Alemtuzumab Exposure and T Lymphocyte Depletion: A Population Pharmacokinetic‐Pharmacodynamic Model of Alemtuzumab Induction Therapy for Kidney Transplantation

Abstract

Alemtuzumab is a T cell‐depleting monoclonal antibody that is used for the prevention of kidney transplant rejection. The duration of lymphodepletion after the current standard induction therapy dose is likely longer than necessary, resulting in prolonged T cell lymphopenia with the associated risk of infections. Here, the interplay between alemtuzumab exposure and T cell dynamics was quantitatively evaluated, and the influence of different doses on T cell recovery was investigated. A population pharmacokinetic‐pharmacodynamic model describing the interplay between 30 mg alemtuzumab induction therapy and T cell dynamics in kidney transplantation was developed using NONMEM, using pharmacodynamic data from the Triton study (NCT02057965). The developed model was used to perform an exposure‐response analysis and investigate dose optimization with model‐derived simulations. In total, 418 peripheral blood T cell measurements from 61 adult kidney transplant recipients were included for model development. A single‐compartment turnover E _max model with a first‐order T cell influx with feedback and a first‐order T cell efflux with parallel alemtuzumab‐stimulated T cell removal best described the data. Higher alemtuzumab exposure was associated with lower individual‐predicted T cells 4 weeks after administration and longer T cell recovery (> 200 cells/μL). In the simulations, a fixed dose of 15 mg improved median recovery times by 19 days as compared to the standard 30 mg dose without influencing early T cell depletion. A population pharmacokinetic‐pharmacodynamic model adequately described T cell dynamics after alemtuzumab induction therapy in kidney transplant recipients. This model can be used to inform future dose‐optimization studies of alemtuzumab in different clinical settings.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Alemtuzumab induction therapy causes a long‐lasting T cell depletion and is associated with adverse outcomes in kidney transplantation. The long duration of T cell depletion is likely a sign of overdosing. However, no formal dose‐finding studies have been undertaken for alemtuzumab in kidney transplantation or other solid organ transplantation.

• WHAT QUESTION DID THIS STUDY ADDRESS?

This study addresses the interplay between alemtuzumab dosing, alemtuzumab exposure, and the depletion and recovery of T cells. Furthermore, it explores the potential effects of alemtuzumab dose adjustments on the kinetics of T cells through model‐derived simulations.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

This study showed that T cell recovery is only partly explained by the exposure to alemtuzumab. Furthermore, it provides a semi‐mechanistic PK‐PD modeling approach to describe cell kinetics as a function of monoclonal antibody therapy which could be used in different settings as well.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

The standard dose of alemtuzumab induction therapy in kidney transplantation can probably be reduced by 50% while remaining a complete T cell depletion of sufficient duration. Clinical studies are necessary to evaluate how this dose reduction will affect the adverse outcomes of alemtuzumab therapy and assure its efficacy.

Kidney transplant rejection remains an important problem after kidney transplantation complicating ~20% of transplantations. ¹ Alemtuzumab is a humanized, monoclonal antibody directed against the glycoprotein CD52 on different immune cells. It is used as a T cell‐depleting drug for both the prevention and treatment of kidney transplant rejection. ² , ³ , ⁴ Treatment with alemtuzumab causes long‐lasting T cell depletion and is associated with serious infections ³ , ⁴ and auto‐immunity. ⁵ , ⁶

The optimal duration of lymphodepletion is unknown. However, with the current dose of 30 mg, depletion lasts for many months after transplantation, ⁷ which is likely longer than necessary. Furthermore, prolonged T lymphopenia is associated with increased morbidity and mortality after kidney transplantation. ⁸ Therefore, reducing the time of T cell depletion may prevent adverse effects of alemtuzumab. Conversely, if lymphocyte depletion is insufficient, it might decrease its efficacy and cause excess rejection.

