ETA1 tending to zero in a simple model

Hi, I am currently model building with a neonatal PopPK dataset for a renally eliminated drug and have encountered the following problem: When I add serum creatinine level (SCR) or post-conceptual age (PCA) as a sole covariate, or almost any combination of two covariates, on the clearance model my ETA1 goes to 1.00E-04 as if I had over-parametrised, yet I only have one ETA term on the CL. This situation then triggers the failure of the covariance step due to a parameter estimate being to close to its boundary. What is the likely cause of this and what strategy can I pursue to avoid it? For completeness the relevant excerpts of a typical control file are given (using SCR as the sole covariate in this case): $SUBROUTINE ADVAN1,TRANS2 $PK TVCL=THETA(1)*EXP(THETA(3)*SCR) CL=TVCL*EXP(ETA(1)) TVV=THETA(2) V=TVV*EXP(ETA(2)) SC=V $ERROR Y=F+EPS(1) $EST PRINT=5 METHOD=1 $COVARIANCE Grateful for any help/suggestions/comments offered! All the best, -- Stephen Montgomery School of Pharmacy Queen's University Belfast 97 Lisburn Road Belfast BT9 7BL Tel: (028) 9097 2033

Dear Stephen, The covariate relationship that you are trying seems unnatural to me. The interpretation of THETA(1) will be the clearance for an individual with SCR=0, and CL will increase as an exponential function of SCR? I would suggest a parameterization with the covariates normalized to a typical value in the population (i.e. with SCR normalized to a typical SCR, TVSCR). A possible "power" parameterization for SCR: TVCL = THETA(1) * (SCR/TVSCR)**THETA(3) A linear effect of PCA could look something like this: TVCL = THETA(1) * (1 + THETA(4) * (PCA-TVPCA)) ; set boundaries for THETA(4) so that the expression between the brackets cant become negative With these two parameterizations the interpretation of THETA(1) will be CL for a typical individual (SCR=TVSCR and PCA=TVPCA). Furthermore it is from my recollection quite doubtful that serum creatinine by itself will be a good predictor of renal function in this population (Gordjani N. et al. Eur J Pediatr. 1988 Nov;148(2):143-5). Perhaps you should also look into some of the available algorithms to predict GFR in this population (modified Schwartz formula etc.). I hope that my small suggestions will help you resolve your problems. Best regards, Martin Bergstrand, MSc, PhD student ----------------------------------------------- Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University ----------------------------------------------- P.O. Box 591 SE-751 24 Uppsala Sweden ----------------------------------------------- [email protected] ----------------------------------------------- Work: +46 18 471 4639 Mobile: +46 709 994 396 Fax: +46 18 471 4003

