In the period 2008-2010, 41 patients (24 males & 17 females) less than 18 years and diagnosed as acute lymphoblastic leukemia were enrolled in the study. The mean age (years), body weight (kg) and height (cm) ± SD of the patients were 6.5 ± 3.4, 17.6 ± 9.9 and 117.2 ± 19.4 respectively. The ranges of age, body weight and height were 3 - 15 years, 13 - 54 kg and 100 - 177 cm respectively. They all have received high dose methotrexate (MTX) according to the treatment protocols followed in the oncology unit. Patients were diagnosed as acute lymphoblastic leukemia (ALL) if at least 25% lymphoblasts were present in the bone marrow (BM) in addition to examination of both BM and peripheral blood smears as well as cerebrospinal fluid (if required) for malignant cells. Treatment applied to the patients followed the protocols applied in St. Jude Research Hospital for treatment of ALL (i.e. BFM 90, high risk I or II, or total XIII) [
Methotrexate (MTX) was administered as intravenous infusion at a dose of 2 gm/m2 over a period of two hour (according to the regimen followed in the hospital) to achieve concentrations in the range of <5 μM at 24 h, and <0.5 μM at 48 h. The treatment protocol consists of 3 cycles of chemotherapy that are given every month for a total of 9 doses. The different treatment regimens used during study involved co-administration of drugs e.g. vincristine, ifosfamide, daunorubicin, L-asparaginase and leucovorin. MTX plasma concentrations determined primarily at 24 hr post-dose were utilized in the building-up of the PK-model. Additionally, any concentrations when available at 48 and 72 hr post dose for any patient were utilized in the pharmacokinetic analysis.
All patients had normal liver & kidney function. The demographics of the study population are listed in
Data were analyzed using the nonlinear mixed-effect modeling approach [
The initial/prior estimates of clearance (CL), volumes of distribution of both central (V1) and peripheral compartments (V2) and inter-compartmental clearance (Q2) were extracted from previous studies on the MTX [7-11]. The number of observations utilized in PK analysis for each subject was limited by MTX concentration primarily at 24 h (and also at 48 and 72 hr post infusion whenever available/patient). The inter-compartment clearance between central and shallow peripheral compartment (Q2) was fixed to literature value.
Different covariates including age, body weight, height, body surface area (BSA), body mass index (BMI), gender and creatinine clearance were assessed if influencing the model performance and parameter estimates. Investigation of covariate-parameter relationships was based on the range of covariate values in the dataset, scientific interest, mechanistic plausibility, exploratory graphics, and previously reported covariate-parameter relationships for MTX. Assessment of each covariate was based on evaluating the difference in objective function value (OFV). The covariates were added to final base model by a standard approach to model selection (forward addition/backward elimination). Body surface area, gender and weight were found to be covariates influencing the final model. The equations applied to check the influence of different covariates on the model as well as estimation of the prediction error model were all derived from the NONMEM library [
For continuous covariates, a power function was utilized (Equation (1)):
where TVPi is the typical value of a PK parameter (P) for an individual i with a COVi value of the covariate, while θ1 is the typical value for an individual with a median covariate value of COVmed and θ2 is the exponent of the power function.
For categorical covariates, the fractional change in the typical parameter value was determined, according to Equation (2):
where, TVPi is the typical value of a PK parameter (P) for an individual i, θ1 is the typical value for an individual in the absence of the covariate and θ2 is the fractional change in the typical value.
All inter-individual error terms in this analysis were described by an exponential error model, or log-normal parameter distribution (Equation (3)).
where:
Pi is the estimated parameter value for individual I;
TVP is the typical population value (geometric mean) of the parameter;
ηpi are individual-specific inter-individual random effects for individual i and parameter P and are assumed to be distributed: η ~ N (0, ω2) with covariance defined by the inter-individual covariance matrix Ω.
For PK observations in this analysis, the residual error model was described by a proportional error model (Equation (4)).
where:
Cij is the jth measured observation in individual i;
Ĉij is the jth model predicted value in individual i;
εij is the proportional residual error for individual i and measurement j.
A bootstrap resampling technique (n = 1000) was applied as internal validation to the final POP PK model and the 95% confidence intervals for the estimates were calculated.
The bootstrap replicates (1000 runs) were generated by sampling randomly from the original data set using the individual as the sampling unit. Population parameters of the final PK model for each data set were estimated using NONMEM. This resulted in a distribution of estimates for each population model parameter. Empirical 95% CIs was constructed by obtaining the 2.5th and 97.5th quantiles of the resulting parameter distributions. Estimates from all NONMEM runs (with successful and unsuccessful minimization) were reported.
A visual predictive check was performed by simulating 1000 datasets using the final model and covariates, dosing times, and PK sampling times contained in the dataset to evaluate the predictability of the model. The statistics (e.g., median and the 90th percentile interval) of the observations and model-simulated predictions that were calculated from the entire data set (all participants) at each time point were compared.
