Population pharmacokinetics of melphalan in paediatric blood or marrow transplant recipients

Abstract

What is already known about this subject

• In one of the largest studies in children to date, we have already published a paper that has described the pharmacokinetics of melphalan using a two-stage approach.

What this study adds

• The current paper is a follow-up study in which a population pharmacokinetic model for melphalan is developed and validated in children.

• There have been no other population pharmacokinetic analyses published on melphalan given as a short infusion.

• Additionally, a nomogram is produced to guide melphalan dosing.

Aim

To develop a population pharmacokinetic model for melphalan in children with malignant diseases and to evaluate limited sampling strategies for melphalan.

Methods

Melphalan concentration data following a single intravenous dose were collected from 59 children with malignant diseases aged between 0.3 and 18 years. The data were split into two sets: the model development dataset (39 children, 571 concentration observations) and the model validation dataset (20 children, 277 concentration observations). Population pharmacokinetic modelling was performed with the NONMEM software. Stepwise multiple linear regression was used to develop a limited sampling model for melphalan.

Results

A two-compartment model was fitted to the concentration-vs.-time data. The following covariate population pharmacokinetic models were obtained: (i) Clearance (l h⁻¹) = 0.34.WT − 3.17.CPT + 0.0377.GFR, where WT = weight (kg), CPT = prior carboplatin therapy (0 = no, 1 = yes), and GFR = glomerular filtration rate (ml min⁻¹ 1.73 m⁻²); (ii) Volume of distribution (l) = 1.12 + 0.178.WT. Interpatient variability (coefficient of variation) was 27.3% for clearance and 33.8% for volume of distribution. There was insignificant bias and imprecision between observed and model-predicted melphalan concentrations in the validation dataset. A three-sample limited sampling model was developed which adequately predicted the area under the concentration–time curve (AUC) in the development and validation datasets.

Conclusions

A population pharmacokinetic model for melphalan has been developed and validated and may now be used in conjunction with pharmacodynamic data to develop safe and effective dosing guidelines in children with malignant diseases.

Introduction

Melphalan is an alkylating agent which is active against a wide range of malignant diseases in children, including both solid tumours and haematological malignancies [1, 2]. It can be administered either as a single high dose (140 mg m⁻² or 180 mg m⁻²) or as part of divided dose regimens (e.g. 3 days of 70 mg m⁻²); alone, or in combination with other anticancer agents (e.g. carboplatin) and followed by autologous or allogeneic blood or marrow transplantation (BMT).

The toxicity of melphalan is substantial. Despite blood or marrow stem cell rescue, profound, life-threatening myelosuppression, including neutropenia and thrombocytopenia, occurs in all patients [3–5]. Both severity and duration of myelosuppression are dose dependent [5]. Gastrointestinal toxicity is the major nonhaematological toxicity of high-dose melphalan and includes mucositis, nausea, vomiting and diarrhoea [3–5]. In a study of Moreau et al.[4], 13 out of 16 patients experienced grade 4 mucositis after 220 mg m⁻² melphalan followed by BMT. Therefore, toxicity restricts the dose that can be given to any individual patient.

Melphalan is eliminated by renal excretion and spontaneous degradation to its mono- and di-hydroxy metabolites [6, 7], the latter pathway being relatively minor (<5%) [7] because plasma proteins retard the hydrolysis rate of melphalan [8]. In water and in urine, however, melphalan undergoes rapid decomposition [7] and this has made it difficult to study the 24-h urinary excretion of melphalan. Highly variable results have been obtained, ranging from 3 to 93% in nine adults (mean ± SD 34 ± 33%), even after paying particular attention to rapidly freezing the urine specimens, suggesting that there may be decomposition in the bladder [6]. However, the fact that >60% of the dose was recovered in the urine of three patients [6] suggests that renal excretion could be a very important elimination pathway for melphalan.

In children, melphalan is currently dosed on a mg m⁻² basis, and there are no guidelines for varying the dose in patients who are very heavy or who have impaired renal function. Many studies have noted wide variability in exposure in patients receiving the same surface area-based dose [9, 10]. Children with high melphalan exposure have been previously shown to have increased toxicity [11], demonstrating a relationship between melphalan pharmacokinetics and melphalan toxicity. A possible relationship between melphalan pharmacokinetics and therapeutic efficacy is suggested by a study reporting reduced disease response in patients with amyloidosis administered reduced melphalan doses [12]. There is therefore the potential for pharmacokinetically guided dosing to improve transplant outcomes and reduce interpatient variability in melphalan exposure.

The aims of this study were (i) to develop and validate a population pharmacokinetic model for melphalan that can be used in conjunction with pharmacodynamic data, to develop a rational basis for melphalan dose selection in children with malignant diseases, and (ii) to develop limited sampling strategies that will aid in the pharmacokinetic monitoring of melphalan.

Methods

Patients

A total of 59 children aged between 0.3 and 18 years who underwent autologous or allogeneic BMT between 1994 and 2003 as part of their treatment for malignant diseases were involved in this prospective, single-centre investigation of the pharmacokinetics of melphalan. The Children's Hospital at Westmead's Ethics Committee approved the study and the parents of all children involved gave informed consent. The characteristics of the children are summarized in Table 1.