Importantly, no formal dose‐finding studies were performed for alemtuzumab in kidney transplantation. The dose for induction therapy is 30–60 mg subcutaneously, which is based on the volume of 1–2 vials. ⁹ Both lower and bodyweight‐adjusted doses of alemtuzumab for induction therapy resulted in similar rejection rates, faster T cell recovery, and fewer infections compared to a fixed dose of 30 mg. ¹⁰ , ¹¹ However, these studies did not monitor alemtuzumab exposure and did not investigate the optimal dosing strategy for improving T cell recovery while maintaining efficacy.

A recent pharmacokinetic study demonstrated that 30 mg of alemtuzumab caused a median alemtuzumab exposure above the lympholytic concentration for 43 days. ¹² Yet, this analysis only investigated the pharmacokinetics of alemtuzumab but not the relation between alemtuzumab exposure and T cell dynamics. The aim of the current study was to describe the interplay between alemtuzumab exposure and T lymphocyte dynamics, and to investigate the influence of different dosing strategies on T cell recovery after kidney transplantation by extending the previous population pharmacokinetic model into a population pharmacokinetic‐pharmacodynamic (PK‐PD) model.

MATERIALS AND METHODS

Data and patients

The clinical, pharmacokinetic, and pharmacodynamic data used to develop the model were obtained from a prospective, randomized, controlled clinical trial: the Triton study (www.clinicaltrials.gov; NCT02057965). ¹² , ¹³ Patients included in the Triton study were adults who received their first kidney transplant and were randomized to receive either autologous mesenchymal stromal cell therapy with early tacrolimus withdrawal or standard tacrolimus maintenance immunosuppression for the entire study period without mesenchymal stromal cell therapy. Additional maintenance immunosuppressive therapy consisted of prednisolone and everolimus for both groups. Alemtuzumab was given as induction therapy to all patients irrespective of randomization, as a subcutaneous bolus of 15 mg for two consecutive days (cumulative dose 30 mg). The study was approved by the Medical Ethical Committee of Leiden University Medical Centre and by the Central Committee on Research involving Human Subjects (CCMO) in the Netherlands (NL43712.000.13). All patients gave written informed consent.

Sampling and measurements

Blood samples were obtained 1 day prior to kidney transplantation, and at 4, 6, 8, and 12 weeks after transplantation. ¹² Additionally, peripheral blood T cell counts were performed at 24 weeks, 52 weeks, and 2 years after transplantation. For all patients with residual material from routine laboratory assessment during the first week after therapy, additional cell counts were measured to gain insight into the early PD effects of alemtuzumab. Alemtuzumab was quantified in serum with a validated, customized enzyme‐linked immunosorbent‐based assay based on human anti‐alemtuzumab antibodies (NC Geoff Hale Developments, Oxford, UK). ¹⁴ Absolute cell counts were measured with flow cytometry using the BD Multitest kit (BD Biosciences), which has an analytical measurement range of 17–5000 cells/μL for CD3+ T cells. ¹⁵ The lower limit of quantification at our laboratory was calculated as 1 cell/μL.

Software and settings

For details regarding the used software and settings, we refer to the Supplementary Methods .

Population pharmacokinetic model

The PK‐PD model was developed as an extension of the population pharmacokinetic model developed by Zwart et al. ¹² In short, this model consisted of a two‐compartmental model with first‐order absorption and parallel first‐order and time‐varying concentration‐dependent elimination, and included between‐subject variability on the first‐order elimination and central distribution volume. ¹² The first‐order elimination (CL), intercompartmental clearance (Q), central distribution volume (V _c), and maximal nonlinear elimination rate (V _max) were allometrically scaled to lean body weight. The model code is provided in the Supplementary Data . Using maximum a posteriori Bayesian estimation, the pharmacokinetic model was used to generate individual‐predicted alemtuzumab concentrations for all participants for every day during the first 2 weeks, followed by one prediction each week up to 2 years after transplantation. The predicted concentrations were then added as pharmacokinetic input to the dataset for pharmacodynamic model development.

