Sample Size

From: Alison_Carter@eisai.com Subject: Sample Size Date: Mon, 12 Jun 2000 11:37:58 -0400 I am an experienced NONMEM user reagrding retrospective studies, however I am now planning a prospective study and I have a question regarding determining an appropriate sample size. I userstand the concept of performing simulations using different sampling strategies and sample sizes until the desired parameters are estimated to within an acceptable amount of error, but how do I determine what is an acceptable amount of error? Any help on this matter would be greatly appreciated. Thanks very much. Alison Carter

From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: Sample Size Date: Mon, 12 Jun 2000 09:34:05 -0700 A difficult question. Unfortunately, it's entirely up to you; there is no general rule. The basic theory (decision theory) assigns costs and probabilities under various courses of action to all relevant states of nature and then advises taking the course of action with least expected cost. The probabilities are where the "acceptable amount of error" come in. In this spirit, you might ask yourself how big a mistake you could tolerate without substantial loss, or some similar question to determine your tolerable range of uncertainty. Generally, for parameters affecting dosage magnitude, e.g. clearance, it is believed (without much empirical evidence one way or the other) that +/- 25 50% is sufficient ... LBS. -- _/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu) _/ _/ _/ _/_ _/_/ Professor: Lab. Med., Bioph. Sci., Med. _/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626 _/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)

From: "Peter I. Lee 301-594-5666 FAX 301-480-8329" <LEEP@cder.fda.gov> Subject: Re: - Sample Size Date: Mon, 12 Jun 2000 12:51:57 -0400 (EDT) Alison, One way to determine the sample size is to estimate the power of the pop PK study. This includes the alpha and beta errors. For example, if you are planning for a study to identify potential drug-drug interaction (DDI), and will calculate difference in AIC between two models, one with and the other without the potential inhibitor/inducer as the covariate. The null hypothesis can be "no clearance difference (Cl,mono -Cl, combined =0)", and the alternative hypothesis can be "a clinical significant difference in clearance (depending on the toxicity of the drug, say 30%)". With estimated inter-/intra- subject variability in PK parameters and considering study design (sampling scheme, dosing time, compliance pattern, include full profile or not, ) you can then simulate (say 200 times) the pop PK "virtue data", assuming the alternative hypothesis. Then the data can be fitted to the two models, with the significance in delta AIC set to p=0.01 or other values. The power of identifying the clearance difference is the ratio of the number of replicates showing significant DDI to the total number of replicate (200). Use the same method to estimate false positive rates, by assuming the null hypothesis (ie delta clearance = 0). You can try several designs and numbers of subjects and determine which ones will give the reasonable power (say ~80%) and false positive rate (say <5%). In addition to the power, the accuracy & precision of the estimated clearance difference will need to be considered as well. Peter Lee Associate Director, Pharmacometrics OCPB/FDA

From: "Stephen Duffull" <sduffull@hotmail.com> Subject: Re: design of PK experiment Date: Tue, 13 Jun 2000 16:26:32 BST Hi Alison An alternative method for designing a population PK experiment would be via assessment of the population Fisher information matrix. A variety of different designs could be evaluated relatively quickly and the best design (based on say the required precision of the parameter estimates) chosen. The design therefore can be based on a number of factors such as the total number of blood samples, the desirable maximum number of patients, the number and timing of blood samples per patient. Evaluation of the population Fisher information matrix would be much more efficient that performing simulation (especially when 200 simulations may be needed per design). A theoretic approach has been developed for evaluation of the matrix and is available via: http://hermes.biomath.jussieu.fr/pfim.htm or you could contact one of the authors: Sylvie Retout (retout@biomath.jussieu.fr) Steve Duffull (sduffull@pharmacy.uq.edu.au) France Mentre (mentre@biomath.jussieu.fr) Hope this helps Steve ============= Stephen Duffull School of Pharmacy University of Queensland Brisbane QLD 4072 AUSTRALIA Ph +61 7 3365 8808 Fax +61 7 3365 1688