Table 1.

Characteristics of children in the model development and model validation datasets

	Model development	Model validation	Significance
Total number of children	39	20
Total number of observations	571	277
Number of concentration observations per patient	15	14	NS*
Median (range)	(10–17)	(8–17)
Age (months)	5.4	6.9
Median (range)	(1.0–15.8)	(0.3–17.6)	NS*
Weight (kg)	18.8	20.3
Median (Interquartile range)	(13.5–28.1)	(13.6–25.9)	NS*
Height (cm)	110	115
Median (Interquartile range)	(92–137)	(95–134)	NS*
Surface area (m2)	0.76	0.83
Median (Interquartile range)	(0.60–1.0)	(0.62–0.98)	NS*
GFR (ml min−1 1.73 m−2)	115	105
Median (Interquartile range)	(94–139)	(86–135)	NS*
Gender, (n), male/female	28/11	10/10	NS†
Number of children with the following diagnoses
ALL	6	4
AML	5	4
Neuroblastoma	13	6
Rhabdomyosarcoma	5	1
Ewing's sarcoma	1	2
Soft tissue sarcoma	2	1
Chondrosarcoma	0	1
Non-Hodgkin's lymphoma	4	1
Hepatoblastoma	1	0
Retinoblastoma	1	0
Mediastinal large cell lymphoma	1	0
Prior carboplatin therapy (n), yes/no	17/22	9/11	NS†
Prior total body irradiation (n), yes/no	16/23	10/10	NS†
Prior busulphan therapy (n), yes/no	7/32	6/14	NS†

ALL, Acute lymphoblastic leukaemia; AML, acute myeloid leukaemia; GFR, glomerular filtration rate.

^*Significance assessed using the Mann–Whitney U-test.

^†Significance assessed using the χ² test.

Drug administration and blood sampling

Melphalan (Alkeran; Wellcome Australia Pty Ltd, Boronia, Australia) was administered as a 15-min i.v. infusion with double maintenance fluids. Children were given melphalan either as single high doses of 140 or 180 mg m⁻² or as part of divided dose schedules (3 days of 70 mg m⁻² or 4 days of 30 mg m⁻² melphalan). Some children received additional chemotherapy such as carboplatin (CPT), busulphan (BU) or total body irradiation (TBI) prior to the melphalan dose (Table 1). Those given carboplatin received a dose on each of 5 days prior to melphalan that was determined using a formula based on glomerular filtration rate (GFR) and surface area (the Calvert formula) that aimed to achieve an area under the concentration–time curve (AUC) of 4 mg ml⁻¹ min⁻¹. GFR was determined by measuring the plasma clearance of ₄₃Tc⁹⁹-diethylenetriaminepentacetic acid.

All patients had a double lumen central line, so that one lumen could be used for drug administration and one for blood sampling. To avoid contamination, 5 ml of blood was withdrawn prior to taking each sample. In some children this 5 ml blood was reinjected into the patient, while in others it was discarded. A median of 15 lithium heparin blood samples were collected from each patient after a single dose to characterize the pharmacokinetic profile. In those patients who had fractionated doses, the pharmacokinetics was only studied on a single day. The blood collection times were prior to the infusion and then at 0, 5, 10, 15, 20, 30, 40 and 50 min, 1, 2, 3, 4, 6, 12 and 24 h after the end of infusion. Plasma fractions were separated by centrifugation at 1200 g for 10 min at 4°C (Beckman CS-15R; Beckman Instruments, Fullerton, CA, USA) and were stored at −40°C until analysis. Samples were analysed within 1 week of collection.

Melphalan assay

Melphalan was measured in plasma samples using our previously published high-performance liquid chromatography (HPLC) assay [9] that had acceptable accuracy and precision. For concentrations ranging from 2.5 to 40 µg ml⁻¹, the between-day coefficient of variation of the assay (%CV) was <10% and the overall deviation from the true concentration was <9%. The limit of quantification was 0.5 µg ml⁻¹, with a %CV of 19%. The limit of detection of the assay was approximately 0.1 µg ml⁻¹. The calibration curve was linear over the range 0.5–40 µg ml⁻¹ melphalan. No compounds interfered with the melphalan assay.

Datasets

Data from 39 children was randomly allocated for developing the population pharmacokinetic model (model development dataset). Data from the remaining 20 children were used for model validation (model validation dataset).

Population pharmacokinetic analysis

Population pharmacokinetic modelling was performed using NONMEM, version 5.1.1 (Globomax, Ellicott City, MD, USA) that had been installed on a Pentium 4 personal computer running Windows XP and Compaq Visual Fortran Compiler (version 6.6). The modelling approach was implemented in a series of steps which are outlined below.

Development of a basic population pharmacokinetic model (step 1)

A basic population pharmacokinetic model for melphalan (without covariates) was developed using the model development dataset. The structural pharmacokinetic model (two compartment) and initial pharmacokinetic parameter estimates were derived from our previous traditional pharmacokinetic study [9] that included data from 52 (of the 59) children in this study.

