Dear Orlando, I think Martin has put the matter to bed in terms of how you ought to parameterise your model. One more thing to consider is that depending how rich are your data, your model might start getting over parametrised. In this case fixing volumes to known physiological values is a good idea. I don't agree with Elke that infusion of metabolites is unethical, and luckily for you neither did Lotsch et al CPT 1998 63;629-39. Morphine is a common drug with well characterised active metabolites, so you should find enough information in the literature to fix volume parameters if needed.
Best wishes, Joe PS All models are wrong, some are useless ________________________________ From: [email protected] [[email protected]] On Behalf Of Martin Bergstrand [[email protected]] Sent: 23 May 2012 18:56 To: 'Nick Holford'; 'e.krekels'; 'Carlos Orlando Jacobo Cabral'; 'nonmem users' Subject: RE: [NMusers] VD as a fraction of another VD Dear Elke, Orlando and Nick, I have to give Nick my full hearted support in this question. Parent drug/metabolite models are common practice in population PK and there should be a kind of best practice for how to parameterize these instead of inventing one new way after another. I do not doubt that the Knibbe model gives an excellent fit to that data and is predictive with respect to external data. That is not the point, the point is that an identical fit to the data could have been obtained by another parameterization that makes for a much more straight forward interpretation. The volume of distribution for the metabolite (e.g. M3G) is unidentifiable in the exact same way that the volume of distribution is unidentifiable for any drug where only data following oral administration is available. The estimate of both Volume and CL for the metabolites will be estimates over Fmet (i.e. the fraction of the parent compound that forms the metabolite). To estimate V2 as a fraction of V1 is a pointless parameterization that serves no purpose. It is reasonable to believe that there will be a high correlation between the volumes of distribution (e.g. V1 and V2) and this can be assessed by applying an OMEGA BLOCK to estimate the covariance (e.g. OMEGA1 and OMEGA2, see below). V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine V2 = THETA(2)*EXP(ETA(2)) ; central volume for M3G/Fm3g $OMEGA BLOCK(2) 0.1 ; VAR_V1 0.08 ; COVAR_V1_V2 0.1 ; VAR_V2 The outcome of this could be that the estimated covariance corresponds to approximately 100% correlation. In this case it is still not clearly justified to reduce the model to assume the same OMEGA variance for both parameters since the magnitude of variability could still differ between the two parameters. To assume 100% correlation but different variances can be done with this parameterization: V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine V2 = THETA(2)*EXP(ETA(1)*THETA(3)) ; central volume for M3G/Fm3g Where THETA(4) relates the standard deviation of V2 to the standard deviation of V1 random effect. This model is hierarchically related to a parameterization that is mathematically equivalent to the parameterization in the Kibbe model: V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine V2 = THETA(2)*EXP(ETA(1)) ; central volume for M3G/Fm3g This parameterization could very well turn out to be a sufficient characterization of the system but it is not true that it cannot be tested if a more complex model is better (see above steps). When it comes to the fraction of morphine that is metabolized into M3G and M6G it can as pointed out not be estimated without access to data following iv. administration of the metabolites or making very strong assumption such as fixing distribution volumes etc. Instead it is better to in the model have all morphine that is eliminated forms both M3G and M6G. This way the estimated clearance parameters for the metabolites will be (CLm3g/Fm3g and CLm6g/Fm6g). By the same logic that it isn’t identifiable to quantify the relative formation of M3G and M6G it is also impossible to characterize any additional rout of elimination. Reducing the model by setting similar volumes of distribution to the one and same parameter is nothing that I would practice and I think that it is more transparent to show the certainty estimates for each parameter in the model. Let me again stress that I do not question the predictive performance of the Knibbe model or that it has been useful for it’s purposes. I have no insight to this . However I don’t think that it has applied a type of parameterization that should be put forward as a good example since it has no advantages compared to the standard parameterization that I suggest that does facilitate a straight forward interpretation and easy comparison to results from other studies (with or without data following iv administration of M3G/M6G). Regards, Martin Bergstrand, PhD Pharmacometrics Research Group Dept of Pharmaceutical Biosciences Uppsala University Sweden [email protected]<mailto:[email protected]> Visiting scientist: Mahidol-Oxford Tropical Medicine Research Unit, Bangkok, Thailand Phone: +66 8 9796 7611 From: [email protected] [mailto:[email protected]] On Behalf Of e.krekels Sent: den 23 maj 2012 16:46 To: 'Carlos Orlando Jacobo Cabral'; 'nonmem users' Subject: RE: [NMusers] VD as a fraction of another VD Dear Orlando, There are multiple models available for morphine in children younger than three years. The model by Knibbe is based on a data-driven analysis, which causes this model to be empirical, but supported by the data. In addition to that and very importantly the Knibbe model is the only model that was proven to have accurate model performance in extensive internal and external validation procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm Res. 2011 Apr;28(4):797-811) Based on the available data, it was not possible to determine the distribution volume of the metabolites in the model. This would require data on the metabolites after direct intravenous infusion of the metabolites, but this is unethical and therefore not possible in children. We were therefore bound to include assumptions in our model. We have chosen to estimate the distribution volumes of the metabolites as a proportion of the central morphine compartment using the following code: V1 = THETA(1)*EXP(ETA1) ; central volume for morphine V2 = THETA(2)*V1 ; volume for M3G By using only 1 eta, we made the implicit assumption that the inter-individual variability in the volume of the metabolites is proportional to the variability in the central volume of morphine. This assumption cannot be proven or disproven with the available data, but to us it does not seem to be too unrealistic to envision that if one of the volumes increases or decreases the others will proportionally increase or decrease as well. Additionally, we found that when estimating the fraction for M3G and M6G independently, their 95% confidence interval overlapped significantly and the same was true for the distribution volume of the peripheral and central compartment of morphine. According to the rule of parsimony these parameters were therefore set to be equal. V3 = V2 ; volume for M6G equal to volume M3G V4 = V1 ; peripheral volume morphine equal to central volume For both adults and children morphine elimination through routes other than glucuronidation has been reported. In our model, with our assumptions, we found that when estimating a clearance parameter for elimination through other routes, 0 was included in 95% confidence interval of this parameter. According to the rule of parsimony we therefore did not include this parameter in the model. I would suggest that for your data you test inclusion of this parameter and decide based on statistical criteria and validation of your model whether you retain it or not. Regards, Elke ________________________________ From: [email protected]<mailto:[email protected]> [mailto:[email protected]] On Behalf Of Carlos Orlando Jacobo Cabral Sent: Tuesday, May 22, 2012 6:42 AM To: nonmem users Subject: RE: [NMusers] VD as a fraction of another VD Dear Nick, I want to try a previously reported PK model (Knibbe et al. Clin Pharmacokinet 2009; 48 (6): 371-385) to fit data similar to mine of morphine and its metabolites in which the volumes of distribution of metabolites were estimated as a fraction of volume of parent drug what seems to show good estimates. But also probably I´ll try to estimate the volumes of metabolites as separate parameters THETA with its corresponding variabilities, do you have any other suggestions?, thank you. And thanks also to Bill and Rob. Kind regards, Orlando. PhD student Carlos Orlando Jacobo Cabral Departamento de Farmacología, Lab.34 Centro de Investigación y de Estudios Avanzados del I. P. N. 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