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.