End of semester MCQ and short answer question

From: "Nick Holford" n.holford@auckland.ac.nz Subject: [NMusers] End of semester MCQ and short answer question Date: Thu, July 14, 2005 8:54 pm Q 1. LLQ is the lower limit of quantitification. Do regulatory Pharmacometric groups endorse? a. Ignoring LLQ values b. Imputing LLQ values as 0 c. Imputing LLQ values as 0.5*LLQ d. Using the actual measurement i.e. ask the chemical analyst to tell the truth e. None of the above Q 2. Beal S. Ways to fit a pharmacokinetic model with some data below the quantification limit. Journal of Pharmacokinetics and Pharmacodynamics 2001;28(5):481-504 Has there been any advance on this in the last 4 years? 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: mmunsaka@tgrd.com Subject: RE: [NMusers] End of semester MCQ and short answer question Date: Fri, July 15, 2005 8:50 am Hello, I am also interested in this question and I a currently looking into this question. I have the following additional references (simple latex syntax) if this may be of use to you (and you have not already seen these). I don't think I have seen any regulatory recommendations on this issue and would be curious as to what the agencies think. I am also interested in other references that other people may have. Melvin Munsaka, PhD Takeda Global Research & Development Center, Inc. =======================================\begin{thebibliography}{99} \bibitem{Cox} Cox, C. (2005). Limits of quantitation for laboratory assays. \emph{Appl. Statist.}, \textbf{54}, 63-76. \bibitem{Clausen} Clausen, W. H. O., Tabanera, R., and Dalgaard (200X?). Solving the bias problem in censored pharmacokinetic data. \emph{ http://pubhealth.ku.dk/upload/application/pdf/f51d6748/rr-05-5.pdf}. \bibitem{Duval} Duval, V. and Karlsson, M. O. (2002). Impact of omission of data below the limit of quantification on parameter estimates in a two-compartment model. \emph{Pharm. Res.}, \textbf{19}, 1835-1840. \bibitem{Graves} Graves, D. A., Locke, C. S., Muir, K. T., and Miller, R. P. (1989). The influence of assay variability on pharmacokinetic parameter estimates. \emph{J. Pharmacok. Pharmacod.} \textbf{17}, 571-592. \bibitem{Jackson} Jackson,A. J. (1992). Inappropriate inclusion of non-quantifiable plasma concentrations in the estimation of exyent of absorption. \emph{Biopharm. Drug Disp.}, \textbf{15}, 629-634. \bibitem{Hing} Hing, J. P., Woolfrey, S. G., Greenslade, D. and Wright, P. M. C. (2001). Analysis of toxicokinetics data using {NONMEM}: {I}mpact of quantification limit and replacement strategies for censored data. \emph{J. Pharmacok. Pharmacod.} \textbf{28}, 465-479. \bibitem{Hoffman} Hoffman, W. P., Heathman, M. A., Chou, J. Z., and Allen, D. L. (200X?). Analysis of toxicokinetic and pharmacokinetic data from anaimal studies. In S. P. Millard and A. Krause (eds), \emph{Applied Statistics in the Pharmaceutical Industry With Case Studies Using S-Plus}. Chapter 4. \bibitem{Humbert} Humbert, H., Cabiac, M. D., Barradas, J., and Gerbeau, C. (1996). Evaluation of pharmacokinetic studies: {Is} it useful to take into account concentrations below the limit of quantification?. \emph{Pharm. Res.}, \textbf{13}, 839-845. \bibitem{Sadler} Sadler, W. A. and Smith, M. H. (1990). Use and abuse of imprecsion profiles: some pitfalls illustrated bu computing and plotting confidence intervals. \emph{Clin. Chem.}, \textbf{36}, 1346-1350. \bibitem{Tod} Tod, M (2005). Handling concentrations below quantification limit in population. Presentation at the 2005 PAGE Meeting.

