How sparse is too sparse?

From: "Robert L. James" rjames@rhoworld.com Subject: [NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 2:26 pm Dear group, I am a NONMEM user with some modeling experience (perhaps 8 PK publications mostly 2-cpt models with time varying covariates). A Pharm company has just approached me to do a simple PK analysis (Cmax, Tmax, half-life, and AUC) on some VERY sparse data. Although there are 150 patients, each patient has only one plasma conc sample following an oral dose on two separate occasions spaced 2 weeks apart (the expected half life of the drug is a few hours). The timing of the single plasma sample following the oral dose was appears to be randomly timed. I don't have the data and so I don't know how well spaced these single samples are. Is this hopeless? The data has already been 80% collected. There are no previous human PK studies. The only plan of action I can think of is to pool the data across patients and fit a simple one-compartment model with either zero- or first-order absorption following an absorption lag. I could also model interoccasion variabilility into the model. Has anyone tried to fit models to data this sparse (1 sample following each of two dosing occasions). Would I be just spinning my electrons to accept this assignment? ---Robert Robert L. James, M.S., M.Stat. Senior Biostatistician Rho, Inc. 100 Eastowne Drive Chapel Hill, NC 27514 (919) 408-8000 x 468 (919) 408-0999 (fax) rjames@rhoworld.com

From: Leonid Gibiansky lgibiansky@emmes.com Subject: RE:[NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 2:58 pm I think population PK would be more appropriate than pooling the data (If by pooling you mean just fitting all of them to one curve). I do not think that you will be able to estimate inter-occasion variability, I would ignore it. Two samples per person is not a lot, so you won't be able to investigate the model in details, but I would try it, population PK has more chances of success in this case than anything else. Leonid

From: fengyan yaf2+@pitt.edu Subject: RE:[NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 3:39 pm Population method should be better than pooling the data. Also for Pop PK, I doubt how precise you can estimate your parameters, because generally you need 1 sample /subject /parameter. So if you only have one sample per subject, then it will be hard to estimate every parameter, unless you fix some based on literature report and estimate part of parameter. Yan Feng

From: Nick Holford n.holford@auckland.ac.nz Subject: RE:[NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 3:46 pm Robert, Its unlikely you will be able to estimate much more than CL/F (and thus AUC if you want) from this kind of data. This is especially so if you only have trough samples. I cannot imagine that you would be able to estimate a lag time. At best you might be able to get CL/F, V/F and Ka. Perhaps this Pharm company would be better off Farming. 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] How sparse is too sparse? Date: Thu, June 10, 2004 3:51 pm Robert, As Leonid indicates, you won't be able to partition out inter-occasion variability with only 1 sample per occasion per subject. I agree with Leonid that you should analyze it using a pop PK model rather than to perform naive pooling. Also, you should point out the limitations of the design and clarify expectations with regards to estimating Tmax, Cmax, t1/2, and AUC. With such sparse sampling and depending on the timing of the samples I suspect that you will get a lot of shrinkage (bias towards the mean) in the empirical Bayes predictions for some of these parameters. At best you might be able to get a good population estimate of CL/F and its IIV from which you can provide information on AUC. Depending on the timing and underlying true model (e.g., 2-comp vs 1-comp) your sparse design may not provide reliable estimates of Tmax, Cmax and t1/2. Ken

From: "Serge Guzy" GUZY@xoma.com Subject: RE:[NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 5:09 pm Apparently, you will not be able to separate intra-individual variability(I mean epsilon) from inter-individual variability(omega). Therefore you will have to assume a fixed, known cste cv error (or any other error model). Serge Guzy; PH.D President POP-PHARM Head Pharmacometrics and Preclinical Statistics; Xoma

From:"Serge Guzy" GUZY@xoma.com Subject: RE:[NMusers] How sparse is too sparse? Date: Thu, June 10, 2004 5:29 pm I do not agree. (in reference to Yan Feng message, Date: Thu, June 10, 2004 3:39 pm [above]) If the sampling times are distributed in a clever fashion (usually log uniform distributed is a good sampling), then population PK has the ability to estimate all the parameters if you have enough patients. The MCPEM algorithm (algorithm optimizing the same fct as FOCE with interaction)has been tested on many models with more than 1 PK parameters with 1 sample per patient and there were no problems as long as the information was there. The only confounding factor I am pretty sure is always present is the intra-individual variability confounded with the inter-individual variability. Serge Guzy President POP-PHARM Head Pharmacometrics and Preclinical Statistics;XOMA

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE:[NMusers] How sparse is too sparse? Date: Fri, June 11, 2004 8:10 am Serge, I can certainly understand that Robert won't be able to separate out intra-individual variability in the PK parameters with only 1 obs/visit (i.e., inter-occasion or between-visit variability within a subject). But he should be able to separate out intra-individual variability in the response (i.e., measurement variability or sigma^2) from the inter-individual variability in the PK parameters since he is getting two measurements on each individual (one measurement on each of two visits). Of course if there is true inter-occasion variability it will be confounded with other sources and most likely will inflate the intra-individual variability in the measured response (sigma^2). Ken _______________________________________________________