Population pharmacodynamic model

Various structural models of incremental complexity were explored to describe the T cell dynamics in our patient population. Model structures incorporating a stimulatory loss indirect response model as defined by Mold et al. were considered. ¹⁶ Furthermore, transit compartment models with a feedback loop as proposed by Friberg et al., ¹⁷ who developed a model to predict the pharmacodynamics of neutrophilic granulocytes after chemotherapy, were evaluated. More complex transit‐turnover models as published by Azzopardi et al., ¹⁸ who developed a model to predict T cell recovery after rabbit anti‐thymocyte globulin (ATG) induction therapy for kidney transplant recipients, were also considered. Alemtuzumab was hypothesized to stimulate the degradation of T cells, in line with its mechanism of action. Both standard E _max models with and without sigmoidicity and linear models were considered to describe the effect of alemtuzumab.

Between‐subject variability (BSV) was modeled on effect parameters: for E _max models, these were the EC50 and E_max parameters, and for linear models, this was the slope parameter. Furthermore, BSV was modeled on parameters that influenced the production of new T cells, which, depending on model type, included the influx of T cells, mean maturation time, and the baseline estimation of T cells. BSV was modeled exponentially.

Measurements below the limit of quantification (BLoQ) were included as raw flow cytometry output, but values below the detection limit were set to 0.9 cells/μL to avoid numerical errors due to an excess of zeros in the dataset. Other BLoQ methods (i.e., M1, M5, M6, and M7) were evaluated as proposed by Johnson et al. ¹⁹ Additive, proportional, and combined error models were evaluated to establish the best description of the residual error.

Covariate analysis

Initial exploration of potential covariate relationships was performed using standard empirical Bayes estimates (EBE) vs. covariate plots. Influences of age, weight, BSA, randomization status, baseline T cells, and baseline co‐morbidities on the parameters with interindividual variability were checked. From this graphical analysis, potential covariates were selected. Further covariate analysis was performed with manual forward inclusion and backward elimination. Categorical variables were included as proportional effects. Continuous variables were centered around the median, and both linear and exponential effects were considered. Models with and without the covariate parameter were compared with a likelihood ratio test with one degree of freedom. A significant covariate effect was defined as a difference in objective function value (dOFV) of 3.84 or larger, which corresponds with a significance level of α = 0.05. For backward elimination, a P‐value of < 0.01 was used (dOFV > 6.64). Also, the degree of decrease of the unexplained between‐subject variability between the covariate model and the base model was used to decide whether to include or exclude a covariate in the final model.

Model evaluation

During structural model development, models were evaluated based on parameter estimate precision (RSEs < 30%), eta and epsilon shrinkage (< 30%), and parameter estimation stability. Furthermore, biological plausibility and the rule of parsimony of the different models were considered while comparing different structural models. The objective function value (OFV) was used for statistical comparison between a candidate model and its precursor. A P‐value < 0.05 (dOFV > 3.84) was considered a statistically significant improvement of the candidate model over the precursor model. Additionally, visual and simulation‐based model evaluations were conducted using standard goodness‐of‐fit (GOF) plots. For the final base and final covariate model, visual predictive checks (VPCs; n = 500) in addition to the GOF plots were evaluated. For the final covariate model, a normalized prediction distribution error (NPDE; n = 1000) analysis and bootstrap procedure (n = 1000 replicates) were conducted.

Exposure‐response analysis

Alemtuzumab exposure was expressed as the area under the concentration vs. time curve from zero to infinity (AUC_0–inf) and the maximal concentration (C _max). The responses were expressed as the individual‐predicted T cell count at 4 weeks after induction therapy and the individual‐predicted time to T cell recovery > 200 cells/μL. All were calculated for each individual study patient with the final PK‐PD model, using maximum a posteriori Bayesian estimation.

