Renal function as a covariate

Hans, I agree with you that what I wrote was not properly explained. Thanks for pointing this out. My previous comment was related to a question about time-varying covariates. You raise other important issues about how to use renal function as a covariate so I have re-named this thread and offer the following explanation. CLCR, as I proposed using it, should be a size standardized value -- I should have used the term CLCRstd to make this clearer. I suggest standardizing a prediction, such as that obtained from the Cockcroft & Gault formula (CLCRCG), to a standard size of 70 kg as follows: CLCRstd=CLCRCG*70/WT then using it as I proposed in the equation below. Note that WT is total body weight when used with CLCRCG because this formula was developed based on creatinine production rate expressed per kg of total body weight. f(age) is an empirical function centered on an age of 40 years. It is of exponential form to avoid extrapolation to negative values. f(renal_function) is CLCRstd/100 where 100 mL/min is a 'normal' CLCR for a 70 kg person. The model assumes CLrenal is linearly related to renal function but more complex models can easily be implemented. CL=(CLnon-renal*f(age) + CLrenal * f(renal_function) ) * allometric WT CL=(THETA(1) *EXP(THETA(2)*(AGE-40)) + THETA(3) * CLCRstd/100 ) * (WT/70)**0.75 This approach applies size standardization consistently to both non-renal and renal components of clearance (see for example Mould et al. 2002, Matthews et al. 2006 for applications). There is a problem with the method you propose of using non-size standardized CLCR to account for a component of clearance. Even if there is no renal elimination of a drug, then if there is a reasonable distribution of size in the sample being studied, then THETA(3) may appear to be different from zero because it reflects differences in size not just renal function. Note that using surface area as a form of size standardization for glomerular filtration rate has no theoretical nor experimental support when compared to theory based allometry (Rhodin et al. 2009). So I do not agree with standardizing CLCR to 1.73 m^2. I know this is frequently done but in fact this is just based on tradition and an out of date theory of scaling based on surface area (see Anderson & Holford 2008). The MDRD method of predicting glomerular filtration rate is a statistical absurdity which does not include any measurement of size for its prediction. I would certainly not recommend using it for any scientific purpose. The choice of units for CLCR is somewhat context dependent. The commonly used Cockcroft & Gault method (CLCRCG) returns values in mL/min so that is why I chose 100 mL/min for a 70 kg person. I would agree that in general it is better to report clearances as L/h/70kg. Describing CLCR as 'renal function' is also traditional but I prefer to calculate the ratio of the predicted CLCRstd in an individual to a standard 'normal' value to obtain a dimensionless renal function variable that is independent of size and is more directly related to the function of the kidneys. This renal function value also gets around the problems of units chosen to express CLCR as long as consistent values are chosen to compare the individual prediction with the 'normal' value. Please look at this recent review of the use of standards for PK Parameters which discusses this issue and also demonstrates how to account for maturation of renal functionfor ages less than 2 years (Holford, Yeo, Anderson 2013). Best wishes, Nick 1. Mould DR, Holford NH, Schellens JH, Beijnen JH, Hutson PR, Rosing H, et al. Population pharmacokinetic and adverse event analysis of topotecan in patients with solid tumors. Clinical Pharmacology & Therapeutics. 2002;71(5):334-48. 2. Matthews I, Kirkpatrick C, Holford N. Quantitative justification for target concentration intervention--parameter variability and predictive performance using population pharmacokinetic models for aminoglycosides. Br J Clin Pharmacol. 2004;58(1):8-19. 3. 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. 4. Anderson BJ, Holford NH. Mechanism-based concepts of size and maturity in pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32. 5. Holford N, Heo YA, Anderson B. A pharmacokinetic standard for babies and adults. J Pharm Sci. 2013;102(9):2941-52.

Hans, Thanks again for your willingness to engage in this discussion. See my reponses below. Best wishes, Nick

Dear Nick, Thank you for your extensive reply. I agree with your view, but I still have two comments. > There is a problem with the method you propose of using non-size standardized > CLCR to account for a component of clearance. Even if there is no renal > elimination of a drug, then if there is a reasonable distribution of size in > the sample being studied, then THETA(3) may appear to be different from zero > because it reflects differences in size not just renal function. I don't understand this. In this case there is no information about THETA(3) in the data, so any value should be considered suspicious, and I don't think that your approach will avoid this. If CLCR is reported in mL/min, why do any conversion to this value to get CL? Consider a drug A that has the same PK properties as creatinine. Assuming that CLCR (in mL/min, or L/h) has been estimated accurately (which cannot be true, but that is another discussion). Then the renal clearance of drug C is equal to CLCR. For modeling and dosing purposes, no further conversion is required. For any other drug B, assuming that its renal clearance is proportional to CLCR, the renal clearance is THETA(3) * CLCR, where THETA(3) is a proportionality factor, which, in my view, is expected to be independent of size, weight etc. This is more straightforward than your approach, avoiding unnecessary conversions. best regards, Hans Johannes H. Proost Dept. of Pharmacokinetics, Toxicology and Targeting University Centre for Pharmacy Antonius Deusinglaan 1 9713 AV Groningen, The Netherlands tel. 31-50 363 3292 fax 31-50 363 3247 Email: [email protected]