From: Paul Hutson prhutson@pharmacy.wisc.edu Subject: Subject: [NMusers] Using BLQ data for SIGMA Date: Mon, 07 Aug 2006 09:58:49 -0500 Good day. I am looking at some old dose escalation PK data in which the doses of drug were injected at higher doses in subsequent days. Short halflife and history allow me to reset the system before each dose. Interestingly, the concentration on the highest (and last) IV bolus dose for one subject is below assay quantitation levels (BLQ) at all time points, but was measurable (albeit at low end of assay validation) at the prior, lower doses. I have read prior postings about using BLQ data as the concentration falls below this limit. This does not appear appropriate in this case, where there is no measurable drug at any time point after the dose.Can anyone offer suggestions on how to incorporate this absence of measurable data? Excluding this dose from the pop fit is the easiest thing to do, but I don't like to leave this data behind. The evidence that the highest dose was associated with lower concentrations on the third day suggests perhaps enzyme induction, but mechanistically based upon what we know of this drug's metabolism, it is unlikely. I am inclined to think that this "lack of data" with BLQ on the highest dose may be more useful in fitting the SIGMA. That is, does it seem reasonable to include this dose event with BLQ results set at "0" (or at the limit of detection?) in order to show to the model that the assay results have low reliability at this concentration range? I look forward to your counsel. Paul -- Paul R. Hutson, Pharm.D. Associate Professor UW School of Pharmacy 777 Highland Avenue Madison WI 53705-2222 Tel 608.263.2496 Fax 608.265.5421 Pager 608.265.7000, p7856 _______________________________________________________ From: Mark Sale - Next Level Solutions mark@nextlevelsolns.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Mon, 07 Aug 2006 09:08:53 -0700 Paul, You are correct that deleting the data will result in bias, see Stuarts really, really good paper on this subject from a few years ago. My suggests are: 1. Use Winbugs. Winbugs is (IMHO), the only really correct way to do this - assuming your model is available in the PKbugs library. Your concern about possible enzyme induction may mean it isn't a standard libary model. WINBUGs does have an ODE solver for complex, nonlinear models, but my experience is that it is pretty hard to make work. Chuanpu Hu implemented this in a very elegant solution a few years ago, I think he had at least a poster somewhere about it. 2. Use the method described in the archives by Lewis et al. It is a numerical approximation to the normal cumulative distribution that, in theory correctly calculated the likelihood contribution of the left censored data. I can send you this code if your interested, it isn't too bad. 3. Wait for NONMEM V 6, which has suggestion #2 built in. Setting the value to 0 was one of the methods in Stuarts paper. I'm sure it wasn't the "winner", but I don't recall how well/badly it worked. WRT the parametric methods (2 and 3) I am concerned that the results may be very very sensitive to the assumption (BUGS makes much more limited assumptions). So, if possible, I would recommend PKBugs. Mark Sale MD Next Level Solutions, LLC www.NextLevelSolns.com _______________________________________________________ From: "Serge Guzy" GUZY@xoma.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Mon, 7 Aug 2006 10:25:31 -0700 I would recommend also to try the MC-PEM methodology. Both PDx-MC-PEM and S-ADAPT allow BQL handling. The contribution to the likelihood for BQL data are estimated by computing the integral from -infinity to LOQ (Stuart Beal method). Both programs allow you to write your own differential equation. Therefore your problem should be able to be handled using the MC-PEM program(s). Serge Guzy President POP-PHARM GUZY@XOMA.COM _______________________________________________________ From: jeffrey.a.wald@gsk.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Mon, 7 Aug 2006 14:23:40 -0400 Paul - It sounds from your posting that you believe the subject actually got the high dose as was intended. What is the likelihood of a dosing error, precipitation of drug, instability, or some other explanatory problem? Assuming that the correct dose was given when it was in fact not will also cause bias in your estimation and subsequent inferences. However, if you feel the dosing was more reliable than the assay results you could in principle include an error term for values that are BLQ but were still measurable. Just treating it as censored data ignores the knowledge contained in the assay results that happen to be falling below the lowest standard. How that would translate in practice with this particular dataset in which the structural model is being challenged by this profile from one subject on one occasion...I think we can only speculate. Good luck, Jeff _______________________________________________________ From: "Stephen Duffull" stephen.duffull@stonebow.otago.ac.nz Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 8 Aug 2006 09:41:22 +1200 Hi all It is my understanding that Stuart's paper and Lewis's comments on handling BLQ data were based on not all the data in a dose interval being censored. I'm not sure that leaving out an entire dose would result in bias - indeed if there were errors in the dose taken (compliance or otherwise) then incorporating the data at the nominal dose would lead to bias in itself. So - I don't think that BUGS, NONMEM VI, Monolix or even MCPEM will be a panacea for your problem (which to me is probably much more fundamental). We have code implementing the various methods in NONMEM (poster at PAGE) and doing it correctly in BUGS (presentation at PAGE several years ago) - but I don't think this is the issue. Steve -- Professor Stephen Duffull Chair of Clinical Pharmacy School of Pharmacy University of Otago PO Box 913 Dunedin New Zealand E: stephen.duffull@otago.ac.nz P: +64 3 479 5044 F: +64 3 479 7034 _______________________________________________________ From: Mark Sale - Next Level Solutions mark@nextlevelsolns.