sample size

From: "Vijay V. Upreti" Subject: [NMusers] sample size Date: Thu, November 11, 2004 6:15 pm Hi all, I have this very simpe question regarding the minimum sample size for population analysis. I have plasma concentration time data from 4 large mammals. There are 10 sampling points and I was just wondering if I can use population analysis for this small sample size. I am aware that NONMEM can be used for modeling single subject data but will n=4 suffice for population analysis, some thoughts please. _______________ Vijay V Upreti Gradaute Student Pharmacokinetics-Biopharmaceutics Laboratory Department of Pharmaceutical Sciences University of Maryland, School of Pharmacy 20 Penn St., Baltimore, MD 21201 Voice: 410-706-7388 Fax: 410-706-5017

From:"Serge Guzy" GUZY@xoma.com Subject: RE: [NMusers] sample size Date: Fri, November 12, 2004 3:37 pm If the data are rich enough as you mention, 4 individuals would be enough to estimate population means and population variances as well as sigma. The results would certainly be very similar to the one obtained using individual fitting software(like Winnonlin). Serge Guzy President POP_PHARM

From:"GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr Subject: RE: [NMusers] sample size Date: Sun, November 14, 2004 3:54 am Hi Vijay, I would certainly not use populaton analysis with 4 individuals even if NONMEM or any other algorithm gives you estimates. Basic idea of parametric population analysis is to estimate parameter statistical distributions, more precisely the first 2 moments mean and variance, of a symetrically distributed random variable . I suggest that, without any fancy population software, you simply try to estimate the mean and variance from 4 simulated normally distributed values, then compute their standard errors of mean and variance. In a second step, try to fit your population model with NONMEM using the data of your 4 mammals and once again have a look at the standard errors of all your parameters (THETA and OMEGA). In both cases, you'll see how bad is the precision of your estimates and realize that they have very little values, except maybe for SIGMA since the estimates will be based on 40 values. The simple laws of statistics still apply in population analysis, which is a powerful tool but certainly not a magic one. Best regards, Pascal ========================================== Dr Pascal Girard EA 3738 Ciblage Thrapeutique en Oncologie Fac Mdecine Lyon-Sud BP12 69921 OULLINS Cedex France Tel 33 4 78 86 31 53 Fax 33 4 78 86 31 49 e-mail : Pascal.Girard@adm.univ-lyon1.fr

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se Subject: RE: [NMusers] sample size Date: Sun, November 14, 2004 4:13 am Hi, I disagree with Pascal. If you look upon the options: Population analysis, standard two-stage, nave pooling or throw away the result of your experiment, population analysis may well be the best option. I dont know anyone who has compared methods with as few as 4 subjects, but we looked at 8 subjects with rich sampling and found that pop analysis was better than STS for the situations we studied (AAPS PharmSci. 2000;2(3):E32). Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se

From: "GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr Subject: RE: [NMusers] sample size Date: Sun, November 14, 2004 4:31 am Hi Mats, I was certainly not recommanding STS neither. Having said this, does better means good estimates? I don't know the work you mention, but did you have a look at the confidence intervals? Did you know the exact structural and PK-PD model (simulated or real data set) ? How large were the random inter-individual variances? Did you have outliers? All this may affect your results with few individuals. That's why I was cautionning any population analysis (one or 2 stages) with only 4 individuals, unless you have adressed all those questions and accept to report your CI. Have a good Sunday, Pascal

From: "Mats Karlsson" Subject: RE: [NMusers] sample size Date: Sun, November 14, 2004 4:38 am Hi again, We looked at simulated data. Have a look at the paper for the details. I certainly agree that less data is less information, but you seemed to suggest that Vijay either should throw away his data or analyse them by some other means. Im still not sure which of the two you recommend. Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se

From: "Steve Duffull" sduffull@pharmacy.uq.edu.au Subject: RE: [NMusers] sample size Date: Sun, November 14, 2004 5:38 pm Hi Vijay (Pascal + Mats) In addition to the comments already - you could compute the amount of information in your current design and then get a feeling for how well a population method would be able to solve your problem. This would allow you to assess whether the design is sufficient to meet your needs vs the slightly different question does a particular tool (e.g. NONMEM) perform well with the data that you have. To do this, you would need to have some feeling as to what the most likely model and parameter values are, and it may well turn out that in some circumstances it is possible to learn about some parameters from as little as 4 intensively sampled subjects. If you have the sampling design, and some feeling for the likely model(s) and parameter values then I am happy to compute the information from the design for you... Steve Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm

