Population Pharmacokinetics of Alemtuzumab (Campath) in Pediatric Hematopoietic Cell Transplantation: Towards Individualized Dosing to Improve Outcome

The laboratory in London, measuring samples from part of the London population, used a quantitative flow cytometry (Q-FACS) assay. Alemtuzumab levels were measured using Q-FACS assays, in modifications of the method described [28]. In short, 1 × 10⁶ human T-cell line-78 (HUT-78) T cells were incubated using fourfold dilutions of patients’ serum in phosphate-buffered saline (PBS), followed by washing and incubation with conjugated secondary antibodies (Alexa Fluor 647 labeled goat anti-human IgG; Life Technologies). Incubations were carried out at room temperature for 30 min each. To construct a reference curve, HUT cells were incubated with known amounts of alemtuzumab (range 10–0.01 µg/mL) containing 25% human serum. Cells were washed and mean fluorescence intensity (MFI) was measured on an FACS Calibur machine (Becton Dickinson Biosciences, Franklin Lakes, NJ, USA). The lower limit of quantitation for alemtuzumab in this assay was 0.1 µg/mL, with a linear response from 0.01 to 0.1 μg/mL. The assay did not change over time.

All samples from Leiden, and part of the samples from London, were measured in Leiden using an enzyme-linked immunosorbent-based assay (ELISA) [29]. Microtiter plates (Corning Corporation, Corning, NY, USA) were coated with a human polyclonal anti-idiotype antibody to alemtuzumab (Geoff Hale Developments, Marston, Oxford, UK), diluted in PBS at a concentration of 0.5 µg/mL, by incubating overnight at 4 °C, followed by blocking with 2% casein in PBS. Samples, controls, and a diluted standard range of alemtuzumab (25.000–100 µg/mL, diluted in 10% pooled human serum) were applied and incubated at 37 °C for 1 h at room temperature. After washing, bound alemtuzumab was detected with biotin-labeled anti-idiotype antibody, 1 h at room temperature, followed by streptavidin poly-horseradish peroxidase (HRP; Sanquin, 8000145253, 2 µg/mL), for 30 min. The lower limit of detection was 0.01 µg/mL. The assay did not change over time.

In both assays, alemtuzumab spiked sera were used as controls. The results of 146 samples tested with both ELISA NC anti-idiotype and Q-FACS were compared. For the correlation, only samples with a measured alemtuzumab concentration > 0.1 µg/mL in Q-FACS were used. Electronic supplementary Fig. S1 shows the reasonable correlation of both assays (R² = 0.89).

For analysis of the PK data, non-linear mixed-effects modeling was employed using NONMEM 7.3.0 (Icon Development Solutions LLC, Hanover, MD, USA). R version 3.2.3 and Pirana version 2.8.2 were used for preparation and visualization of data. First-order conditional estimation (FOCE) with interaction was used throughout the model development. Alemtuzumab concentrations were logarithmically transformed and simultaneously fitted. Samples that were reported to be below the limit of quantification (BLQ), which only occurred in the tail-end of the concentration, were set at half the BLQ, with subsequent samples being removed in accordance with method M6 [30]. Interindividual variability on PK parameters was assumed to follow a log-normal distribution, and were implemented in the model according to Eq. 1:where \(P_{i}\) is the individual or post hoc value of the parameter in the ith individual, \(P_{\text{pop}}\)is the population mean for this parameter, and \(\eta_{i}\) is the interindividual variability of the ith person, which samples from a normal distribution with a mean of 0 and a variance of ω². An additive error model was used, which, due to logarithmically transformed data, should be seen as a proportional error model. Here, the jth observation for the ith individual was described using Eq. 2:where \(Y_{i,j}\) is the observed concentration, \(C_{{{\text{pred}},i,j}}\) is the jth predicted concentration for individual i, and \({\varepsilon }\)is the error, sampled from a normal distribution with a mean of 0 and a variance of σ².

Several criteria were applied in the process of model building and selection. A decrease in objective function value (OFV) over 3.84 points between nested models was considered statistically significant; this correlated with p < 0.05 based on a Chi-square distribution with 1 degree of freedom. Goodness-of-fit (GOF) plots were evaluated, including observed versus both individual- and population-predicted concentrations, as well as conditional weighted residuals (CWRES) versus time and observed concentrations. Additionally, parameter uncertainty and \(\eta\)shrinkage were evaluated to assess model performance.

