Validation of published population pharmacokinetic model
The predictive performance of the published rFIX-Fc population PK model
by Diao et al.16 was assessed with our data using
NONMEM software (v7.4.1, Icon Development Solutions, Gaithersburg,
Maryland, United States)25. Data visualization and
evaluation were performed in R (version 4.1.1), Pirana (version 2.9.8)
and PsN (version 4.8.1). Predictive performance was visualized in
goodness-of-fit (GOF) plots showing predicted versus observed FIX
activity levels. A priori population predicted (PRED) activity was
obtained using typical PK parameters which can be calculated on basis of
patient characteristics (e.g. body weight). Individual PK parameters
were obtained after Bayesian estimation providing a posteriori
individual predicted activity (IPRED). Next, predictive performance was
evaluated by comparing predicted versus observed FIX activity levels.
The prediction error (PE, Eq. 4) was determined to assess bias. The root
mean squared error (RMSE, Eq. 5) was determined to elaborate on
differences between individual predictions of the published and novel
model.
\begin{equation}
\left(4\right)\text{\ PE}=\ (\frac{C_{\text{pred}}-C_{\text{obs}}}{C_{\text{obs}}})*100\%\ \nonumber \\
\end{equation}\begin{equation}
\left(5\right)\ RMSE=\ \sqrt{\frac{\sum_{j=1}^{n}{(C_{\text{ipred}}-C_{\text{obs}})}^{2}}{n}}\nonumber \\
\end{equation}Cpred represents the population predicted and Cipred the
individually predicted FIX activity level of measurement j .Cobs represents the observed FIX activity level. The total number
of measurements is denoted by n . A negative or positive PE
indicates a systematic under- or overestimation of population predicted
FIX activity levels. A median PE between -5% and 5% is deemed as not
biased. RMSE was determined for peak (time after dose 0-2 h), mid (time
after dose 2-120 h) and trough (time after dose 120-300 h) FIX activity
levels separately.
Furthermore, for patients <12 years of age, we investigated
potential bias due to possible relationships between covariates and
population PK parameters volume of central compartment (V1), volume of
peripheral compartment (V2), clearance (CL) and intercompartmental
clearance (Q). Therefore, we plotted interindividual variability (ETA;η ) in these PK parameters against the patient characteristics age
and body weight. Plots of an unbiased model should not show trends,
indicating that η in these PK parameters are divided randomly
over patient characteristics.
Finally, terminal elimination half-lives (t1/2) were
determined by post hoc calculation for patients <12 years of
age, patients ≥12 and <18 years of age and adults. Results
were compared with results from the novel model (see below). As the
t1/2 estimates are influenced by the number of
compartments26, the respective compartments of both
models were taken into account.