From: "Mats Karlsson" Subject: RE: [NMusers] sample size Date: Mon, November 15, 2004 4:16 am Hi Steve, Vijay wrote: "I have plasma concentration time data from 4 large mammals." Would it not be more straightforward and logical to actually analyse the data rather than guess upon the model and then use an approximation to investigate how well the design can characterize it? Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se

From: "Steve Duffull" sduffull@pharmacy.uq.edu.au Subject: RE: [NMusers] sample size Date: Mon, November 15, 2004 4:23 am Mats If you know nothing about the drug - then I agree. However if the experiment was supposed to be answering a question then it is possible that the investigators may know something in which case the design could be assessed - this assessment could also answer the yet to be asked question ... 'how many more animals are needed [to answer the question of interest]?' Steve Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm

From: "GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr Subject: RE: [NMusers] sample size Date: Mon, November 15, 2004 4:44 am Hi Mats and All, The initial question of Vijay was: "I am aware that NONMEM can be used for modelling single subject data but will n=4 suffice for population analysis?. My answer still is that I don't think anyone can pretend building a population model with n=4. Now if the question is "May I take advantage of population framework for estimating individual parameters, and get better results than modelling single subject?" I agree that it may be worth trying. You simply have to keep in mind that the objective of this initial analysis with n=4 is getting "individual parameters", not population ones. Now I agree that it can also be considered as the very first step of a population analysis. For this latter objective, Vijay could use Steve's suggestion which is assessing how much mammals, points/mammals as well as value of sample times that would be necessary to estimate, with a certain requested precision, the population parameters. Best regards, Pascal

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se Subject: RE: [NMusers] sample size Date: Mon, November 15, 2004 5:15 am Hi Steve and Pascal, Steve, Even in the case you have some information about your system, I don't see how the performing an assessment on the design before analyzing the data is more informative than analyzing the data and then assess the appropriateness of the design. Your guess at what the true model is must be better after looking at the data. I can't imagine the situation where you would 1) guess at the appropriate model, 2) assess the design and find that it is not sufficient to characterize it, and therefore 3) throw away your data. You are always going to analyse your data so why not take advantage of the information you gain. Pascal, I just reacted to your statement "I would certainly not use populaton analysis with 4 individuals even if NONMEM or any other algorithm gives you estimates." As it seems, we all agree that population, or non-linear mixed effects, modeling actually may be the way to go here even if the amount of information is limited with only 4 subjects.* Also, I do believe we are interested in information about population parameters, not individual parameters (unless we want to treat these specific 4 large mammals). These individuals are of interest only because they can tell us something about the population. The information will be very scarce, but it will be information about the population. *My guess is that nonlinear mixed effects modeling may be best, but wouldn't be surprised is in some situations (balanced design, not very nonlinear systems, ...) nave pooling could give more precise and less biased estimates for some population parameters. Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se

From: "Steve Duffull" Subject: RE: [NMusers] sample size Date: Mon, November 15, 2004 6:36 am Hi Mats and Pascal Firstly, Mats I agree that analysing the data is always the sensible option (never throwing data away). Secondly, I am not in absolute agreement with Pascal --- it is possible that the population characteristics of some drugs may be able to be determined with as little as 4 patients/animals. For argument, if in the example cited, the system were adequately described by a 1-cpt first order input-output model with exponential BSV on all parameters and mixed residual error function and you had 10 samples per animal for each of the 4 animals and the sampling times extended for at least 3 half-lifes then it is possible to estimate CL, V, Ka and BSV(CL, V, Ka). The standard errors of the BSV parameters are not going to be great but not terrible (approx 70-80%). Estimating the proportional component of the residual variance will be for all intents and purposes not possible. Thirdly, analysing the data using NONMEM and then assessing the design helps to learn about deterministic identifiability issues - i.e. are all parameters (fixed effects and variance effects estimable). I believe that in some cases it is important to be informed from both what is theoretically possible to learn from the design as well as to learn from the actual data gathered from the performing design itself (they may be different things). Steve Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm ______________________________________________________