Why standards are useful for predicting doses

Abstract

Germovsek and colleagues have recently concluded that a standard approach to modelling pharmacokinetics is not wrong and appears to be at least as useful as other ad hoc methods for describing drug concentrations. There are other advantages of this approach including learning about biology, comparing different studies, detecting errors and rationalizing dose prediction. A standard approach to size and maturation is not a panacea but provides the framework for challenging new ideas and supports a consistent method of dosing in patients of all ages.

Table of Links

LIGANDS
busulfan	paracetamol
morphine	tramadol

This Table lists key ligands in this article that are hyperlinked to corresponding entries in http: //www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS Guide to PHARMACOLOGY 1.

Commentary

Germovsek and colleagues have recently concluded that a standard approach to modelling pharmacokinetics in neonates, infants and children is not wrong and appears to be at least as useful as other ad hoc methods for describing drug concentrations 2. There are other advantages of this approach that we believe are important to recognize and are applicable to all humans of whatever age or size.

• Learning about biology: When a standard model for size derived from theory based allometry 3 with strong experimental support in all mammals 4 is used, variation in human body size alone can account for 100‐fold difference in clearance 5. Variability in renal function accounts for about 10‐fold difference in clearance. Variability due to maturation in utero and after birth in neonates and infants also accounts for about 10‐fold differences in clearance. A size‐independent measure for renal function can be defined as 1 in a standard size man with a standard glomerular filtration rate (GFR) for that size 6. A size independent measure for maturation can be defined as 1 in a standard size adult man 7. Using standard but independent models allows quite different influences on clearance to be quantified and compared. This means that the biology influencing organ function and development can be investigated while accounting for other important factors in a consistent way. This is particularly important when we must rely upon normal and disease associated variation of size, organ function and development, which are often correlated, in order to learn about these processes.

We illustrate this principle of learning about biology in Figure 1. This shows the standard model for maturation for GFR and five medicines after standardizing for allometric size. Weight and age are clearly separate predictors otherwise all maturation curves would be the same if weight was the only variable. Empirical allometry approaches based on weight alone with a constant allometric exponent cannot describe these differences in ontology.

• Comparing different studies: The use of a standard model can be helpful for summarizing and comparing results in different studies. This is further aided by use of a standard subject such as 70 kg, 176 cm, 40‐year‐old man with GFR of 6 l h^–1 to estimate and report standard parameters. The choice of a standard size is always possible because it only changes the scale of the parameter value and does not affect the estimation process 8. Scaling size to the median weight observed in a study guarantees that parameters are study specific and requires rescaling to a standard subject for direct comparison. We routinely scale parameters to 70 kg even if they are obtained in neonates. This allows the influence of immaturity and/or organ dysfunction to become clearer by direct comparison with standard values.

• Detecting errors: The use of nonstandard scales for parameters can make it difficult to detect errors. For example, the plasma clearance of a common drug has been reported in this journal as 0.234 l min⁻¹ kg^0.75. This can be scaled to 70 kg as 0.234 × (70/1)^0.75 l min⁻¹, which is 340 l h^–1 70 kg^–1. This is clearly a very improbable value for any drug and was certainly wrong for the drug in question, which has a widely confirmed value around 25 l h^–1 70 kg^–1. A standard method of reporting parameters, and insistence by editors and reviewers that authors compare the values with those in the literature would quickly detect this kind of problem.

• Rationalizing dose prediction: Perhaps the most important clinical goal of pharmacokinetics is to be able to predict doses in individuals. Maintenance dose rates and loading doses (1), (2) can be calculated based on a standardized clearance and volume of distribution 5 and the target concentration 9. The individual dose rate and loading dose can be calculated from the standard values using covariates such as weight, sex, age and height. A web‐based tool using these methods is used by clinicians at our institution to predict the initial and subsequent doses of busulfan 10. We do not report pharmacokinetic parameters because these are not familiar but rely on the clinician to judge whether the proposed dose is appropriate.

$${\text{DoseRate}}_{\mathrm{STD}}={\text{Clearance}}_{\mathrm{STD}}\times \text{Target Concentration}$$ (1)

$${\text{LoadingDose}}_{\mathrm{STD}}={\text{Volume}}_{\mathrm{STD}}\times \text{Target Concentration}$$ (2)

Figure 1.

Different biological mechanisms of elimination are shown as a function of postnatal age (PNA) using theory based allometric size scaling. Glomerular filtration rate (GFR) may be seen as a reference for the different rates of maturation of common metabolic pathways. Sources: GFR 14, vancomycin data pooled from 15, 16, paracetamol 8, morphine 8, tramadol 17, busulfan 12

Simple guidance for individualized dosing based on applying standard models for maturation (GFR) and allometric size is shown in Table 1. The fractions are rounded for simplicity but differ at most by 18% from the exact value.

Table 1.

Weight or age based maintenance doses to achieve the same target concentration. Postmenstrual ages (PMA) up to full term then postnatal age (PNA)

Typical weight kg	Age	Fraction of adult dose
0.75	25 weeks PMA	1/300
1	30 weeks PMA	1/120
3	Full‐term 40 weeks PMA	1/30
6	3 months PNA	1/10
7	6 months PNA	1/7
9	1 year PNA	1/5
12	2 years PNA	1/4
19	5 years PNA	1/3
34	10 years PNA	1/2
50	15 years PNA	3/4
70	Adult	1

The standard model approach has limitations when using genotypes, which may not have a natural standard value because the most frequent variant may be quite different in different study populations. Necessarily empirical models for factors such as age are often centred on the median age in an adult population. The choice of a standard age of say 40 years will not materially affect the estimates but would help pragmatically for the reasons described above.

We do not want to claim that models such as theory based allometry are the ‘truth’. Controversy still rages in the wider biological world 4 about the details of allometric theory but pragmatically there is no evidence in humans that using this method is worse than any other and there is widespread support for using it (see 11 for a recent review in this journal). A direct test in humans using an adequate design 7 has provided precise estimates of the allometric exponents for clearance and volume that were similar to the theoretical values 12. The combination of a standard theory based allometric size model and a standard maturation model provided better predictions of morphine doses in a large external data set than other empirical allometry and age methods 13. Thus, we agree with Germvosek and colleagues 2 that there are good reasons to prefer a standard approach. This will help us understand biology better and lead to more consistent dosing decisions.

Competing Interests

There are no competing interests to declare.

Holford, N. H. G. , and Anderson, B. J. (2017) Why standards are useful for predicting doses. Br J Clin Pharmacol, 83: 685–687. doi: 10.1111/bcp.13230.