The development of this population model is based on previously published pediatric data , with a total of 25 renal and 18 liver transplant recipients between 0.5 to 16 yr of age (median age nine yr). Demographic data of the 26 male and 17 female patients are shown in Table 1. All patients received both v-GCV (powder for oral solution) and intravenous GCV. The doses were based on adult dose recommendations adapted to children by BSA scaling; 520 mg/m2 of v-GCV and 260 mg/m2 for intravenous GCV (administered as a one h infusion), both adjusted for estimated renal function by the Schwartz formula . Patients received four doses: Intravenous GCV on days 1 and 2 and v-GCV on days 3 and 4. Blood samples for determination of GCV concentrations on day 2 were drawn pre-dose (−2 to 0 h), immediately at the end of the infusion (one h) and between 2–3, 5–7, and 10–12 h post-dose. On days 3 and 4, samples were drawn pre-dose and between 0.25–0.75, 1–3, 5–7, and 10–12 h post-dose. In renal transplant recipients a sample between 22 and 24 h after the day 4 dose was also collected. Serum creatinine was measured daily.
Table 1. Median (range) demographic data of patients used for development and validation of the non-parametric population model
| ||Patients used for development of population model (n = 43) ||Patients used for model validation (n = 61) ||The combined data set (n = 104) [12, 22]|
|Age (yr)||10.0 (0.5–16)||7.8 (0.3–16.9)||9.9 (0.3–16.9)|
|Kidney and liver|| ||1||1|
|Body weight (kg)||26.0 (6.1–81.6)||23.5 (5.8–89.4)||25.9 (5.8–89.4)|
|Height (cm)||129 (59–185)||126 (62–173)||127 (59–185)|
|BSA (m2)||0.97 (0.31–2.04)||1.00 (0.32–2.07)||0.98 (0.31–2.07)|
|Cockcroft-Gault GFR (mL/min)||80 (29–165)||69 (16–142)||73 (16–165)|
|Schwartz GFR (mL/min/1.73 m2)||113 (48–212)||107 (46–196)||112 (46–212)|
The population model was validated on an external data set previously presented . The demographics of these 61 validation pediatric patients were comparable to the population used for model development, as shown in Table 1. They received once daily v-GCV (either powder for oral solution or tablets or a combination of both) as primary prophylaxis for up to 100 days after transplantation. In addition to kidney and liver transplants, these data also include heart and one combined kidney–liver transplants. The dose of v-GCV was administered according to the Pescovitz algorithm (Dose [mg] = 7*BSA [m2]*GFRSchwartz [mL/min/1.73 m2]). Blood samples for determination of plasma GCV concentrations were obtained between 3 to 14 days post-transplant at the following time points; pre-dose and 1–2, 3–7, and 7–12 h post-dose. Additional single samples were up to the discretion of the treating physician. These clinical trials were performed in accordance with the Helsinki declaration and local Ethics Committee approvals.
Furthermore, four SOT patients treated with v-GCV at our transplant center served as a “standard of care” validation population. Their demographic data are summarized in Table 2.
Table 2. Clinical data on the four patients treated with valganciclovir in a clinical setting at our transplant center and their model calculated AUC0-τ.
|Patient||Age (yr)||Sex||Weight (kg)||Height (cm)||P-creat (μm)||Tx organ||Indication for valganciclovir||Dose administered||Dose (Pescovitz-algorithm)||Dose (SCH algorithm)||Dose (NEW algorithm)||Model calculated AUC0-τ (mg*h/L)|
|1||4.25||F||19||102||26||Kidney||CMV disease||150 mg BID||900 mg BID (988 mg)||225 mg BID||504 mg BID||17.1|
|2||8.5||F||23||117||38||Kidney||Primary proph.||450 mg QD||900 mg QD (914 mg)||450 mg QD||479 mg QD||55.2|
|3||15||F||55||162||55||Heart||Primary proph.||450 mg BID||900 mg QD (1591 mg)||900 mg QD||1053 mg QD||26.5|
|4||8.0||M||24||130||41||Heart||Primary proph.||450 mg BID||900 mg QD (1014 mg)||450 mg QD||520 mg QD||58.8|
Plasma concentrations of GCV in the two published populations were analyzed with validated specific LC-MS/MS assays as previously presented [9, 12], while samples from the four patients from our center were analyzed with a validated specific LC-UV assay . Assay characteristics in short; LC-MS/MS: LLoQ is 0.04 μg/L, overall accuracy between 99% and 105% and inter-assay variability between 0.7% and 12%, LC-UV: LLoQ is 0.1 μg/L, overall accuracy between 90% and 117% and inter-assay variability between 10% and 20%. The standard deviations (s.d., i.e., assay error) for measured (observed) GCV are derived from the analytical validation data , resulting in the following error polynomial: s.d. = −0.0045291 + 0.12022645*[obs], where [obs] is the observed concentration of GCV.