First, different estimation methods were tried, including the first-order (FO) method, the first order conditional estimation method (FOCE) and the FOCE method with η–ε interaction. A number of pharmacostatistical models were also generated that varied in the following: (i) the random effects model for interpatient variability (additive vs. exponential) and (ii) the error model for intrapatient variability (additive vs. proportional vs. combined additive and proportional). A number of evaluation criteria were then used to select the most appropriate pharmacostatistical model, including (i) a low value for the objective function (OFV), (ii) a low estimate for sigma (the residual error term which comprises the intrasubject variability, the assay error and the model misspecification error), (iii) low estimates of intersubject variability in the pharmacokinetic parameters, (iv) good agreement between model-predicted and observed melphalan concentrations, (v) low imprecision in estimating the population pharmacokinetic parameters and (vi) normally distributed residuals with a mean that is not significantly different from zero using Student's t-test.

Population estimates of the following pharmacokinetic parameters were obtained: clearance (CL), volume of distribution into the central compartment (V) and the distributional rate constants (k₁₂ and k₂₁). The precision in the population estimates was evaluated by the calculation of percentage relative standard error (the standard error of the population pharmacokinetic parameter estimate divided by the population estimate, multiplied by 100). Interpatient variability in the pharmacokinetic parameters was estimated by calculating the %CV, determined by taking the square root of the ETA value for that parameter and multiplying by 100. ETA is the variance associated with the parameter values.

Assessment of the influence of covariates on the pharmacokinetic model (step 2)

Our previous pharmacokinetic analysis using the two-stage approach [9] provided a preliminary exploratory analysis of the influence of different covariates on melphalan pharmacokinetic parameters. The influence of individual candidate covariates on specific pharmacokinetic parameters was also assessed by adding these to the basic population pharmacokinetic model, in turn, and noting the changes in (i) the objective function, (ii) the distribution of residuals and (iii) the agreement between model-predicted and observed melphalan concentrations. A decrease in the objective function of >6.63 corresponds to a significance level of P < 0.01 (d.f. = 1). Covariates screened included weight (WT, in kg), weight^0.75 (WT^0.75), height (HT, in cm), body surface area (BSA, in m²), age (years), gender, GFR (ml min⁻¹ 1.73 m⁻²), prior CPT therapy (0 = no, 1 = yes), prior TBI (0 = no, 1 = yes), prior BU therapy (0 = no, 1 = yes) and dose group (mg m⁻²).

Development of a covariate population pharmacokinetic model (step 3)

Covariates found to influence significantly specific pharmacokinetic parameters during the initial screening procedure were cumulatively added to the population pharmacokinetic model in a forward stepwise manner in order of their contribution to the reduction in the objective function, until there was no further reduction in the objective function. A backwards elimination step was then performed in which the influence of each covariate was removed from the model in descending order of their contribution to the change in the objective function. This was done by nullifying the coefficient of each covariate (THETA). The difference in the objective function before and after nullifying the coefficient of a given covariate approximates the χ² distribution with 1 d.f. Covariates were retained in the model if their removal increased the objective function value by >6.63 ( d.f. = 1).

Validation of the covariate population pharmacokinetic model (step 4)

Predictions of melphalan concentrations were made using the covariate population pharmacokinetic model in the 20 children in the validation dataset. This was done by fixing the values of the fixed-effects and random-effects parameters to the values estimated in the model, then determining the population-predicted concentrations using the POSTHOC argument in the $ESTIMATION command in NONMEM. In the database, DV (representing melphalan concentration) was set to 1 for all time points so that only covariate information would be used to obtain the population-predicted concentrations. Residuals (predicted − observed concentration) were calculated and the predictive performance, in terms of bias and precision, was determined as previously described [13].

Derived pharmacokinetic parameters

Data from the total group of 59 children were used to derive a number of additional pharmacokinetic parameters for melphalan from the POSTHOC estimates of the primary pharmacokinetic parameters. Clearance and volume of distribution were normalized for weight and surface area. The elimination rate constant (k) was calculated by dividing the estimates of CL by the estimates of V. The AUC was determined by dividing the dose (mg) by the individual posterior Bayesian estimates of CL (l h⁻¹). The distributional half-life (t_1/2α) and the elimination half-life (t_1/2β) were calculated by dividing 0.693 by α and β, respectively, where

Dosing using the covariate population pharmacokinetic model

Using the equation Dose (mg) = AUC × CL (l h⁻¹) and the population pharmacokinetic model for CL (CL = 0.34 × WT − 3.17 × CPT + 0.0377 × GFR), the doses required for targeting an AUC of 9 µg ml⁻¹ h⁻¹ (the median value obtained for the children in the 140 mg m⁻² dose group, no carboplatin) were determined for different weight and GFR values that were within the range observed in the children studied.

The dosing nomogram was then tested in our population of children by (i) estimating each individual's AUC had they been given a 140 mg m⁻² melphalan dose, (ii) estimating each individual's AUC had they been given a dose determined by the nomogram, targeting an AUC of 9 µg ml⁻¹ h⁻¹ and (iii) comparing the distribution of AUC values using the two dosing methods. As this analysis implies linear melphalan pharmacokinetics with dose, linearity was checked by testing dose (mg m⁻²) as a covariate in the population pharmacokinetic model.