Model simulations

Simulations with the final population PK‐PD model were performed to assess the effect of different alemtuzumab dosing strategies on T cell dynamics. The patient population for model simulations was based on one thousand real‐life kidney transplant recipients, who had previously consented to the use of their data for research purposes. The anonymized age, sex, weight, length, and mode of dialysis were extracted from the national Dutch transplant database. With these characteristics, the LBW was calculated, and baseline T cell counts were simulated based on the values and previously reported correlations between age, sex, and T cells (see Supplemental Methods for details). ²⁰ , ²¹ , ²² , ²³

Different pragmatic, fixed, single‐dosing regimens of 15, 10, 7.5, and 5 mg were compared to the study's regimen of 15 mg for two consecutive days. In addition, bodyweight‐adjusted dosing regimens were evaluated in which these doses were standardized to the lean bodyweight (LBW) of 57.4 kg. For each dosing regimen, a simulation was performed with the one‐thousand simulation patients. The efficacy endpoint of the simulations was the median time of repopulation to a T cell count > 200 cells/μL, which is the clinical threshold for T cell recovery. ⁴ This threshold is associated with a lower risk of opportunistic infections after lymphocyte depletion. ²⁴ , ²⁵ It was computed with the interval‐censored, cumulative incidence function. ²⁶ The safety endpoints were the maximal time until T cell depletion and the duration of total depletion. In clinical practice, total T cell depletion is considered a T cell count < 20 cells/μL. With the current fixed 30 mg dose, almost all patients acquire complete T cell depletion within 3–4 days. ³ This is comparable to the depletion rate after ATG induction therapy. ³ , ²⁷ Therefore, we aimed for T cell depletion of 97.5% of patients within 4 days after the first alemtuzumab administration. Second, it was assessed if the T cell depletion was adequately sustained. Adequate sustainment of depletion lasted at least 4 weeks after alemtuzumab for 97.5% of patients. This definition was based on empirical data after both induction and antirejection therapies, which showed depletion was complete and sustained at 1 month after therapy. ³ , ²⁷ , ²⁸ , ²⁹

RESULTS

Patients and measurements

In total, 479 peripheral blood T cell measurements of 61 patients were available between baseline and 2 years after transplantation (Table  1 ). Because of the heterogeneity in late T cell observations and the disproportional influence of late T cell counts on the parameter estimation of the population pharmacodynamic model, T cell measurements beyond one‐and‐a‐half years of follow‐up were excluded (n = 51). In addition, one early post‐transplant cell count was excluded because it was increased temporarily as a result of a documented CMV infection and had a disproportionate effect on parameter estimation. Moreover, nine early measurements that were obtained at the first and second day of alemtuzumab induction therapy were excluded because they were the only patients with measurements during alemtuzumab administration. As a result, a total of 418 T cell measurements were included for model development, of which 70 (16.7%) were BLoQ including 35 (8.4%) measurements below the lower limit of detection. The included T cell measurements are depicted in Figure 1 .

Table 1.

Clinical characteristics of the included patients (n = 61).

Characteristic	n	Mean	Median (IQR)	Range
Demographics
Sex
Male	50 (82.0%)
Female	11 (18.0%)
Age		49.9	51.0 (20)	19–74
Body size
Total bodyweight (kg)		81.6	80.4 (22.5)	54.6–119
Height (cm)		177	179 (12)	158–198
Blood volume (L)		6.07	6.12 (1.21)	4.16–7.86
Co‐morbidities
Hypertension
No	5 (8.2%)
Yes	56 (91.8%)
Hypercholesterolemia
No	43 (70.5%)
Yes	18 (29.5%)
Diabetes
No	52 (85.3%)
Yes	9 (14.8%)
Baseline absolute cell counts
Leukocytes (109 cells/L)		7.85	7.30 (3.41)	3.74–15.1
Lymphocytes (109 cells/L)		1.52	1.48 (0.86)	0.56–2.82
T cells (cells/μL)		965	967 (732)	43.5–2.240
Treatment allocation
Mesenchymal stromal cells	33 (54.1%)
Control	28 (45.9%)

Figure 1.