Population pharmacokinetic modeling and validation
The non-parametric pharmacokinetic modeling was performed in Pmetrics (version 0.40, Laboratory for Applied Pharmacokinetics, Los Angeles, CA, USA)  using the algebraic model solver. We chose to use a non-parametric approach because for certain advantages over parametric methods : (i) to better detect outlier patients if present; (ii) to detect any unexpected subpopulations; (iii) and to build a model that could be used for multiple-model adaptive control as implemented in the BestDose clinical dose optimization software package produced by LAPK (Laboratory for Applied Pharmacokinetics; www.lapk.org). We intend to use this tool prospectively for v-GCV TDM.
To be consistent with a previous population model of GCV in pediatric patients , the structural model was set to three compartments with first-order v-GCV absorption from the dosing compartment into the central compartment (including conversion to GCV) after a delay or lag time, and distribution to and from a peripheral tissue compartment. As intravenous data were available, the model was parameterized with central clearance (CL), inter-compartment clearance (Q), central and peripheral volumes of distribution (V, Vp), and an absolute bioavailability (FA) term was also introduced. The data used in the present analysis come from oral administration of both v-GCV tablets as well as oral solution. This was however not differentiated in the model since the two formulations previously have been shown to be bioequivalent .
Both the additive lamda and multiplicative gamma error models in Pmetrics were tested during the model development, using the assay error polynomial as presented above. As many multiples of 80 021 grid points as possible were applied (limited by hardware storage capacity), with uniform initial distribution, and the analyses were run on a MacBook Pro (2.66 GHz Intel Core 2 Duo processor, 8 GB 1067 MHz DDR3 memory and running OS X, version 10.8.2; Apple Inc, Cupertino, CA, USA).
All pharmacokinetic disposition parameters were allometrically scaled to body size using total body weight and coefficients of 3/4 for clearances and 1 for volumes . Covariates were scaled to the median population values and continuous covariates were extrapolated between observations. Covariates were included stepwise, followed by a reduction of the resulting model by taking one covariate out of the model. Both the old and new Schwartz formulas' as well as the Cockcroft-Gault formulae for estimation of GFR were tested [10, 17, 18]. The estimated GFRs, individually converted to the unit of mL/min for the Schwartz formulas, were included in the model to the power of a parameter (GFRcl) that was estimated in the model.
Model selection was based on comparison of the AIC, the fit of both the population and individual predicted vs. observed plots and biological plausibility.
The model was evaluated for its predictive accuracy on the external validation data set of 61 new patients receiving v-GCV for primary prophylaxis after transplantation. From the Bayesian prior model parameter joint density, Pmetrics calculated the Bayesian posterior joint density for each subject in the external validation set. The median marginal parameter values of each posterior density were used to calculate the predicted GCV concentrations, given individual v-GCV dosing and patient covariates. The following statistics were computed: PE (predicted minus observed concentrations), bias (mean weighted PE), imprecision (bias-adjusted mean weighted squared PE), and the R2 and slope of the individual predicted vs. observed plots. These statistics in the external validation set were compared to the same statistics in the model development subjects. Analyses in the external data set were performed with only single kidney and single liver transplant recipients as well as in all 61 patients, including heart and one combined kidney-liver transplant, all together.
For prediction of concentrations in the four patients monitored during standard clinical conditions, the two data sets previously mentioned were combined, and new population parameter estimates were established. The new model, now including data from 104 patients, was used as a prior and data from the four patients from our clinic were included in the analysis. Steady-state samples from three of these patients had been obtained before the morning dose (zero h), and 0.5, 1, 1.5, 2, 4, 6, 9, and 12 h after the dose. Patient one, however, only donated two blood samples at trough and two h after the morning dose. At the time of sampling, the hospital protocol for prophylaxis in heart transplants was to split the daily dose into twice daily administrations.
Current v-GCV dose algorithm evaluation
To evaluate the current Pescovitz and SCH dosing algorithms, a Monte Carlo simulation of patients spanning 0.5–16 yr, having poor and good renal function was performed. Based on WHO weight and height curves the 5% and 95% quintiles for the following ages were used: 0.5, 3, 6, 12, and 16 yr . Three GFRs were applied to the 10 age/size combinations, representing poor, moderate, and normal renal function: 25, 75, and 125 mL/min/1.73 m2, respectively. Each of these 30 fictive patients served as a simulation template for 1000 GCV time-concentration profiles calculated from parameters sampled from the model population joint density, including the full covariance matrix. Simulated GCV concentrations were corrupted by noise using the same error polynomial as in the population model. Simulated parameter values were restricted to be physiologically plausible by applying the same boundaries as in the model. Four or seven doses of v-GCV, depending on the fictive patient's renal function were administered and the steady-state AUC0–24 was calculated from 144 to 168 h after the first dose administered. For each simulated population, the probability of the AUC0–24 lying between 40 and 60 mg*h/L was calculated as the number of simulated profiles within that range divided by the total number in that population, that is, 1000.