Development of a limited sampling model for melphalan

Stepwise multiple linear regression was used to develop a limited sampling model (LSM) for melphalan AUC using the concentration–time data from the children in the model development dataset. In this analysis, AUC was the dependent variable while individual melphalan concentrations at 5 min, 15 min, 30 min, 1 h and 2 h after the end of infusion were the independent variables. The concentration data at the remaining time points were not included in the analysis due to missing data in some patients. The derived model was tested using the data from the children in the model validation dataset. Pearson's correlation coefficient was used to compare LSM-predicted and NONMEM-determined AUC values. Bias and precision were assessed as previously described [13].

Melphalan AUC_0–∞ determined using a two-stage pharmacokinetic analysis and a five-sample limited sampling strategy were also tested for correlation with the NONMEM-determined AUC values in the total cohort of children. Both compartmental and noncompartmental methods were used to determine melphalan AUC_0–∞ from a reduced number of concentration data points (n = 5) measured at 5 min, 15 min, 30 min, 1 h and 2 h post infusion end. This analysis was performed using the computer software Kinetica 4.0 (Innaphase, Philadelphia, PA, USA).

Results

Comparison of the model development and model validation datasets

The children in the model development and model validation datasets had similar characteristics and there were no significant differences between the two groups in the clinical and demographic data shown in Table 1.

Development of a basic population pharmacokinetic model

The FOCE method that took into account the η–ε interaction was found to provide the lowest value for the objective function, a low sigma value and adequate agreement between predicted and observed concentration data. Interpatient variability was best described using an exponential random effects model, which may be defined as: θ_i=·EXP(η_i), where θ_i represents the pharmacokinetic parameter for the i^th individual, is the typical value of pharmacokinetic parameter in the population (e.g. population mean) and η_i quantifies the deviation of θ_i from with a distribution (0, ω²).

Intrapatient variability was best described by the combined additive and proportional error model, which may be defined as: where are the predicted and Y the measured concentrations in the i^th individual at the j^th sampling time and where ε₁ (proportional component) and ε₂ (additive component) are random effects quantifying the residual errors with a distribution (0, σ²). Residual errors (ε) represent the differences between the model and the data and include intrapatient variability, assay error and model misspecification error.

The Basic population pharmacokinetic parameters are shown in Table 2. Varying the initial estimates of the pharmacokinetic parameters had little effect on the population estimates.

Table 2.

Basic population pharmacokinetic model for melphalan

Pharmacokinetic parameter	Population estimate (θ) (%RSE)	Interindividual variability* (%RSE)	95% CI
CL (l h−1)	10.1 (10%)	60 (20%)	9.39, 10.81
V (l)	4.81 (14%)	58 (38%)	4.14, 5.48
k12 (h−1)	1.81 (18%)	61 (18%)	1.08, 2.54
k21 (h−1)	1.86 (12%)	64 (39%)	1.05, 2.67
Residual variability†
Proportional (%)	0.092 (19%)
Additive (mg l−1)	0.007 (69%)
Objective function	−80.429

^*Interindividual variability was expressed as percentage coefficient of variation and was calculated by taking the square root of ETA (the variance associated with the parameter values) and multiplying by 100.

^†Proportional component of residual variability was expressed as %CV, while the additive component was expressed as standard deviation. RSE, Relative standard error, calculated as standard error (SE)/population estimate and expressed as a percentage; 95% CI, lower and upper limits of the 95% confidence interval, calculated as θ ± 2 SE.

Development of a covariate population pharmacokinetic model

In the preliminary screening phase several covariates individually reduced the objective function by 6.63 or more. For clearance, these were WT, WT^0.75, age, HT, BSA, GFR, CPT and TBI. For volume of distribution, the covariates were WT, WT^0.75, HT and CPT. For k₁₂, the only covariates were WT and HT. For k₂₁ only CPT reduced the objective function by ≥6.63. The covariates, dose group (mg m⁻²) and BU, did not significantly influence any pharmacokinetic parameter.

In the forward stepwise model building phase the cumulative inclusion of WT, CPT and GFR as a function of clearance and WT as a function of volume of distribution reduced the objective function by >6.63 at each addition. All of these covariates were determined to be essential in the model during the backward elimination phase, as shown by an increase of >12 in the value of the objective function after the influence of the covariate was removed from the model (Table 3). All other covariates that individually influenced the pharmacokinetic parameters (including k₁₂ and k₂₁) were not included, as their cumulative inclusion did not result in a significant decrease in the value of the objective function.

Table 3.

