time variant covariate ?

Date: Thu, 10 Jun 1999 12:35:30 -0400 From: Nagaraja <nagaraja@ufl.edu> Subject: time variant covariate ? Dear NONMEM users, I am modeling the quinine population pharmacokinetics. I would like to analyze the relationship between the volume of PK parameters and the hematocrit. However, I have different values of hematocrit at each of the time points. Is it possible to input time variant covariable in a population analysis. Or is it better to analyze the relationship as PK-PD between quinine concentrations and the hematocrit. I am waiting for your kind suggestions and Thanks in advance. Raj N.V. Nagaraja, Post Doc. Res. Associate Dept of Pharmaceutics, University of Florida, Gainesville, FL-32610

Date: Thu, 10 Jun 1999 10:48:53 -0700 From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: time variant covariate ? Time-varying covariates can be handled. The easiest way is to approximate them as a step function as follows: A covariate is considered to be constant at the value specified on a given record, over the time period from the previous record to the current one. Thus, if covariate X has value 0 at time 0 and value 10 at time 10, one might add "other" records at times 2,4,6,8 with recorded values of X = 1,3,5,7, with values 0 and 10 at times 0 and 10, respectively. A PK parameter, e.g., clearance, which is a function of X, for example TVCL = THETA(1) + THETA(2)*X will then change in steps; TVCL will have the value THETA(1) + THETA(2) for the advance from time 0 to time 2; THETA(1) + 3* THETA(2) for the advance from time 2 to time 4, etc. If the covariate must change continuously, this too can be handled, but only by using differential equations and defining the function that yields X(T) in the $DES block. 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

Date: Fri, 11 Jun 1999 12:33:04 +0200 From: Mats Karlsson <Mats.Karlsson@biof.uu.se> Subject: Re: Nagaraja Dear Nagaraja, In addition to Lewis reply, I think an idea of Taright et al (abstract below) may be important. In short, variability between individual in a covariate may be differently related to the PK parameter than variability within a subject. E.g. hematocrit may vary between subjects but not be particularly related to the parameter in question, whereas changes in hematocrit within a subject can be a surrogate for a progressing disease that may be important for the clearance of the drug. One way of handling such differences are to make 2 covariates from the hematocrit (HEM), namely baseline hematocrit (BHEM), which is the starting (or average) value and delta-hematocrit (DHEM), the difference from the individuals starting (or average) value. Hope it was clear, I can't follow up on this discussion as I'll be away for two weeks. Best regards, Mats Presented at PAGE -97 http://userpage.fu-berlin.de/~page/index.cgi NON-STATIONARITY OF KINETIC PARAMETERS IN MULTI-OCCASION DESIGNS Namik Taright, France Mentré and Alain Mallet, INSERM U436, Mathematical and Statistical Modelling in Biology and Medicine 91 boulevard de l'Hôpital, 75013 Paris, France Several studies in pharmacokinetic literature reveal variations in time of individual kinetic parameters. An interesting one is that of Tornatore et al. (1995) about methylprednisolone pharmacokinetics during chronic immunosuppression in renal transplant. They showed variations in individual parameters between visits. They also showed an alteration in population characteristics of clearance and volume. These results indicate a non-stationarity of the parameters and also suggest individual trajectories that need to be modelled in view of therapeutic drug monitoring. We extend the work of Harrison and Stevens (1976) about non-constancy of parameters in simple linear regression to the context of population pharmacokinetics. Our work follows that of Karlsson and Sheiner (1993) who prompt the use of an inter-occasions variability model. We propose second-stage models accounting for the non-stationarity of individual parameters. These models relate pharmacokinetic parameters to covariates and comprise two effects. First, a so-called cross-sectional effect relating parameters to covariates at the first occasion, which accounts for the usual interindividual variability. Second, a longitudinal random effect accounting for the impact of time-varying covariates on the pharmacokinetic parameters across occasions. Estimation is done with conditional maximum likelihood after first-order expansion of the nonlinear regression model around Bayesian estimates of random effects using a pseudo-EM algorithm. Illustrations on simulated data sets are shown. Results based on several experimental designs with various number of subjects and occasions are given, including bias and precision of the estimates. Graphical techniques are used for model building. Based on Bayesian estimates of parameters and residuals of the second-stage model, these techniques might help for detecting the inadequacy of simpler models. Nested models are compared with adequate likelihood ratio tests. Usefulness of such models will be discussed. Tornatore, Reed and Venuto (1995) Ann. Pharmacother 29, 120 -124. Harrison and Stevens (1976) J. R. Statist. Soc. B. 38, 205 - 247. Karlsson and Sheiner (1993) J. Pharmacokinet. Biopharm. 21, 735 - 750 ________________________________________________________ Mats Karlsson, PhD Uppsala University Div. of Biopharmaceutics and Pharmacokinetics Dept. of Pharmacy/ Box 580, SE-751 23 Uppsala, Sweden Internet: mats.karlsson@biof.uu.se Phone: +46 18 471 41 05 Fax: +46 18 471 40 03