Stephen, 1. I assume you are modelling a drug such as gentamicin, amikacin or vancomycin. 2. The model that Martin proposed is an empirical model. It is like the model proposed in the MDRD formula for predicting GFR (Wikipedia). Its the way that stastisticians 'think' but it ignores what is known about biology and thus cannot be relied upon for prediction. eGFR = 186 x (Scr)**(-1.154) x (age)**(-0.203) x (0.742 if female) x (1.212 if African American) Note the MDRD statisticians almost got it right for SCr. They estimated the SCr function was SCR**(-1.154) which is almost the same as the correct value of SCR**(-1). They got it more wrong however when they did not include weight in the model so it can never work properly outside a fairly narrowly defined adult population. Size enters indirectly via sex and race but otherwise this model is statistical madness. Martin's model can be made biological by fixing THETA(3) to -1 (but see below for a simpler solution). 3. The simplest mechanistic approach for using Scr is to assume that renal clearance is proportional to creatinine clearance (CLcr). At Scr steady state the drug renal clearance will be proportional to weight and inversely proportional to Scr. Thus a simple biological model would be: CL=THETA(1)*WT/Scr * EXP(ETA(1)) e.g. Grimsley & Thomson 1999 for vancomycin The disadvantage of this model is that THETA(1) is confounded with creatinine production rate (and a linear function of WT is not realistic over bigger weight ranges). If you use something like the Schwartz (1984) method for predicting CLcr then you can try: CL=THETA(1)*CLcr * EXP(ETA(1)) THETA(1) can now be interpreted as the fraction of CLcr that predicts the drug clearance. Note that the Schwartz method unfortunately predicts CLcr per 1.73 m**2 because of the belief that glomerular filtration rate scales with surface area. This is another piece of empirical stuff that is not supported by observation (Rhodin et al. 2009) Many drugs have a non-renal clearance component as well which you can try to estimate it like this: CL=(THETA(1)*CLcr + THETA(2)) * EXP(ETA(1)) 4. Because CLcr will be very closely related to weight (exactly how depends on the way that weight enters into the prediction formula) the effects of weight and Scr can be disentangled by standardizing the CLcr to 70 kg then adding an allometric scale factor. CL=(THETA(1)*CLcrSTD + THETA(2)) *(WT/70)**0.75 * EXP(ETA(1)) Now THETA(2) is the non-renal clearance expected in a 70 kg person. See Anderson et al (2007) where a more mechanistic way of predicting CLcrSTD in neonates is proposed. 5. Finally, you should consider a more realistic way of describing CL maturation than a linear function of PCA. When a large range of PCA is considered then maturation can be described by a sigmoid model (Rhodin et al. 2009, Anderson & Holford 2009). Unfortunately, all maturation models are necessarily empirical because they are based on time which itself explains nothing. Nevertheless, the sigmoid maturation model at least has sensible predictions at the extremes e.g. CL is zero at PCA=0 and CL approaches the adult mature value as PCA gets longer . 4. If you get an estimate of OMEGA for ETA(1) which is close to zero then you may indeed have found the Holy Grail of covariate searching. If you explain all the between and within subject variability with Scr then OMEGA will be zero! Best wishes, Nick http://en.wikipedia.org/wiki/Renal_function#Estimated_GFR_.28eGFR.29_using_Modification_of_Diet_in_Renal_Disease_.28MDRD.29_formula Grimsley C, Thomson AH. Pharmacokinetics and dose requirements of vancomycin in neonates. Arch Dis Child Fetal Neonatal Ed. 1999;81(3):F221-7. Schwartz GJ, Feld LG, Langford DJ. A simple estimate of glomerular filtration rate in full-term infants during the first year of life. J Pediatr. 1984;104(6):849-54. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M, et al. Human renal function maturation: a quantitative description using weight and postmenstrual age. Pediatr Nephrol. 2009;24(1):67-76. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH. Vancomycin pharmacokinetics in preterm neonates and the prediction of adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84. Anderson BJ, Holford NHG. Mechanistic basis of using body size and maturation to predict clearance in humans. Drug Metab Pharmacokinet. 2009;24(1):25-36. Stephen Maxwell Montgomery wrote: > Martin, > > Thank you for your reply. I have followed your suggestion for normalising the > SCR to the dataset median value but I am still stuck with ETA1=1.00E-04, as > before, irrespective of whether I model as SCR**THETA(x) or EXP(THETA(x)*SCR), > the second of which gives a significantly lower objective function value. > Likewise for centring PCA... > > The reason I wish to test SCR as a covariate rather than pursue a calculated GFR > approach is that the drug in question is nephrotoxic, and each patient's GFR is > likely to change over the course of treatment - I was hoping the SCR values would > be able to model that effect to some degree and thus reduce the unexplained > variability. Certainly scatter plots of estimated CL as a function of SCR from the > output of NONMEM run with either no model or an allometric weight model only for > both CL&V shows a trend to the naked eye of declining CL with increasing SCR, > which looks slightly more like an exponential decline than a linear decline in both > cases. Objective function values drop considerably when SCR is included as a > covariate, either alone or in combination with other covariates. > > All the best, > > -- > Stephen Montgomery > School of Pharmacy > Queen's University Belfast > 97 Lisburn Road > Belfast > BT9 7BL > > Tel: (028) 9097 2033 > ________________________________________