Backwards elimination: effect on objective function value of deletion of statistically significant covariates in the covariate population pharmacokinetic model for melphalan

Model	OFV	Δ OFV	Significance	Interpretation
CL = f(WT, CPT, GFR)	−177.345			Full Model
V = f(WT)
CL = f(WT, CPT)	−164.55	+12.795	P< 0.01	GFR affects CL
V = f(WT)
CL = f(WT, GFR)	−162.328	+15.017	P< 0.01	CPT affects CL
V = f(WT)
CL = f(WT, CPT, GFR)	193.879	+371.224	P< 0.01	WT affects V
CL = f(CPT, GFR)	−132.238	+45.107	P< 0.01	WT affects CL
V = f(WT)

The population pharmacokinetic parameters from the final covariate population pharmacokinetic model are summarized in Table 4. Compared with the basic model (Table 2), the covariate model had reduced interindividual variability in CL (27% vs. 60%), V (34% vs. 58%), k₁₂ (52% vs. 61%) and k₂₁ (62% vs. 64%). All the pharmacokinetic parameters were reliably estimated as the relative standard error was <45%. There was generally good agreement between observed and population-predicted melphalan concentrations in the model development dataset (Figure 1A), with the magnitude of the weighted residuals being small and randomly distributed over the entire range of population-predicted concentrations (Figure 1B). The covariate population pharmacokinetic model adequately predicted melphalan concentrations in an individual, as shown in Figure 2.

Table 4.

Melphalan population pharmacokinetic parameter estimates using the final covariate population pharmacokinetic model (model development dataset)

Parameter	Meaning	Population mean (95% CI)	Variability in estimation
			SE	%RSE
θ1	Constant in CL model	Fixed to zero
θ2	Constant in V model	1.12 (0.11, 2.13)	0.506	45%
θ3	Constant in k12 model	1.70 (1.16, 2.24)	0.270	16%
θ4	Constant in k21 model	1.84 (1.39, 2.29)	0.224	12%
θ5	Coefficient for WT in CL	0.34 (0.26, 0.42)	0.0405	12%
θ6	Coefficient for CPT in CL	−3.17 (−4.62, −1.72)	0.725	23%
θ7	Coefficient for GFR in CL	0.0377 (0.021, 0.054)	0.00838	22%
θ8	Coefficient for WT in V	0.178 (0.120, 0.236)	0.0288	16%
IIVCL	Interindividual variability in CL	27.3% (21, 32)	0.0143	32%
IIVV	Interindividual variability in V	33.8% (20, 43)	0.0366	32%
IIVk12	Interindividual variability in k12	52.2% (30, 68)	0.0924	34%
IIVk21	Interindividual variability in k21	61.7% (28, 83)	0.151	40%
σ	Residual variability*
	Proportional (%CV)	9.3% (7, 11)	0.00189	22%
	Additive (mg l−1)	0.00731 (−0.004, 0.019)	0.00565	77%
Objective function	−177.345

Structural models:

where WT = weight (kg), CPT = prior carboplatin therapy (0 = no, 1 = yes), GFR = glomerular filtration rate (ml min⁻¹ 1.73 m⁻²). IIV, Interindividual variability in the pharmacokinetic parameters, expressed as percentage coefficient of variation (%CV); variability in estimation: SE, standard error; RSE, relative standard error, calculated as standard error/population estimate and expressed as a percentage.

^*Proportional component of residual variability was expressed as %CV, while the additive component was expressed as standard deviation. 95% CI, Lower and upper limits of the 95% confidence interval, calculated as θ ± 2 SE.

Figure 1.

Diagnostic plots of the covariate population pharmacokinetic model for melphalan in the model development dataset (39 children, 571 observations). (A) Scatterplot of observed and population-predicted melphalan concentrations. (B) Plot of weighted residual vs. population-predicted melphalan concentrations

Figure 2.

Melphalan concentration–time profile in a child who received 180 mg m⁻² melphalan. •, Individual observed concentrations; —, population-predicted concentrations using the covariate population pharmacokinetic model

Model validation

The predictive performance of the covariate population pharmacokinetic model is shown in Table 5. There was insignificant bias and imprecision between measured and model-predicted melphalan concentrations. Mean prediction error (bias) was not significantly different from zero using Student's t-test. A scatterplot of observed vs. population-predicted concentrations (Figure 3A) showed that the differences between pairs of predicted and observed values were generally small. A frequency histogram (Figure 3B) confirmed that the residuals approximated a normal distribution with a mean close to zero.

Table 5.

Prediction errors on melphalan concentrations in the validation dataset (n = 277) by the covariate population pharmacokinetic model for melphalan

Parameter	Mean (mg l−1)	95% CI (mg l−1)
Bias (mean prediction error)	−0.0260	−0.2669, 0.2148
Precision (root mean square prediction error)	2.1056	1.2752, 2.6909

95% CI, Lower and upper limits of the 95% confidence interval.

Figure 3.

Post hoc assessment of predictive performance of the covariate population pharmacokinetic model in the validation dataset (20 children, 277 concentration observations). (A) Scatterplot of observed vs. population-predicted melphalan concentrations. (B) Superimposed histogram and fitted normal curve plots of frequency of occurrence vs. residual (predicted − observed concentration)

Derived pharmacokinetic parameters

The derived pharmacokinetic parameters for the total group of children, the group who had prior carboplatin and the group who had no carboplatin are presented in Table 6.

Table 6.