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Mon, 07 Aug 2006 14:56:11 -0700 Steve, Stuarts paper dose discuss only data missing from within a dosing interval. But, I am pretty sure that an entire dose interval data being missing will bias the result in a similar way. Consider the case where you have IOV (although I'm pretty sure it applies in the absence of IOV as well). If the mean CL is 1.0, with an IOV SD of 0.5, but any value of CL greater than 1.6 will result in all data being BQL, you will get an estimate of CL less than 1.0 (because you deleted some the data with CL > mean, but retained all the data with CL < mean). It occurs to me that the most likely cause(s) of Pauls observation are: 1. clincal error - (placebo, or nothing given rather than the correct dose), or someone left the samples on the benchtop overnight and the drug all degraded. 2. IOV being in an academic setting, you of course would never see problems like #1 - or any other problems with clincal trial conduct ;-) , but I assure you they occur in industry settings. Chuanpu - please comment, you know this area better than I (unless I'm wrong about all this, then please keep your opinions to yourself). Mark Sale MD Next Level Solutions, LLC www.NextLevelSolns.com _______________________________________________________ From: "Stephen Duffull" stephen.duffull@stonebow.otago.ac.nz Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 8 Aug 2006 10:41:40 +1200 Mark I hadn't thought of IOV as a contributor here. But taking your example a little further. If you had IOV greater than some arbitrary value that resulted in censoring of data as BLQ then you would presumably also get the other end of the spectrum too - with concs that are much higher than expected. So you would probably see some signal from IOV to support this phenomena - and indeed simulations from your model would predict BLQ observations for some dose levels. In this case you would have reason to believe that there is some need to account for BLQ data. In the absence of this signal it seems to me that execution error (which even happens in academia but of course at a much slower rate) is a much more probable cause. Steve -- Professor Stephen Duffull Chair of Clinical Pharmacy School of Pharmacy University of Otago PO Box 913 Dunedin New Zealand E: stephen.duffull@otago.ac.nz P: +64 3 479 5044 F: +64 3 479 7034 _______________________________________________________ From: bulitta@ibmp.osn.de Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 08 Aug 2006 03:55:24 +0200 Dear Dr Hutson, As proposed before, I would also rate an error in the clinical part or sample storage / sample transport most likely from my experience as a clinical monitor. What is written in the final study report or clinical report about the dose of the profile which was completely below the quantification limit (BQL)? By how much was the dose increased in this subject? You might try to test the ?high between occasion variability (BOV) hypothesis?: a) Estimate the PopPK model with BOV while ignoring the profile which is completely BQL. b) Estimate the PopPK model with BOV while setting all concentrations of the profile which is completely BQL to zero or to a very small concentration.** Both a) and b) will probably yield biased estimates. However, a) and b) might give you an idea about the range of ?possibly true? models. If these two models yield similar answers to your ultimate modeling objectives, this procedure might be sufficient and you might stop here. In case a) and b) yield substantially different answers, I would study the distribution of eta?s (outlier?) and the variance of the BOV terms in cases a) and b). If case b) yields an extremely large BOV for clearance (e.g. a BOV larger than the population parameter variability reported in literature for your drug and group of patients), you might argue that this is objective evidence for a clinical error and that case a) is the most appropriate model choice. (This assumes that there is no relevant auto-induction occurring in this patient.) **As a modification of case b), you might impute a more realistic profile for the BQL samples of the highest dose profile. You could e.g. use the average profile in this subject at the lower doses and multiply each concentration by the same factor so that the peak concentration of the imputed profile for the highest dose is e.g. 75% of the limit of quantification. I realize that this approach may lack statistical consistency, however, might be a practical approach before using more sophisticated analysis techniques. Hope this helps. Best regards Juergen -------------------------------- Juergen Bulitta, MSc Pharmacometrician, IBMP - Institute for Biomedical and Pharmaceutical Research Paul-Ehrlich-Str. 19, D-90562 Nurnberg-Heroldsberg, Germany -------------------------------- _______________________________________________________ From: "GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 8 Aug 2006 10:40:29 +0200 Dear All, Without entering into the debate of which method is a "panacea" for this issue (to quote Steve), I just want to mention a very elegant example of Stuart's method, with differential equations, implemented by Samson, Mentré and Lavielle with SAEM in Monolix software. It was presented at last PAGE meeting in the Lewis Sheiner session: http://www.page-meeting.org/?abstract=935 Cheers, Pascal Dr Pascal Girard EA 3738, Ciblage