■ RESULTS
The final analysis dataset consisted of 836 concentration-time points
from 107 subjects of which 53 are preterm neonates, 13 are term neonates
and 41 are infants. Demographics and anthropometrics of the individual
studies and the pooled final analysis dataset are presented in Table 1.
The sequential model building process is summarized in Table 2. A
three-compartment structural model was selected. The effect of BW on all
structural model parameters was accounted for by allometrical scaling
using fixed exponents (Equation 3).
\(\theta_{i}=\theta_{70,pop}\cdot\left(\frac{\text{BW}}{70}\right)^{a}\cdot e^{\eta_{\theta,i}}\)(3)
The allometric exponent (\(a\)) was fixed to 0.75 for clearances and 1
for volumes 17. A reference BW of 70 kg was selected
to represent mean adult BW. Plots of the BW corrected elimination
clearance vs. PMA, GA and PNA revealed the need to account for age on
top of BW despite the high level of correlation between age and weight
in this population (Figure 1A-D)9. An
PMA-dependent Emax-type maturation term was introduced to account for
elimination clearance maturation (Equation 4).
\(CL_{i}=CL_{70,pop}\cdot\left(\frac{\text{BW}}{70}\right)^{0.75}\cdot\frac{\text{PM}A^{\gamma}}{\left(\text{PMA}50^{\gamma}+PMA^{\gamma}\right)}\cdot e^{\eta_{CL,i\ }}\)(4)
PMA50 is the PMA at half maximal maturation and \(\gamma\) is a Hill
slope factor. Introducing this PMA-dependent Emax-type maturation term
on top of the weight-proportional model improved the model fit
(ΔAIC=-202.37). A generalized logistic function, better known as a
Richard’s curve, which is a sigmoidal function originally developed to
empirically describe growth phenomena, was adapted in an attempt to
account for elimination clearance maturation with improved flexibility
(Equation 5) 18.
\(CL_{i}=CL_{70,pop}\cdot\left(\frac{\text{BW}}{70}\right)^{0.75}\cdot\left(1-\left(1-\left(\left(\frac{\text{PMA}}{PMA50}\right)^{\gamma}\right)\cdot\left(1-\left(\frac{1}{2}\right)^{-\delta}\right)\right)^{-\frac{1}{\delta}}\right)\cdot e^{\eta_{CL,i\ }}\)(5)
\(\delta\) is an additional shape factor. Introducing the adapted
Richards equation did not improve the model fit. In order to account for
the asymmetry in the observed elimination clearance in function of age,
a term accounting for accelerated maturation immediately after birth,
henceforth refered to as the birth acceleration term, was developed and
introduced on top of both the PMA-dependent Emax-type maturation model
(Equation 6) and the adapted Richards maturation model (Equation 7).
\(CL_{i}=CL_{70,\text{pop}}\cdot\left(\frac{\text{BW}}{70}\right)^{0.75}\cdot\frac{\text{PM}A^{\gamma}}{\left(\text{PMA}50^{\gamma}+PMA^{\gamma}\right)}\cdot\frac{\left(1+FB_{\text{MAX}}\cdot\left(1-e^{-\frac{\ln(2)\cdot PNA}{T_{\frac{1}{2}}}}\right)\right)}{1+FB_{\max}}\cdot e^{\eta_{CL,i\ }}\)(6)
C\(L_{i}=CL_{70,pop}\cdot\left(\frac{\text{BW}}{70}\right)^{0.75}\cdot\left(1-\left(1-\left(\left(\frac{\text{PMA}}{PMA50}\right)^{\gamma}\right)\cdot\left(1-\left(\frac{1}{2}\right)^{-\delta}\right)\right)^{-\frac{1}{\delta}}\right)\cdot\frac{\left(1+FB_{\text{MAX}}\cdot\left(1-e^{-\frac{\ln(2)\cdot PNA}{T_{\frac{1}{2}}}}\right)\right)}{1+FB_{\max}}\cdot e^{\eta_{CL,i\ }}\)(7)
Two additional parameters were introduced to the model:\(FB_{\text{MAX}}\), the fractional increase relative to the value at
birth and \(T_{\frac{1}{2}}\), the half-life of the maturation
immediately after birth. Inclusion of the birth acceleration term
improved the model fit for both models. No significant differences
between the PMA-dependent Emax-type maturation model fit and the adapted
Richards maturation model fit were observed regardless of inclusion of
the birth acceleration term. In absence of a population with different
gestational age, a PMA-dependent Emax-type maturation model more than
adequately accounts for elimination clearance maturation. However, it
was observed that postnatal maturation is influenced by the GA of the
neonate. A final maturation model accounting for gestational maturation,
driven by GA, and postnatal maturation, driven by PNA and GA, further
improved the model fit (Equation 8).
\(CL_{i}=CL_{70,pop}\cdot\left(\frac{\text{BW}}{70}\right)^{0.75}\cdot\left(M_{birth,38}\cdot\left(\frac{\text{GA}}{38}\right)^{\alpha}+\left(1-M_{birth,38}\cdot\left(\frac{\text{GA}}{38}\right)^{\alpha}\right)\cdot\left(1-e^{-\frac{\ln\left(2\right)\cdot PNA\cdot\left(\frac{\text{GA}}{38}\right)}{T_{\frac{1}{2}}}}\right)\right)\cdot e^{\eta_{CL,i\ }}\)(8)
Where \(M_{birth,\ 38}\) is the fraction of elimination clearance
maturation at the time of birth after a 38 week gestational period,\(\alpha\) is a shape factor and\(T_{\frac{1}{2}}\) is the time to
achieve 50 % of postnatal elimination clearance maturation (in weeks).
Addition of the final maturation term on top of the weight-proportional
model reduced the unexplained BSV for elimination clearance, calculated
as the square root of the exponential variance of η minus 1, from 175.9
% for the weight-proportional model down to 71.1 % for the final
maturation model. A PNA covariate effect (Equation 9) was introduced to
V1, to account for the observed changes of allometrically scaled V1 in
function of postnatal age.
\(V_{1,i}=V_{1,70,pop}\cdot\left(\frac{\text{BW}{\ \cdot\ e}^{\left(-\ \frac{\text{PNA}}{52\cdot}*\beta\right)}}{70}\right)\cdot e^{\eta_{V_{1},i\ }}\)(9)
Here, \(\beta\) is a shape factor. No other covariate effects were
identified. The final model is the intrauterine-postnatal maturation
model with a PNA covariate effect on V1. Goodness of fit
plots and visual predictive checks of the final model fit are provided
in Figure 2 and Figure 3. The iterative model building process is
summarized in Table 2. The population parameter estimates,
inter-individual variability estimates of the respective parameters,
residual error estimates, precision of the estimates and objective
function values of the final model fit are summarized in Table 3.