Derived pharmacokinetic parameters for melphalan in children

Parameter (units)	Total group	No carboplatin group	Carboplatin group
Number of children	59	33	26
Age (years)	5.63 (2.84–9.94)	6.11 (3.06–11.81)	5.01 (2.74–8.13)
CL (l h−1 kg−1)	0.47 (0.36–0.57)	0.50 (0.43–0.63)	0.40 (0.32–0.48)
CL (l h−1 m−2)	12.5 (8.4–16.0)	14.9 (12.3–17.0)	8.6 (7.6–11.7)
V (l h−1 kg−1)	0.23 (0.16–0.29)	0.24 (0.20–0.29)	0.21 (0.13–0.29)
V (l h−1 m−2)	6.0 (4.3–7.5)	6.8 (5.3–8.0)	4.5 (3.4–6.8)
k (h−1)	2.1 (1.7–2.8)	2.2 (1.8–2.9)	1.9 (1.6–2.6)
t1/2α (h)	0.12 (0.10–0.15)	0.11 (0.09–0.13)	0.14 (0.11–0.16)
t1/2β (h)	0.83 (0.70–1.05)	0.73 (0.64–0.92)	0.96 (0.78–1.18)
AUC (µg ml−1h−1)
Dose group
180 mg m−2		10.3, 12.3, 12.5	20.7 (15.3–23.9)
		(n = 3)	(n = 26)
140 mg m−2		9.0 (7.9–10.7)
		(n = 20)
100 mg m−2		13.7
		(n = 1)*
70 mg m−2		5.0 (3.7–6.3)
		(n = 6)
30 mg m−2		1.7, 2.4, 2.7
		(n = 3)

Data are median (interquartile range), except when n < 3 and actual values are presented.

^*This patient was scheduled to receive 140 mg m⁻²melphalan, but received a reduced dose due to impaired renal function.

Dosing guidelines

An example of how the population pharmacokinetic model for melphalan CL can be used to guide melphalan dosing is shown in Table 7. The nomogram for determining the melphalan dose in children is:

Table 7.

Melphalan dose (mg)^* required to achieve a target AUC of 9 µg ml⁻¹ h⁻¹ (the median value obtained by children in the 140 mg m⁻² dose group, no carboplatin), in children with various weights and renal function, with and without prior carboplatin therapy

	No carboplatin											Carboplatin
GFR (ml min–1 1.73 m–2)
Weight (kg)	50	70	90	110	130	150	170	190	210	230	250	50	70	90	110	130	150	170	190	210	230	250
10	48	54	61	68	75	81	88	95	102	109	115	19	26	33	39	46	53	60	67	73	80	87
15	63	70	76	83	90	97	104	110	117	124	131	34	41	48	55	61	68	75	82	89	95	102
20	78	85	92	99	105	112	119	126	132	139	146	50	56	63	70	77	84	90	97	104	111	117
25	93	100	107	114	121	127	134	141	148	155	161	65	72	79	85	92	99	106	112	119	126	133
30	109	116	122	129	136	143	149	156	163	170	177	80	87	94	101	107	114	121	128	135	141	148
35	124	131	138	144	151	158	165	172	178	185	192	96	102	109	116	123	129	136	143	150	157	163
40	139	146	153	160	167	173	180	187	194	200	207	111	118	124	131	138	145	152	158	165	172	179
45	155	161	168	175	182	189	195	202	209	216	223	126	133	140	146	153	160	167	174	180	187	194
50	170	177	184	190	197	204	211	217	224	231	238	141	148	155	162	169	175	182	189	196	203	209
55	185	192	199	206	212	219	226	233	240	246	253	157	164	170	177	184	191	197	204	211	218	225
60	201	207	214	221	228	234	241	248	255	262	268	172	179	186	192	199	206	213	220	226	233	240
65	216	223	229	236	243	250	257	263	270	277	284	187	194	201	208	214	221	228	235	242	248	255
70	231	238	245	252	258	265	272	279	285	292	299	203	209	216	223	230	237	243	250	257	264	270
75	246	253	260	267	274	280	287	294	301	308	314	218	225	232	238	245	252	259	265	272	279	286
80	262	269	275	282	289	296	302	309	316	323	330	233	240	247	254	260	267	274	281	288	294	301

^*Dose was obtained from population mean values.

As there is variability around the mean, dose would need to be individualized, by first administering a 10-fold lower test dose, measuring the AUC and using this information to determine the full dose required to target the desired AUC.

where WT is weight (kg), CPT = prior carboplatin therapy (0 = no, 1 = yes) and GFR is glomerular filtration rate (ml min⁻¹ 1.73 m⁻²).