Thérapeutique en Oncologie Fac Médecine Lyon-Sud, BP12 69921 OULLINS Cedex France Tel +33 (0)4 26 23 59 54 / Fax +33 (0)4 26 23 59 76 Master Recherche aMIV, parcours Bio-Mathématiques et Pharmacologie http://miv.univ-lyon1.fr/ _______________________________________________________ From: "TRANCHAND BRIGITTE" Brigitte.TRANCHAND@adm.univ-lyon1.fr Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 8 Aug 2006 11:09:26 +0200 Dear all, The debate is very interesting. However, in this particular case it seems that it is about ONE patient in ONE occasion. What about the others at this last dose level? From my experience in such a case I keep the data of the patient in memory, but analyse the data omitting this patient. Omitting this entire occasion cannot lead to bias for the population analysis, except if the model is not stable (not enough patients, misspecification,...). I agree with Steve when he says that execution errors (problems in conservation, transfer to laboratory, drawing samples,...) may happen in academia but of course at a much slower rate. Are the samples assayed in the same handling? Brigitte ------------------------------------------------------------------------------------------ Dr Brigitte Tranchand EA3738 CTO Fac Médecine Lyon-Sud BP12 69921 OULLINS Cedex France Tel 33 4 26 23 59 53 e-mail : Brigitte.Tranchand@adm.univ-lyon1.fr ------------------------------------------------------------------------------------------ _______________________________________________________ From: Chuanpu.Hu@sanofi-aventis.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 8 Aug 2006 10:03:58 -0400 Dear Mark, Steve, and all, (By commenting here, I am implying that I don't think Mark is wrong about all this. ;-) ) It looks clear that everyone agrees that, if we trust the dosing info, then the correct way is to model BQL data. (For this purpose I like WinBUGS, but that may just mean that I don't know other software well.) The issue is what if we don't trust the nominal dose. It is of course interesting to investigate whether the dose/assay is wrong, however my guess is we may never know for sure. Similarly, I suspect it would be difficult finding conclusive evidence that IOV caused the BQL. In principle, dosing uncertainty can be modeled as well, e.g., in the spririt of (Mu and Ludden, "Estimation of Population Pharmacokinetic Parameters in the Presence of Non-compliance", JPP 2003), however this is more complex. In Paul's case, I would first look at the results of modeling BQL vs. deleting them, and see how much difference there is. This will give a sense of the robustness of the conclusions. Attempts to account for dosing error, or IOV, should give inbetween results. Ultimately, I think the issue is robustness of the conclusions, as we likely will not be able to quantify how uncertain we are about the dose. Chuanpu ------------------------------------------------------------------- Chuanpu Hu, Ph.D. Biostatistics sanofi-aventis 9 Great Valley Parkway, Room 242 Malvern, PA 19355-1304 Tel: (610) 889-6774 Fax: (610) 889-6932 ------------------------------------------------------------------- _______________________________________________________ From: Leonid Gibiansky leonidg@metrumrg.com Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 08 Aug 2006 10:57:31 -0400 It is interesting that BQL topic is so popular. In 1999 I asked a question how to treat BQL, and below is Lewis Sheiner reply (even at that time it was a very old topic) It looks like setting the BQL values to BQL/2 and using additive error of at least SD=BQL/2 approximates the problem well enough without need to wait for NONMEM VI, WinBugs or any other software. I am not sure whether you need to model BQL in this particular case, but if yes, NONMEM V is capable to deliver a reasonable answer if you have a reasonable model (more than one point should be retained if you need to use the entire BQL profile). Leonid _______________________________________________________ From: LSheiner lewis@c255.ucsf.edu Subject: RE: [NMusers] Using BLQ data for SIGMA Date: Tue, 05 Oct 1999 08:15:17 -0700 All - The BQL thing just doesn't go away ... I have a feeling we've been through this before. The BQL observations are left censored. They could be any value between 0 and QL. The likelihood contribution for such an observation is therefore the integral of the distribution of observations centered at the prediction, from 0 to QL. This distribution, unfortunately, cannot be normal since such a distribution implies that the "observation" BQL might be negative, so on might use log(y) vs log(f), or approximate the distribution of epsilon near 0 by a half-normal, or such. Unfortunately, this "fix" involves modifying the objective function so that it can include integrals like the ones I described above. That is not easy, and it is why I suggested as a simple expedient, 1. Delete all but the first in each continuous series of BQL observations 2. Set the remaining (first) one DV = QL/2 3. Use an additive plus proportional error model with the SD of the additive part >= QL/2. This should preserve whatever "information" the BQL possesses, and does not require modifying the likelihood. I admit I haven't studied this, but before resporting to elaborate schemes, I would like to see some evidence that this simple one has problems. I agree with Jim's issue with Leonid's solution; introducing discontinuities in the objective function is, it seems to me, more dangerous than approximating an integral with a point on the integrant, as I have suggested. LBS. -- Lewis B Sheiner, MD Professor: Lab. Med., Biopharm. Sci., Med. Box 0626 voice: 415 476 1965 UCSF, SF, CA fax: 415 476 2796 94143-0626 email: lewis@c255.ucsf.edu _______________________________________________________