population size and confidence power

From: "Lin Lin" llin@thresholdpharm.com Subject: [NMusers] population size and confidence power Date: Mon, April 4, 2005 2:31 pm Could anyone explain a little bit on how big the population size (6 or 1000) would be needed in a study in order to reach the enough confidence power at the final PK/PD model? Could NONMEN provide this information or this information has to be predetermined by a statistic program (SAS)? Many thanks. Lin Lin Threshold Pharmaceuticals 1300 Seaport Blvd Redwood City, CA Email llin@thresholdpharm.com

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: Re: [NMusers] population size and confidence power Date: Mon, April 4, 2005 3:27 pm Lin, SAS will not help you. You will need either a good consultant who knows the drug and can estimate the size based on his/her knowledge and intuition and/or a simulation study. The population size will depend on: Study design (dosing and sample times) Complexity of the PK behavior (one-exponential vs two-exponential vs. three exponential decay, linear or nonlinear, etc.) Precision of the PK measurements (intra-patient PK variability) Variability of the PK parameters (inter-patient PK variability) Precision of the PD measurements (intra-patient PD variability) Variability of the PK/PD parameters (inter-patient PK/PD variability) When you know these parameters (or guess based on either earlier studies or similar drugs), you simulate the study, fit the model and look on the results (parameter bias, precision, confidence interval of the parameter estimates). You may need to do it more than once to investigate how results depend on your assumptions. Simulations may include extra layer or uncertainty (about population parameters: rather than select values for simulations you may assume their distributions). As a rough estimate, 6 is definitely too small, 1000 should be sufficient. I would say 200-300 should be sufficient unless you have a high variability of PK and/or PK/PD parameters or strong non-linearity. Leonid

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] population size and confidence power Date: Mon, April 4, 2005 3:48 pm NONMEM (note spelling) is not designed to directly compute power. However, it is possible to use NONMEM (via simulation) to estimate the power of a design to test a particular hypothesis. IMHO any 'a priori' power prediction requires the user to specify: 1. The model parameters (CL, V, Emax, EC50, etc) and the effect size of interest e.g. 30% difference in CL in a sub-population or Emax with some particular value. 2. The random effect size e.g. 50% apparent CV in CL, (and V etc) plus 10% residual error. 3. The hypothesis testing procedure e.g. likelihood ratio test 4. A design e.g. 20 subjects with samples taken at 6 specified times 5. A model e.g. one compartment disposition with bolus input and immediate drug effect described by an Emax model Once you have thought about the problem and you can specify all these features you are in a position to explore the power of the design by varying the number of subjects in the design to see how power varies. You can use NONMEM to simulate a large number of studies with a particular design and then test the hypothesis for each simulated study. If 80 out of 100 such studies fail to reject the null hypothesis then you could conclude that the power of the design is about 80%. Your question is a bit ambiguous and perhaps you have something else in mind e.g. you want to estimate a confidence interval for a parameter of the model. The most robust method for doing this with NONMEM is to use a bootstrap approach (see http://wfn.sourceforge.net/wfnbs.htm for some background on how this might be done). Or perhaps you are interested in deciding which model is most suitable for making predictions of response. The posterior predictive check and similar procedures that use the model to simulate predicted values may be helpful (Yano et al 2001). Nick Yano Y, Beal SL, Sheiner LB. Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check. J Pharmacokinet Pharmacodyn 2001;28(2):171-92 -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] population size and confidence power Date: Mon, April 4, 2005 4:08 pm Oops... Nick Holford wrote: "If 80 out of 100 such studies fail to reject the null hypothesis then you could conclude that the power of the design is about 80%." This should have read: "If 80 out of 100 such studies reject the null hypothesis then you could conclude that the power of the design is about 80%. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] population size and confidence power Date: Mon, April 4, 2005 5:04 pm Lin Lin, To add to Nick's comments regarding the various quantities that need to be specified, for the hypothesis testing procedure (Nick's item 3 below) we must also specify the type I error rate (alpha). To this end, it is good practice to perform simulations under the null hypothesis of no effect and show that we only reject the null hypothesis alpha percent ( e.g., 5% if alpha=0.05) of the time. This is important as different estimation methods may perform differently regarding maintaining the type I error rate (see papers by Wahlby et al in JPP 2001;28:231-252 and JPP 2002;29:251-269). Inflated type I errors are likely to result in inflated estimates of power when using the test assuming that the type I error rate is maintained. Ken _______________________________________________________