Had the nomogram been used to determine the melphalan dose (targeting an AUC of 9 mg l⁻¹ h⁻¹) in our population of patients, the expected AUC values would have been mean ± SD 9.5 ± 3.0 µg ml⁻¹ h⁻¹, median (interquartile range) 9.4 (7.4–10.8) µg ml⁻¹ h⁻¹, with a minimum of 4.3 µg ml⁻¹ h⁻¹ and a maximum of 22.9 µg ml⁻¹ h⁻¹ (Figure 4A). If a 140 mg m⁻² dose had been used in our total population, the expected AUC values would have been mean ± SD 12.5 ± 4.6 µg ml⁻¹ h⁻¹, median (interquartile range) 11.2 (8.7–16.6) µg ml⁻¹ h⁻¹, with a minimum of 5.3 µg ml⁻¹ h⁻¹ and a maximum of 24.9 µg ml⁻¹ h⁻¹ (Figure 4B). Use of the nomogram reduced the SD in AUC values and produced a tighter interquartile range compared with the 140 mg m⁻² dose. However, there were still patients with AUC values considerably higher or lower than the median. The single AUC value (of 22.9 mg l⁻¹ h⁻¹) that was outside the normal curve in Figure 4A belonged to the 0.3-year-old baby (the only patient <1 year old).

Figure 4.

Histograms showing the distribution of expected AUC values in our population of 59 children using (A) a dose determined with the nomogram and (B) a 140 mg m⁻² dose

A limited sampling model for melphalan

In the development dataset the highest correlation between AUC and melphalan concentration occurred at the 2-h post infusion end time point (n = 39, r = 0.941, P < 0.001). Correlation coefficients (r) >0.9 also occurred with melphalan concentrations measured at 5, 15, 30, 50 and 60 min post end of infusion.

Using stepwise multiple linear regression, it was possible to derive a three-sample LSM for melphalan using concentration data from the 15 min, 1 h and 2 h time points.

The final LSM had the following equation:

where C_x, is the melphalan concentration at x min or h after the infusion end.

This LSM explained 97.2% of the variability in AUC in the development dataset.

The LSM-predicted AUC correlated well with the NONMEM-determined AUC in both the development (r = 0.985, P < 0.001) and validation (r = 0.922, P < 0.001) datasets, as shown in Figure 5A and B, respectively. In the validation dataset, mean prediction error (bias) was 0.186 mg l⁻¹ h⁻¹[95% confidence interval (CI) −0.348, 0.721] and was not significantly different from zero. Precision was 2.96 mg l⁻¹ h⁻¹ (95% CI 1.14, 4.03).

Figure 5.

Correlation between NONMEM-determined AUC and LSM-estimated AUC in the (A) development and (B) validation datasets

In the total cohort of children there was close correlation between NONMEM-determined AUC values and AUC values determined using a five-sample limited sampling strategy and the compartmental (r = 0.981, P < 0.001) and noncompartmental (r = 0.978, P <0.001) pharmacokinetic analysis methods implemented by the Kinetica software. Therefore, melphalan concentrations measured at 5 min, 15 min, 30 min, 1 h and 2 h post end of infusion can reliably determine AUC values using both compartmental and noncompartmental methods.

Discussion

To improve knowledge of melphalan pharmacokinetics in children with malignant diseases we have developed a two-compartment population pharmacokinetic model which provided unbiased and precise predictions of melphalan concentrations in an independent group of children. There was a tendency for the model to underpredict concentrations >20 mg l⁻¹ (shown in Figure 1A) and one possible reason for this is that there were a number of children in whom a three-compartment model might have better described the data [9]. However, as previously discussed [9], the majority of children had a biphasic decline in concentrations following the end of infusion, supporting the choice of a two-compartment model. A number of previous pharmacokinetic studies, that used traditional two-stage pharmacokinetic analysis techniques, have also found the two-compartment model to be the most appropriate [10, 14]. There has been only one other population pharmacokinetic study of melphalan, but in that study melphalan was administered as a 24-h continuous infusion and a one-compartment model was found to be the most appropriate under those circumstances [15].

After testing a wide variety of patient characteristics and clinical factors, it was found that weight, prior carboplatin therapy and GFR influenced clearance, while weight influenced volume of distribution. Inclusion of these factors significantly improved the population pharmacokinetic model based on the likelihood ratio test. These results are in agreement with our previous pharmacokinetic study on melphalan, which used a two-stage pharmacokinetic analysis technique [9], with the only difference being that, in that analysis, prior TBI therapy was also found to influence clearance. In this population analysis, prior TBI therapy was found to be significant in the preliminary screening phase, but did not improve the model in the forward stepwise model-building phase. This covariate was therefore not incorporated into the model as it would not have improved the ability of the model to make predictions of melphalan concentrations.

Our study population had a broad weight range (7.7–104 kg) and we found that melphalan clearance and volume of distribution were both a function of weight. In children, clearance and volume of distribution are commonly weight related and weight has been included in covariate population pharmacokinetic models for amphotericin B [16], ondansetron [17] and ketotifen [18].

As renal excretion is an important elimination pathway for melphalan [6], an effect of renal function on melphalan clearance can be expected. In our study, a lower normalized GFR was associated with decreased melphalan clearance and, under these circumstances, lower doses are required to target a particular AUC in children of specific weights (Table 7). This finding is consistent with previous studies showing increased melphalan toxicity [3, 19] and improved outcome with reduced doses [3] in patients who have impaired renal function. Decreased melphalan clearance has also been demonstrated in dogs with renal dysfunction [20].