Date: Fri, 11 Jun 1999 14:27:21 +0200 From: Pascal Girard <pg@upcl.univ-lyon1.fr> Subject: Re: Nagaraja Thank you Mats for remembering us about Taright's work presented at PAGE97! One of my fellow here in Lyon is modelling pop PK of Tacrolimus in liver transplanted patients. Preliminary results will be presented at PAGE next week. Other very recent and not definitive results we have (not shown on next week poster) indicate that inclusion in the CL submodel of hematocrit or hepactic markers as transaminase, using a step function to interpolate the covariate -just as suggested by Lewis- and a multiplicative model, dramatically reduces the NONMEM objective function (-170 just for transaminase and -187 for transa & HEM). Graphics also indicate much better goodness of fit. However what I am puzzled about is the fact that, when introducing these time varying covariates, interindividual variability on CL and V is slightly increased, and intraindividual variability is decreased for the only additive term of error model (which is additive and multiplicative - I also have to say that most concentrations are through levels). Has anyone experienced this situation? Any comments on this? Cheers, Pascal Girard ------------------------------------------------------------------ Service Pharmacologie Clinique PG@upcl.univ-lyon1.fr Faculte RTH Laennec Tel : +33 (0)4 78 78 57 26 BP 8071, rue Guillaume Paradin Fax : +33 (0)4 78 77 69 17 69376 LYON Cedex 08 FRANCE http://www.spc.univ-lyon1.fr

Date: Fri, 11 Jun 1999 14:32:19 +0200 From: Pascal Girard <pg@upcl.univ-lyon1.fr> Subject: NON-STATIONARITY OF KINETIC PARAMETERS ... France, Namik, > NON-STATIONARITY OF KINETIC PARAMETERS IN > MULTI-OCCASION DESIGNS > Namik Taright, France Mentré and Alain Mallet, Avez vous publie ce travail sous une forme ou une autre? Pensez vous que votre methode soit implementable avec NONMEM, et si non votre programme peut il etre reutilise ou votre algorithme reimplemente avec Splus? Merci d'avance, Pascal Girard ------------------------------------------------------------------ Service Pharmacologie Clinique PG@upcl.univ-lyon1.fr Faculte RTH Laennec Tel : +33 (0)4 78 78 57 26 BP 8071, rue Guillaume Paradin Fax : +33 (0)4 78 77 69 17 69376 LYON Cedex 08 FRANCE http://www.spc.univ-lyon1.fr

Date: Fri, 11 Jun 1999 08:18:14 -0700 From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: Nagaraja Pascal, Assuming the baseline model does not have inter-occasion variability as a separate component, it makes sense that introducing a time-varying intra-individual covariate will decrease apparent intra-individual variability (epsilon variance): some of this variability was really inter-occasion variabiliy, which is now partly explained by the occasion-specific covariate. That it reduces the additive, ratherthan the multiplicative part of the error variance has no particular meaning to me. BeforeI paid too much attention to it, I'd try fixing the additive part to its original value, and seeing if the multiplicative part can compensate so as to yield almost as good a fit. I also can't say I have any immediate intuition about why inter-individual variability should go up; my guess would have been that it would stay about the same, and you do say "slightly," so perhaps it, too, is not meaningful (again, you might try fixing it to the original value and see if the GOF appreciably worsens). Lewis. 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