Mario González-Sales (1), Nick Holford (2), Guillaume Bonnefois (3), Julie Desrochers (3).
(1) Modeling Great Solutions, Andorra, (2) Department of Pharmacology and Clinical Pharmacology, New Zealand, (3) Syneos Health, Canada.
Introduction: Notwithstanding the extensive confirmatory observations supporting the use of allometric theory, [1-8] the use of allometric exponents (Ae) still remains a controversial issue [9,10]. Some modellers prefer to estimate Ae and others do not. Modellers opting for the estimation of Ae may argue that it improves the model fit to the data because the value of the objective function value (OFV) may decrease. Modellers using theory-based Ae may argue that such a decrease in the OFV is due to model misspecification arising from covariates correlated with body mass.
Objective: To answer the following question: “When should pharmacometricians try to estimate allometric exponents as model parameters?”
Methods: Non-linear mixed effect modeling and a parametric bootstrap were employed to assess how design features affect the uncertainty of pharmacokinetic Ae using a hypothesis testing approach. The model used in this analysis was a one-compartment model with bolus input and first-order elimination. The model accounted for body composition using theory-based Ae of 3/4 for clearance (CL) and 4/4 for distribution volume and maturation using a sigmoid Emax model [11]. The covariate data from McCune et al. [11] was used to obtain realistic covariate distributions. Design features included different size distributions (i.e. only adults, infants and children or adults, infants and children), the number of subjects (i.e. 30, 100, 300, 1000 and 2000), the number of observations per subject (i.e. 8, 4 and 2), and the magnitude of between subject variability (BSV) (i.e. 10%, 30% and 50%). The hypothesis testing approach was similar to the two one-side test (TOST) used for bioequivalent assessment [12]. The null hypothesis (H0) of non-inferiority (H0L) was defined as:
H0L: AeE – AeT > δL
where δL represents the effect size -0.0833 for the inferiority test, AeE is the value of the Ae estimate and Ae T represents the theoretical value of the Ae 3/4 for CL. This effect size is consistent with an inferiority test Ae of 2/3 e.g. if size scales according to body surface area which is proportional to mass2/3. The H0 of non-superiority (H0U) has the same theoretical exponent of 3/4 and a superiority test Ae of 1 e.g. if size scales linearly with mass:
H0U: AeE – AeT < δU
where δU represents the effect size 0.25 for the superiority test. The alternative hypotheses (i.e. HaL and HaU) were defined as the complement of the null hypotheses. Consistent with the TOST approach, a type one error of 5% was used for each test with a total error of 10%. Therefore, if the 90% confidence interval of the alternative Ae distribution minus the theoretical value of 3/4 was within the limits of (> δL and < δU), both Ha (i.e. HaL and HaU) were rejected and theory-based exponents for CL were confirmed.
Results: A decrease in the dispersion of the size distribution, the number of subjects, the number of observations per subject and an increase in BSV increases the uncertainty of the Ae estimates. Studies conducted in adults (>18 years old) with a drug exhibiting 30% BSV in CL may not be able to distinguish between Ae of 3/4 and 2/3 even when 1000 subjects are included in the design. The results showed that estimate of the Ae can be expected to have large uncertainty with common trial designs and models. In some cases (e.g. 50% BSV in CL and narrow mass distribution (adults only) or 30% BSV in CL and 30 subjects) negative Ae were estimated. These biologically implausible results have been reported for theophylline in a small number of obese subjects [13]. This finding exemplifies the problem of drawing conclusions from inadequate designs based on the best fit to the data.
Conclusions: We recommend that Ae should only be estimated when the design of the study can be expected to give sufficiently precise estimates to challenge the theory-based values. Given the high potential risk to estimate the “wrong” value for the Ae just to fit the data obtained from typical designs, the results of this analysis should encourage pharmacometricians to rely more on the extensive theoretical and confirmatory evidence that the CL in humans changes as a function of mass with an exponent of 3/4.
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Reference: PAGE () Abstr 9351 [www.page-meeting.org/?abstract=9351]
Poster: Methodology - Other topics