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] End of semester MCQ and short answer question Date: Sun, July 17, 2005 11:34 am Thanks to those who took the test and responded to me. Not all responses were sent back to the open lists so I have anonymised all the responses. Question 1 ========== Extra marks were given to the PharmPK user who pointed out I should have used BLQ instead of LLQ. "I think what you meant to say in items 1(a) to (c) is "BLQ" (below the limit of quantitation) instead of "LLQ", since a value that is at the LLQ can just be reported as such as it is contained within the validated range." Quite correct! What I meant to ask would have been better expressed as follows. I have changed "LLQ" to "LLOQ" and use "quantification" (not "quantitation") for consistency with the FDA Bioanalytical guidance (see below). Q 1. LLOQ is the lower limit of quantification. Measured concentrations less than LLOQ are said to be below the limit of quantification (BLQ). Do regulatory Pharmacometric groups endorse? a. Ignoring BLQ values b. Imputing BLQ values as 0 c. Imputing BLQ values as 0.5*LLOQ d. Using the actual measurement i.e. ask the chemical analyst to tell the truth e. None of the above The most definitive material pertinent to Q1 came from the following quote from the Code of Federal Regulations. It was provided by a ex senior FDA person who would have dealt commonly with this kind of issue. This person and another current senior FDA person said they knew of no FDA guidance requiring the use of LLQ to modify data used for PK analysis. "Sec. 320.29 Analytical methods for an in vivo bioavailability or bioequivalence study. (a) The analytical method used in an in vivo bioavailability or bioequivalence study to measure the concentration of the active drug ingredient or therapeutic moiety, or its active metabolite(s), in body fluids or excretory products, or the method used to measure an acute pharmacological effect shall be demonstrated to be accurate and of sufficient sensitivity to measure, with appropriate precision, the actual concentration of the active drug ingredient or therapeutic moiety, or its active metabolite(s), achieved in the body." There is a 2001 Bioanalytical Method Validation guidance that defines LLOQ as concentrations with 20% CV ( http://www.fda.gov/cder/guidance/4252fnl.pdf). It says nothing that I can see about whether LLOQ should be applied when doing a PK analysis. Note that Bioanalytical Method validation statistics such as LLOQ are used to describe the properties of the assay. This guidance does not define how the concentrations are to be used. A subsequent 2003 Bioavailability and Bioequivalence document describes PK procedures but does not mention the use of LLOQ ( http://www.fda.gov/cder/guidance/5356fnl.pdf). There seems to be a common mis-perception that FDA requires the use of LLOQ in a PK analysis however no-one has provided any written evidence of this policy so far. My interpretation of these responses is that the closest answer to Q1 should be: "d. Using the actual measurement i.e. ask the chemical analyst to tell the truth" Question 2 ========== Almost full marks to the nmusers peson who gave a list of references of various opinions on dealing with BLQ values. Some credit was lost for using an obscure (Latex <grin>) character based formatting convention and providing a non-retrievable reference to recent work attributed to M. Tod. A prominent user of NONMEM responded: "The only advances have been I) my increasing conviction that whenever the pattern of BLQ values is consistent with the observed PK, that (a) [ignoring BLQ values], along with the adjustment described by Beal (2001) to account for the bias, is the way to go, and (II) the addition of a feature in NONMEM version VI that allows this sort of thing to be easily done." Nick

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: Re: [NMusers] End of semester MCQ and short answer question Date: Sun, July 17, 2005 12:26 pm Nick, Your option d. Using the actual measurement i.e. ask the chemical analyst to tell the truth" should help to limit LLOQ somehow but at the end you will still get some zero values that are measurements below LLOAATDCFZ (lower limit of assay ability to distinguish concentration from zero). Then, you will need to choose among 3 other options: a. Ignoring 0 values b. Using 0 values as 0 c. Imputing 0 values as 0.5*LLOAATDCFZ Remembering the advice of "a prominent user of NONMEM" (I am not sure whether this is the same user as your adviser, but I found on more than one occasion that the advices were good), I usually use (a). Do you have any examples where this would lead to the incorrect model? Also, have you found any examples where option (d) was better (resulted in a more precise or more stable model) than option (a)? Unfortunately, information concerning NONMEM VI is not relevant to the most of mortals except those few who were granted this tool (I guess, as a recognition of the special contribution to the NONMEM development). Thanks Leonid

