Body Weight-Dependent Pharmacokinetics of Busulfan in Paediatric Haematopoietic Stem Cell Transplantation Patients

Abstract

Background and Objectives: The wide variability in pharmacokinetics of busulfan in children is one factor influencing outcomes such as toxicity and event-free survival. A meta-analysis was conducted to describe the pharmacokinetics of busulfan in patients from 0.1 to 26 years of age, elucidate patient characteristics that explain the variability in exposure between patients and optimize dosing accordingly.

Patients and Methods: Data were collected from 245 consecutive patients (from 3 to 100 kg) who underwent haematopoietic stem cell transplantation (HSCT) in four participating centres. The inter-patient, inter-occasion and residual variability in the pharmacokinetics of busulfan were estimated with a population analysis using the nonlinear mixed-effects modelling software NONMEM VI. Covariates were selected on the basis of their known or theoretical relationships with busulfan pharmacokinetics and were plotted independently against the individual pharmacokinetic parameters and the weighted residuals of the model without covariates to visualize relations. Potential covariates were formally tested in the model.

Results: In a two-compartment model, body weight was the most predictive covariate for clearance, volume of distribution and inter-compartmental clearance and explained 65%, 75% and 40% of the observed variability, respectively. The relationship between body weight and clearance was characterized best using an allometric equation with a scaling exponent that changed with body weight from 1.2 in neonates to 0.55 in young adults. This implies that an increase in body weight in neonates results in a larger increase in busulfan clearance than an increase in body weight in older children or adults. Clearance on the first day was 12% higher than that of subsequent days (p < 0.001). Inter-occasion variability on clearance was 15% between the 4 days. Based on the final pharmacokinetic-model, an individualized dosing nomogram was developed.

Conclusions: The model-based individual dosing nomogram is expected to result in predictive busulfan exposures in patients ranging between 3 and 65 kg and thereby to a safer and more effective conditioning regimen for HSCT in children.

Appendix

Model of Random Variability

$${{\rm{P}}_{{\rm{ig}}}} = {{\rm{P}}_{{\rm{pop}}}} \times {{\rm{e}}^{{\rm{\eta i}} + {\rm{\kappa ig}}}}$$

((Eq. 1))

Equation 1 describes the inter-individual variability and day-to-day (inter-occasion) variability[29] of the structural parameters within the population, in which lognormal distribution was assumed. P_ig represents the individual pharmacokinetic parameter for subject i on occasion g. P_pop is the typical value of the population pharmacokinetic parameter. An occasion (g) was defined as all measurements performed in 1 day, and κ_ig is the random effect between days. η and κ are random variables that follow the normal distribution, with a mean value of 0 and variance of ω² and π², respectively.

$${\rm{log}}{{\rm{\;C}}_{{\rm{ij}}}} = {\rm{log}}{{\rm{\;C}}_{{\rm{pre}}{{\rm{d}}_{{\rm{ij}}}}}} + {\rm{\varepsilon }}$$

((Eq. 2))

Equation 2 describes the intra-individual variability: the differences between the observed and predicted concentrations. This residual error includes, among other factors, model misspecification and measurement errors. The intra-individual variability was modelled using an additive error, equivalent to a proportional error model in the untransformed scale. C_ij is the observed concentration for subject i at time j, and${{\rm{C}}_{{\rm{pre}}{{\rm{d}}_{{\rm{ij}}}}}}$ is the predicted concentration for individual i at time j. ɛ is a random variable that follows the normal distribution, with a mean value of 0 and variance of σ².

Other Model Equations

$${\rm{C}}{{\rm{L}}_{{\rm{da}}{{\rm{y}}_1}}} = {\rm{C}}{{\rm{L}}_{{\rm{pop}}}} \times (1 - {\rm{fractio}}{{\rm{n}}_{{\rm{da}}{{\rm{y}}_{2 - 4}}}})$$

((Eq. 3))

Equation 3 describes the clearance at day_2–4, estimated as a fraction of clearance at day₁. CL_day1 is the typical value of clearance at day₁. CL_pop is the typical value of clearance. Fraction day_2–4 is the clearance at day_2–4 expressed as a reduction factor of day₁.

Covariate Functions

The nature of the influence of continuous covariates on each pharmacokinetic parameter was tested using a linear function (equation 4) and an allometric function (equation 5):

$${{\rm{P}}_{\rm{i}}} = {{\rm{P}}_{{\rm{pop}}}} \times {\left( {{{{\rm{Co}}{{\rm{v}}_{\rm{i}}}} \over {{\rm{Co}}{{\rm{v}}_{{\rm{mean}}}}}}} \right)^1}$$

((Eq. 4))

$${{\rm{P}}_{\rm{i}}} = {{\rm{P}}_{{\rm{pop}}}} \times {\left( {{{{\rm{Co}}{{\rm{v}}_{\rm{i}}}} \over {{\rm{Co}}{{\rm{v}}_{{\rm{mean}}}}}}} \right)^{{\rm{L1}}}}$$

((Eq. 5))

In equation 4, P_i is the individual parameter for subject i with Cov_i. P_pop is the typical value of the population pharmacokinetic parameter. Cov_i represents the covariate such as body weight, BSA or age for subject i, and Cov_mean represents the mean value of the covariate.

In equation 5, P_i is the individual parameter for subject i with Cov_i. P_pop is the typical value of the population pharmacokinetic parameter. Cov_i represents the covariate such as body weight, BSA or age for subject i, and Cov_mean represents the mean value of the covariate. L1 represents the scaling exponent of the allometric function, which is one fixed estimated value in the case of an allometric function with a single scaling exponent.

In equation 6, the allometric function with a scaling exponent that varies with body weight, BSA or age is shown, in which P_i is the individual parameter for subject i with Cov_i P_pop is the typical value of the population pharmacokinetic parameter. Cov_i represents the covariate such as body weight, BSA or age for subject i, and Cov_mean represents the mean value of the covariate. In the scaling exponent, L2 represents the intercept and M is the exponent, which allows the scaling exponent to change with the covariate body weight, BSA or age.

$${{\rm{P}}_{\rm{i}}} = {{\rm{P}}_{{\rm{pop}}}} \times {\left( {{{{\rm{Co}}{{\rm{v}}_1}} \over {{\rm{Co}}{{\rm{v}}_{{\rm{mean}}}}}}} \right)^{{\rm{L}}2 \times {\rm{Co}}{{\rm{v}}^{\rm{M}}}}}$$

((Eq. 6))

Potential categorical variables were modelled using equation 7:

$${{\rm{P}}_{\rm{i}}} = {{\rm{P}}_{{\rm{pop}}}} \times {{\rm{P}}_{\rm{c}}}^{{\rm{CCov}}}$$

((Eq. 7))

where CCov is the categorical covariate, P_i is the individual parameter for subject i, P_pop is the typical value of the population pharmacokinetic parameter in the absence of the covariate of interest (CCov = 0), and P_c is the fractional change in the typical value of the pharmacokinetic parameter caused by the covariate.