Interoccasion variability (IOV) was tested to assess changes in parameters between the respective doses according to Eq. 3:where, compared with Eq. 1, κ_i is the IOV for the mth occasion. Individual PK parameters (post hocs) were estimated using the POSTHOC option in NONMEM.

The elimination of antibodies is often dependent on the concentration of substrate [31, 32], therefore non-linear elimination pathways were explored. No data on target concentrations over time (i.e. CD52 or lymphocytes) were available, therefore full target-mediated drug disposition (TMDD) models, as previously described, were not persued [32, 33]. Instead, non-linear elimination pathways were explored by incorporating clearance (CL) described by Michaelis–Menten kinetics (Eq. 4):where V is the elimination rate, V_max is the maximum elimination rate, C is the alemtuzumab concentration, and K_m is the Michaelis–Menten constant, the concentration at which 50% of the maximum elimination rate is reached.

Patient characteristics, including body size parameters (actual body weight, age, body surface area), and transplant- and disease-specific variables (sex, underlying disease, stem cell source, number of HCTs received, treatment center) were studied as possible covariates for their relation with PK parameters. In line with previous reports, the role of lymphocyte counts on alemtuzumab PK was also investigated as CD52 is almost exclusively expressed on these cells. Cell counts drawn before the first infusion of alemtuzumab were available; the lymphocyte counts are greatly reduced after the first dose and were therefore not taken in the included patients. Therefore, we considered baseline lymphocyte counts drawn within 48 h before infusion of the first alemtuzumab dose as a covariate. No other biochemical markers were evaluated as a covariate.

To assess the covariate relations, post hocs, interindividual variability, and CWRES were plotted against covariates, both before and after inclusion of the covariates, to evaluate potential relationships. Stepwise covariate modeling was performed in parallel. Lastly, only those covariates where a physiological or pharmacological mechanism could be hypothesized were included. Continuous covariates such as age and body weight were tested in a linear and power function (Eqs. 5 and 6):where P_i and Cov_i are the parameter and covariate value for the ith individual, respectively, \(P_{\text{pop}}\) is the population mean for this parameter, and Cov_median is the standardized value for the covariate. In the linear relationship equation (Eq. 5), l represents the slope factor of the linear function, while, in the power relationship equation (Eq. 6), k is the scaling factor. Additionally, because the influence of bodyweight on CL appeared more complex, variations of Eq. 6 were explored, where k is dependent on the covariate value of the ith individual, as proposed by Wang et al. [34]. and implemented in several other models [35, 36]. Evaluated variations included a maximum effective concentration (E_max) approach and a power function according to Eq. 7:where k is the exponential scaling factor in Eq. 6, k₀ is the value for the exponent for an individual with a hypothetical bodyweight of 0 kg, k_max is the maximum decrease of the exponent, k₅₀ is the bodyweight at which 50% of k_max is reached, and ϒ is the Hill coefficient determining the steepness of the sigmoidal decline. In the power function, a represents the coefficient and b is the exponent. This model was developed in order to reflect the changing influence of weight with age during growth of the child.

Potential covariates were evaluated using forward inclusion and backward elimination, with a significance level of < 0.005 (− 7.9 points in OFV) and < 0.001 (− 10.8 points in OFV), respectively. Building of the covariate model was comparable with the development of the structural model. In addition, after inclusion of a covariate, a decline in unexplained interindividual variability had to be achieved before inclusion into the final model [37].

The model was thoroughly evaluated for robustness. To assess the predictive performance of the model, bootstrap analyses were performed, stratified on treatment center. One thousand datasets were created using random selection from the original dataset; the final model was fit to each data set. For each parameter, median values from the thousand fits for each parameter, as well as 95% confidence intervals (CIs), were compared with parameter estimates of the final model.

In addition, a normalized prediction distribution of errors (NPDE) was performed, where the prediction discrepancies are simulated, taking into account the correlation between observations in the same individual and the predictive distribution [38]. Finally, prediction-corrected visual predictive checks (VPCs) were created to assess the predictive performance of the final model compared with the measured concentrations.