Re: Reporting Modeling Results

John, Leonid correctly points out that it makes no difference in terms of parameter estimation what weight is used for parameter 'normalization' because this is just a linear scaling factor. My colleague, Brian Anderson, and I have preferred to consider this 'normalising' weight as a standard weight. We do not try to make anything 'normal' but simply choose a scale that will provide us with a parameter that represents a standard human. We use a weight of 70 kg as the standard (Holford 1996). This makes it easier to compare parameters estimated in different populations, e.g. adults and children, because the parameters are scaled to the same standard size. Recently we have pointed out that use of a size standard with a suitable model for maturation allows the simple prediction of adult clearances from data collected in children (Anderson et al 2007b). We note that this cannot be done in the reverse direction i.e. adult data cannot be used to predict the maturational changes in clearance which occur in very young humans. Leonid mentions that results are "routinely reported as V/kg or CL/m^2, etc" but this is simply tradition without any discernible scientific rationale - especially the use of the square metre as the standardising factor. Drugs are not eliminated to any important extent via the skin so there is no mechanistic reason for this. The surface area method is a hangover of discredited theories of allometric scaling. The per kg method of scaling clearance is also a problem because it leads to the misguided viewpoint that clearance is larger in children in adults (Anderson & Holford 1997). Perhaps you can help your investigator colleague to read some of the published literature in this area so that he/she can get a clearer understanding of the size scaling issue. The bottom line: 'We conclude with the proposal that, at least in terms of pharmacokinetics, the widely quoted aphorism “Children are not small adults” should be changed to “Children are small adults — babies are young children.” ' Anderson & Holford 2007a Nick 1. Holford NHG. A size standard for pharmacokinetics. Clinical Pharmacokinetics 1996;30:329-332 2. Anderson BJ, McKee AD and Holford NHG. Size, myths and the clinical pharmacokinetics of analgesia in paediatric patients. Clin Pharmacokinet 1997;33:313-27 3. Anderson BJ, Holford NH. Mechanism-Based Concepts of Size and Maturity in Pharmacokinetics. Annu Rev Pharmacol Toxicol 2007a Oct 3; [Epub ahead of print] 4. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V and Holford NH. Vancomycin pharmacokinetics in preterm neonates and the prediction of adult clearance. Br J Clin Pharmacol 2007b;63:75-84 Leonid Gibiansky wrote: > > Hi John, > I think you can safely separate statistics/mathematics and clinical use. > I would fit the model in the shape and form suitable to get the best > results (normalized to a typical patient in your case) and then report > the results in the form most convenient for the clinical use. If this is > per-kg values, then report it as they request. If you look in the > literature, results are routinely reported as V/kg or CL/m^2, etc. > > On a side not, I am actually surprised that you got different results > with different scaling. For the allometric scaling with fixed power, two > parameterizations: > > CL=TCL*WT^0.75 and CL=TCL*(WT/10)^0.75 > > differ by the fixed factor > (1/10)^0.75 = 0.18 > > I am not sure how this can influence your model CI so strongly. I would > check how you stratify the bootstrap data sets. Could it be that > stratification on something else depend on parameterization? > > If you would estimate the power: > > CL=TCL*(WT/10)^THETA() > > then parametrization would be more likely to affect CI, but for the > fixed power I would look for other explanations of the differences. It > would be easier to discuss the model if you would attach the PK block of > the nonmem code. > > Leonid > > -------------------------------------- > Leonid Gibiansky, Ph.D. > President, QuantPharm LLC > web: www.quantpharm.com > e-mail: LGibiansky at quantpharm.com > tel: (301) 767 5566 > > John Mondick wrote: > > I would like to get some feedback from the group concerning the reporting > > of modeling results. I have a Pop PK model developed from data arising from > > 124 pediatric patients, age 1 to 48 months. All of the structural > > parameters have been scaled allometrically, with the median body weight > > used as the reference value. After accounting for body size, a covariate > > model was incorporated to describe maturational changes in CL for young > > children. The maturation of clearance was modeled using an exponential > > model proposed in: > > > > Andersen et al. Population clinical pharmacology of children: modelling > > covariate effects. Eur J Pediatr. 2006 > > > > Two parameters are estimated as part of this model * the fractional change > > in CL for a typical one month old patient (beta - estimated to be 0.76 > > (0.589, 0.96) for this analysis) and a maturational half-life (TCL - 3.82 > > (1.57, 6.95) months). CI’s are from the bootstrap. > > > > The problem that I am running into is how to report the modeling results. > > It seems very natural to me to report the model results normalized to > > median body weight (L/h/10.4 kg^0.75). One of the study investigators > > disagrees with me and would like to report the results on a per kg basis > > (L/h/kg^0.75). This seems to be counterintuitive to me, as I tend to think > > about what represents the “typical patient.” It also makes no sense to me > > to represent the CL in a one kg child. The argument is that reporting in > > this manner makes more sense to clinicians and that there is no such thing > > as a typical child. > > > > So in an attempt to appease the investigator, I fit the same model with no > > weight normalization. The estimated parameters are equivalent to what would > > be scaled from the weight-normalized model, but there is no covariance > > matrix (not surprising). It becomes problematic when the bootstrap results > > are considered * beta = 0.78 (0.005, 0.995), TCL = 3.90 (0.001, 6.018). > > Again, this is not surprising given that the covariate model is not > > centered. > > > > I have attempted to make several compromises, including reporting the > > parameter estimates in both median weight-normalized terms and normalized > > per kg. I have also included scaled CL estimates for typical patients at > > several ages and body weights. This hasn’t met the approval of the > > investigator, who is now insisting that I report the model building > > procedure from the median weight model, but report scaled parameters only > > on a per kg basis. This is wrong in my opinion and is actually more > > confusing to someone who is trying to understand the model. > > > > Can I get the group’s opinion on this? Am I being stubborn looking at the > > world through a modeler’s point of view? > > > > Thanks, > > > > > > > > > > John Mondick PhD > > Research Assistant Professor > > Division of Clinical Pharmacology and Therapeutics > > The Children's Hospital of Philadelphia > > Tel (267) 426-2292 > > FAX (215) 590-7544 > > Email: [EMAIL PROTECTED] > > > > -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090 www.health.auckland.ac.nz/pharmacology/staff/nholford