Observed T cell counts on the linear (a) and semi‐logarithmic scale (b) over time.

Population pharmacokinetic model

The observed pharmacokinetics of alemtuzumab are depicted in Figure S1 . The parameters of the population pharmacokinetic model are listed in Table S1 . All parameters were adopted from the previously developed model, and applied without modification. ¹²

Population pharmacodynamic base model

A single‐compartment structural model best described the T cell dynamics after alemtuzumab, conforming to the model by Mold et al. ¹⁶ Transit compartments as applied by Friberg et al. and Azzopardi et al. were evaluated, ¹⁷ , ¹⁸ but were found too complex for the available data. Moreover, the incorporation of separate proliferation and transit compartments would require making assumptions about the effects of alemtuzumab in these compartments. Such compartment‐specific alemtuzumab effects are currently unknown and no data was available in this study to estimate these. T cell generation was determined by an influx parameter (kin). Kin represented cell renewal through mitosis and was therefore modeled as a first‐order constant in accordance with the model proposed by Friberg et al. ¹⁷ Modeling kin with BSV was shown to significantly improve the model (dOFV −78). A zero‐order kin, as incorporated in the stimulatory loss indirect response model of Mold et al., ¹⁶ was also evaluated, but did not adequately describe T cell recovery. Also, in line with Friberg et al., ¹⁷ a positive feedback mechanism was incorporated on kin which enabled a faster increase in T cells during the initial repopulation phase. The feedback mechanism in the final structural model did not include an exponential tuning parameter as applied by Friberg et al., ¹⁷ as this parameter did not statistically significantly improve our model.

The physiological turnover of T cells was represented by a first‐order efflux (kout), which was set equal to kin in accordance with the model of Friberg et al. ¹⁷ Alemtuzumab‐induced removal of T cells was modeled as a parallel, first‐order drug‐induced stimulation–degradation drug effect (Edrug). Edrug was best modeled as an E _max relationship without sigmoidicity. Modeling EC50, but not E _max, with BSV was shown to significantly improve the model (dOFV −74).

The baseline T cell count (Tbase) was separately modeled, as pre‐transplantation Tbase was frequently much lower than the repopulated T cell count. Estimating Tbase as a separate parameter with BSV led to estimation problems, whereas estimating Tbase without BSV was considered not in line with physiology. Considering that Tbase is determined mainly by kin, it was decided to model Tbase as a function of kin. Different mathematical relationships were tested, and describing Tbase as an exponential function of kin resulted in a robust model with a large decrease in OFV (dOFV −63.7) as compared to the models that included Tbase as a separate parameter without BSV. The exponent was estimated as a separate parameter (base).

A proportional error model best described the residual unexplained variability. Neither of the implemented BLoQ methods resulted in a better fit of the base model to the data and was thus discarded. All base model parameter estimates are summarized in Table 2. The GOF and VPC plots of the base model are depicted in Figures S2 and S3 , respectively.

Table 2.

Population pharmacodynamic parameter estimates of the structural model and of the final model, with bootstrapping medians and confidence intervals

Parameter	Base model			Final model			Bootstrap (1000 replicates)
	Estimate	RSE (%)	Shrinkage (%)	Estimate	RSE (%)	Shrinkage (%)	Median estimate [95% CI]a
Population values
kin (day−1)	0.00292	22.7		0.00548	30.7		0.00530 [0.00259 to 0.141]
base	5.62	5.29		4.82	7.6		4.85 [1.48 to 5.71]
E max (day−1)	1.78	13.1		2.41	24.8		2.38 [1.69 to 55.5]
EC 50 (mg/L)	0.113	39.7		0.0786	25.8		0.0805 [0.0458 to 0.185]
Baseline T cells on kin				0.454	25.3		0.460 [0.174 to 0.732]
Baseline T cells on EC50				−1.28	33.5		−1.27 [−2.31 to −0.0653]
Between‐subject variability
kin (CV%)	28.2	12	15	24.2	14.3	19	22.9 [13.1 to 29.8]
EC50 (CV%)	90.7	21	18	106.8	18.3	15	105 [51.9 to 144]
Random residual variability
Proportional error (CV%)	72.7%	5.2	5	71.1	4.4	5	70.8 [64.9 to 75.7]