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] End of semester MCQ and short answer question Date: Sun, July 17, 2005 12:58 pm Leonid, LL0AATDCFZ and its bigger brother LLOD (lower limit of detection) are just as arbitrary and capricious as LLOQ when it comes to PK analyis. I accept they can be helpful statistics for those involved in the care and feeding of bioanalytical methods. However, if the chemical analyst (or the computer connected to the measuring device) was required to report the truth then if the concentration was really zero it should report a random variable with mean 0 (assuming the measurement process does not get truncated at zero). The variance of this random variable is a component of the additive residual error we estimate every day for PK models. So I don't see any need to apply LL0AATDCFZ. Just give me the true measurement value. One thing is sure about the true concentration -- until sufficient time has passed for less than one molecule to be left in the body then the concentration is not 0. This is longer than most people live... Stuart Beal has offered some examples of what happens if answer (a) is used (treat BLQ values as missing). You can also find some more examples in Duval V, Karlsson MO. Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model. Pharm Res 2002;19(12):1835-40. I'm afraid I don't have any personal experience comparing the true measurement with the obscured values reported by chemical analysts. Nick

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: Re: [NMusers] End of semester MCQ and short answer question Date: Sun, July 17, 2005 2:14 pm Nick, Thanks for the reference, results seems very reasonable: if you ignore zeros, predicted concentrations may decay not as fast as they should (leading to lower CL, higher V). However, this might be strongly related to the design and sampling. In my examples, fraction of BQLs was relatively small (less than 5%), most zeros were very suspicious (related either to the non-compliance or data errors) because LLOQ was 3-4 orders of magnitude less than Cmax while sampling points were not that far from the dose to warrant zeros. With the good design, fraction of BQLs in the data set is small, and efforts that are needed to include those are not warranted by the gain that you may get from inclusion of those points. As to the true values, you may be forced to use special segment of the error model to account for the BQL measurements. This can be very similar to LLOQ/2 imputation with BQL variance fixed at (LLOQ/2)^2. My justification of the idea to ignore zeros (or not to use "true" values) is that we are not interested in the very fine details of the PK behavior (the deaper you look, the more compartments you may descover) and restrict the model to the range of concentrations that are relevant to your problem. Sampling should also be consistent with the goal of the study: samples should be located at characteristic points of the profiles (while BQLs are definitely not in that range/position). One can imagine situations when zeros are important: for example, if there is a sub-population with much higher CL: ignoring zeros may hide the fact that concentration decay for a sub-population is much faster than was expected, especially if the sample timing was not designed for the sup-population with the high CL. But even in this case, BQL values may help you to discover the problem with your design, but will not help to build the correct model: it is difficult to build correct model based on the very noisy measurement. If you do not have sufficient non-BQL time points to define the terminal phase and impute some BQL values (or use the true value that will be a reflection of the random noise generated by the instrument), the model for the subpopulation will be defined by the timing of the sampling point rather than by the actual CL. If you have sufficient number of non-BQL time points to define the terminal phase, ignoring the BQLs should not adversely affect the model. Leonid

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] End of semester MCQ and short answer question Date: Sun, July 17, 2005 3:25 pm Leonid, Your discussion agrees with what Stuart Beal wrote. In most cases treating BLQ values as missing is fine. In some special cases there is a small amount of useful info from knowing that it is BLQ (but not missing). Imputation of BLQ with LLOQ/2 is a quick and dirty way to partially recover some of this information. Nick _______________________________________________________