■ 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.