Base, exponential function for estimation of default T lymphocyte count; CV, coefficient of variation; EC50, Half maximal effective concentration; E _max, Maximal drug effect; kin, first‐order influx of T lymphocytes.

^a Median parameter estimate and 95% confidence interval as derived from the bootstrap analysis (N = 1000).

Covariate model

The association between the covariates and BSV was assessed by EBE plots (Figures S4 and S5 ). On kin BSV, these plots indicated potential covariate effects: randomization status, sex, age, weight, height, blood volume, baseline T cell count, and a co‐morbidity of hypertension, and were therefore included for stepwise covariate modeling. On EC50 BSV, the EBE plots indicated potential covariate effects for age, weight, height, blood volume, baseline serum creatinine, and baseline T cell count, which were also included in the stepwise covariate modeling.

Inclusion of the baseline value of T cells as covariate on kin (cov_Tbase_k _in ) resulted in a significantly better model fit compared to the base model (dOFV −8.6). Subsequent inclusion of baseline T cells as covariate on EC50 (cov_Tbase_EC ₅₀ ) further improved the model (dOFV −10.2). Higher baseline T cells were associated with higher individual kin and lower individual EC50. For both covariate relations, an exponential relationship best described the covariate effects. No other covariate effects resulted in improvement of the model. The final model is described in Eq. 1.

$$\begin{array}{c}\frac{\text{dTcells}}{\mathit{dt}}=k_{\text{in}}\times e^{{\mathrm{cov}}_{{\text{Tbase}}_{k_{\text{in}}}}\times \left(k_{\text{in}}^{\text{base}}-0.96691\right)}\times e^{{\eta }_{k_{\text{in}}}}\times \frac{k_{\text{in}}^{\text{base}}}{\text{Tcells}}\times \text{Tcells}-k_{\text{out}}\hfill \\ \times \text{Tcells}-\frac{E_{\max }\times C}{\left(E{C}_{50}\times {\mathrm{e}}^{{\mathrm{cov}}_{{\text{Tbase}}_{E{C}_{50}}}\times \left(k_{\text{in}}^{\text{base}}-0.96691\right)}\times {\mathrm{e}}^{{\eta }_{E{C}_{50}}}\right)+C}\times \text{Tcells}\hfill \end{array}$$ (1)

Tcells: T cell count at a given time t; k _in: T cell synthesis rate; k _out: T cell degradation rate; E _max: the maximal alemtuzumab effect; EC50: the alemtuzumab concentration at which its effect is at 50% of E _max; C: alemtuzumab concentration; base: exponent for describing the baseline T cell count as a function of k _in; cov_Tbase_k _in : parameter describing the covariate relationship between the baseline T cell count and k _in; cov_Tbase_EC ₅₀: parameter describing the covariate relationship between the baseline T cell count and the EC ₅₀.

The parameters of the final covariate model are included in Table  2 . The model code is included in the Supplementary Materials .

Model evaluation

The GOF and VPC plots of the final model are shown in Figure 2 and Figure S6 , respectively. Individual fits are shown in the Figure S7 . The GOF plots indicated conformity of the observed and predicted T cells. The CWRES indicated a slight but acceptable overprediction of baseline values and gradual overprediction during later follow‐up, which was in agreement with the VPC (Figure S6 ) and NPDE plots (Figure S8 ). The results of the bootstrap analysis of the final model showed good parameter estimate robustness, as the estimates were all close to the median parameter estimates of the bootstrap analysis (Table  2 ).

Figure 2.

