monit.  22: 346-353, 2000.I also threw in the one on creatinine clearance as it is really needed in patients with changingrenal function.All the best,Roger`
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• On 28 Jul 2016 at 09:30:35, Edward O'Connor (efoconnor.-at-.gmail.com) sent the message
`	Let's see.  You used a non parametric approach on non normalized data then a parametric approach onnormalized data!  What do the individual responses look like?  What tests did you do to determinefirst the selection of wilcoxon then selection of paired t then the selection of a transform tonormalize the data.  Did you run on transformed data in the t test first and did you run transformeddata in the wilcoxon?  When buying apples it is best to avoid oranges.`
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• On 28 Jul 2016 at 14:14:11, QRW (wxmwqr.-a-.163.com) sent the message
`Dear All,Thank you so much for the reply and the suggestions.The aim of our study is to test the changes of PK in two different physiological conditions (PK1 andPK2). Although the number of animal is limited, I agree that the paired-t test is a good statisticalmethod for our PK analysis because each animal serviced as self-control in the PK1 and PK2 studies.I will report the results with statistical analysis and visual analysis to confirm the PK changes.I read some of PK references, and find that there are a lot of different statistical methods usedfor PK data analysis. However, most of author did not explain why selected such statistical method.I would like to ask for a big favor.  Could you please share some of references or guidance, such asFDA guidance, in which talk about or give some criteria for using statistical method in PK dataanalysis?Thanks JXiaoming`
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• On 28 Jul 2016 at 22:46:14, Roger Jelliffe (r.jelliffe.-at-.usc.edu) sent the message
`Dear Xiaoming:        The FDA is stuck in parametric methods, as they let themselves be regulated by the industrythey are supposed to regulate. They are mostly oriented about what the industry  wants, and in myopinion, while they do many good things, they are not concerned with optimal individualized dosageregimens, as they should be. They still go along with the industry's one size fits all for dosing.So, instead of setting standards as they should do, they behave in a totally passive form and arecontent with parametric approaches to modeling. I would forget any FDA guidance in PK/PD analysis.It simply is not the best.Again, you might look at:Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and NonparametricPopulation Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two MonteCarlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers andSubpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and SimulationPackage for R. Therap. Drug Monit. 34: 467-476, 2012.Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function, without aUrine Specimen. Am. J. Nephrology, 22: 320-324, 2002.Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals mostPrecisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.Therap. Drug Monit.  22: 346-353, 2000.See what YOU think after looking at these papers. The Pmetrics software for population modeling,including modeling of large nonlinear and interacting systems of multiple drugs together, isavailable at www.lapk.org. Michael Neely has done a superb job with this software. Relevant clinicalsoftware, BestDose, is also available there. Both are free.Very best regards,Roger JelliffeRoger Jelliffe MDProfessor of Medicine Emeritus, Founder and Director Emeritus,Laboratory of Applied Pharmacokinetics and Bioinformatics, USC School of Medicine,Consultant in Infectious Diseases, Children’s Hospital of Los Angeles`
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• On 1 Aug 2016 at 12:26:52, Jaime Algorta (jaime.algorta.at.ehu.es) sent the message
`Dear Xiaoming, with only 4 you cannot use t-test, even after log-transform because normality cannotbe assumed. The non-parametric Wilcoxon is preferred.Regards,JaiPhone`
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