Similar to our previous study [9], melphalan clearance was affected by prior carboplatin therapy. The derived pharmacokinetic parameters shown in Table 6 for the no carboplatin and carbopatin groups compared favourably with our previous results using the traditional two-stage approach [9], providing confidence in the population pharmacokinetic modelling procedure. For example, in the traditional analysis clearance was 15.5 l h⁻¹ m⁻² and 10.2 l h⁻¹ m⁻² in the no carboplatin and carboplatin groups, respectively, whilst in this population analysis, the values were 14.9 l h⁻¹ m⁻² and 8.6 l h⁻¹ m⁻², respectively. The AUC values obtained for the different dose groups also compared very favourably.

Table 7 gives an example of how the population pharmacokinetic model for clearance can be used to guide melphalan dosing in children. Use of the nomogram in our population of patients is expected to reduce variability in exposure compared with the 140 mg m⁻² dose, producing a tighter interquartile range. However, it should be noted that the nomogram still needs to be tested prospectively. It should also be remembered that the doses shown in Table 7 were obtained from population mean values. As there is variability around the mean, with some individuals still expected to have very high or very low exposure (shown in Figure 4A), further dose individualization would be required. The nomogram described in this study may not be applicable to children <1 year old as there was only one child of this age group in our population and, in this child, the nomogram-predicted AUC was the highest in the series, shown as an outlier in Figure 4A.

High-dose melphalan is usually administered as a single dose. Therefore, the only way to individualize doses would be to administer a lower test dose a few days before the scheduled full dose, measure the AUC and use this information to determine the dose required to target a particular AUC. Linearity in melphalan pharmacokinetics is suggested by the fact that mg m⁻² dose was not selected as a covariate in the model-building procedure. Additionally, the test dose method has been previously used successfully to adjust the dose to achieve a target AUC in individuals not receiving carboplatin [21]. However, carboplatin administration affects the linearity of melphalan pharmacokinetics, so that a test dose does not accurately predict the pharmacokinetics of a full dose [9, 22] and, thus, pharmacokinetically guided dosing is not possible in patients receiving carboplatin.

Therapeutic drug monitoring of melphalan would be facilitated by the three-sample LSM that was developed as part of this investigation. It should be noted that this LSM, developed using multiple linear regression, is applicable only to the 15-min infusion time. In the future, use of approaches such as d-optimality may provide a more robust LSM that is less sensitive to variations in infusion time. While the LSM-predicted AUC values were very close to the NONMEM-determined AUCs in most patients in the development and validation datasets, Figure 5B shows that there were discrepancies in a few patients in the validation dataset. In a prospective evaluation of the LSM, it would therefore be wise to collect five blood samples at 5 min, 15 min, 30 min, 1 h and 2 h post end of infusion, so that a two-stage pharmacokinetic analysis may also be performed. Bayesian methodology in combination with limited sampling may also be used to determine melphalan AUC values in those populations where population pharmacokinetic parameters have been determined.

The melphalan HPLC assay is rapid, easy, precise and reproducible. With a retention time of <10 min, it is entirely feasible that melphalan concentrations from a test dose may be monitored in a timely manner. The capital cost of establishing a melphalan therapeutic monitoring service is the cost of an HPLC system that will be dedicated to the analysis of melphalan. The cost of a basic system which includes a single HPLC pump, an injector, a UV detector and an integrator is approximately AU$40 000 (£16 000). The main cost of maintaining this service is the cost of personnel: a scientist employed fulltime would be required. Thus, the cost of targeting melphalan concentrations is a small proportion of the total cost of transplantation and would be easily justified if melphalan exposure is shown to be an important determinant of transplant outcome.

In our example of how to use the population pharmacokinetic model for melphalan to guide dosing we targeted an AUC of 9 µg ml⁻¹ h⁻¹, which was the median value obtained by children who received the 140 mg m⁻² dose and no carboplatin (representing the largest dose group in the no carboplatin series). Proportional changes in the target AUC would be required for lower or higher dose groups (e.g. a target for the twofold lower dose of 70 mg m⁻² would be a twofold lower AUC of 4.5 µg ml⁻¹ h⁻¹). Targeting median AUC values reduces the variability in exposure, ensuring that a greater proportion of patients are within a tighter interquartile range. However, ideally, a pharmacodynamic study should be performed to identify a target AUC that is associated with good transplant outcome and acceptable toxicity. These studies need to be performed in uniform patient populations receiving uniform conditioning. Such a pharmacodynamic study is difficult in our population of children with 11 different diagnoses, receiving both autologous and allogeneic transplants with multiple conditioning regimens using multiple drugs.

In conclusion, a covariate population pharmacokinetic model for melphalan has been developed and validated in children with malignant diseases. A dosing nomogram was produced that now needs to be tested prospectively. A three-sample limited sampling model was developed that will facilitate pharmacokinetic monitoring of melphalan. Two-stage pharmacokinetic analysis with a five-sample limited sampling strategy was also shown to provide reliable estimates of AUC. Further pharmacodynamic studies are now required to identify a target AUC that is associated with a good transplant outcome and acceptable toxicity.