Goodness‐of‐fit plots of the final model. Linear observed T cell count over linear individual‐predicted T cell count (a) and population‐predicted T cell count (b). Log‐transformed observed T cell count over log‐transformed individual‐predicted T cell count (c) and population‐predicted T cell count (d). CWRES over log‐transformed predicted T cell count (e). CWRES over time in days (f). Red lines represent loess regression fits. CWRES, conditional weighted residuals.

Exposure effect analysis and clinical simulations

Higher C _max and AUC_0–inf values were both associated with lower individual‐predicted T cells at 4 weeks after induction therapy, and longer recovery times of the individual‐predicted T cells (Figure 3 ). Simulation of different dosing regimens also demonstrated that the T cell dynamics are dose‐dependent: the lowest dose resulted in the highest T cell counts over time (Figure S9 ). Furthermore, the course of T cell counts deviated the most between one and three hundred days after administration. T cell recovery differed between 240 days (30 mg fixed dose) and 189 days (5 mg fixed dose; Table S2 , Figure 4 ).

Figure 3.

Exposure effect plots of the model‐derived pharmacokinetic exposure and pharmacodynamic effect parameters in the observed population. C_max vs. individual T cell prediction 4 weeks after therapy (a), AUC vs. individual T cell prediction 4 weeks after therapy (b), C_max vs. T cell recovery time (c), AUC vs. T cell recovery time (d). AUC, area under the curve; C_max, maximum concentration.

Figure 4.

Simulated cumulative incidence of T cell recovery after alemtuzumab induction therapy. 15 mg fixed dose (a), 10 mg fixed dose (b), 7.5 mg fixed dose (c) and 5 mg fixed dose (d), compared to the current fixed 30mg dose (solid gray line), including the median difference of repopulation in days. T cell recovery was defined as a T cell count > 200 cells/μL.

Sustained, complete T cell depletion after each simulated dose lasted for 97.5% of patients until 21 (5 mg), 28 (7.5 mg), 32 (10 mg) and 39 days (15 mg) after induction therapy, with T cell counts increasing over time for lower doses (Figure 5 ). Importantly, in addition to the current, fixed dose of 30 mg, only with the 15 mg and the 10 mg fixed dose regimens did all patients acquire complete T cell depletion within 4 days after administration (Table S2 , Figure 5 ). LBW‐adjusted dosing did not result in substantially different T cell depletion – and repopulation as compared to fixed dosing (Figures S10–S12 ).

Figure 5.

Simulated median cell depletion dynamics during the first 4 weeks after alemtuzumab induction therapy. 15 mg fixed dose (a), 10 mg fixed dose (b), 7.5 mg fixed dose (c) and 5 mg fixed dose (d), compared to the current fixed 30 mg dose (solid gray line).

DISCUSSION

A population PK‐PD model was developed which adequately described T cell dynamics after alemtuzumab induction therapy in adult kidney transplant recipients. Through simulations, it was concluded that dose reductions up to 10 mg may facilitate earlier T cell recovery after alemtuzumab induction therapy while maintaining a fast and sustained initial T cell depletion below the lympholytic concentration to ensure efficacy.

The present exposure effect analysis and model simulations showed that reduced alemtuzumab dosing regimens can result in earlier T cell recovery (> 200 cells/μL). Unfortunately, the sample size of this study was not sufficient to model clinically relevant endpoints such as rejection and infection rate. Yet, we believe the endpoints of T cell dynamics provide an objective evaluation of each dosing regimen on important aspects of lymphocyte‐depleting therapy.

Our model simulations show that there is a trade‐off between the speed of complete T cell depletion and T cell recovery. Once complete T cell depletion was acquired, it was sustained for 3–6 weeks, which is comparable to reported lymphocyte counts after lymphocyte‐depleting induction therapy in other studies. ³ , ²⁷ , ²⁸ , ²⁹ Most likely, the slow recovery of T cells is only partially dependent on the sustained exposure to alemtuzumab, as even with the lowest dose, the simulated median recovery time was still 6 months. Besides alemtuzumab overexposure, the slow recovery of T cells after alemtuzumab most likely results from the slow process of homeostatic proliferation. This is supported by findings in which thymopoiesis was shown to contribute only modestly to T cell recovery after ATG induction therapy in adults. ²⁸ A reduced thymic output was associated with persistent depletion, ³⁰ and T cell counts were higher after alemtuzumab induction therapy in children, ³¹ who have preserved thymic function. Furthermore, co‐medication used in solid organ transplantation, that is, valganciclovir and mycophenolate, can inhibit lymphocyte proliferation. In the present analysis, the data were not sufficient to assess the effects of co‐medication on T cell recovery.

Although the simulation showed that the improvement in recovery time with reduced alemtuzumab dosing is limited, any reduction in recovery time should be considered therapy optimization, as sustained depletion of T cells in kidney transplantation is associated with adverse outcomes. ⁸ , ³⁰ However, it is a prerequisite that the reduced dosing regimen is equally effective as the current dose. Simulations with the 7.5 and 5 mg dosages showed a slower initial decline in cell counts, which could indicate reduced therapy efficacy. Importantly, it is questionable to what extend the model simulations of each simulated dose can be validly extrapolated. The original PK model incorporated parallel first‐order and time‐varying Michaelis–Menten elimination of 30 mg of alemtuzumab. ¹² This time‐varying Michaelis–Menten elimination accounted for the target mediated drug disposition (TMDD) of T cell‐bound alemtuzumab, which is a major route of elimination for monoclonal antibodies. ³² Specifically, in kidney transplantation, alemtuzumab induction fully depletes a relatively low number of circulating T cells within the first days after administration. Therefore, the contribution of TMDD to overall alemtuzumab clearance was assumed to decline within 7 days after administration. ¹² For modeling purposes, this time‐varying TMDD was modeled solely as a function of time and not of cell count. Lower doses will cause a slower and possibly incomplete target saturation and depletion, which will likely lead to an increase in the relative contribution of rapid drug clearance by TMDD. ³² , ³³ , ³⁴ This mechanism can lead to incomplete and inadequately sustained T cell depletion after alemtuzumab, not accounted for by the current definition of TMDD in the original PK model. The dose at which this occurs is unknown, but the observation that the 7.5 and 5 mg doses required more than 4 days to acquire complete T cell depletion could indicate incomplete target saturation. For these doses, the results of the simulation should, therefore, be interpreted with caution.

The present results support reducing the induction dose of alemtuzumab in kidney transplantation. We suggest an initial adaptation of the standard 30 mg alemtuzumab regimen to a single dose of 15 mg. This 50% dose reduction should be monitored in clinical practice, preferably as part of a prospective dose‐finding study, to assure its efficacy during the first weeks after administration. In case of incomplete or non‐sustained T cell depletion, a top‐up dose should be considered. This is similar to the top‐up dosing regimen for pediatric hematopoietic cell transplantation. ³⁵ Ideally, prospective dose‐finding studies should include clinical outcomes such as rejection rates and infections, in addition to T cell dynamics.

While interpreting the model simulations, the unexplained BSV and residual error should be considered, as they were of substantial magnitude. In part, this is inherent to PD modeling, as PD data are known to have more variability than PK parameters. ³⁶ This appears to be especially relevant for T cell dynamics, which are highly variable between individuals, ³⁷ result from complex physiological mechanisms, and are affected by many external factors, including maintenance immunosuppressive treatment and the occurrence of infections. ³⁸ , ³⁹ Importantly, the residual error and BSV of the currently developed model were in line with those reported in other publications. ¹⁶ , ¹⁸ , ³⁵ With sensitivity analysis no individual outliers were found as the cause of the relatively high residual error, as the magnitude of the residual error was evenly distributed over all included individuals.

The developed model has limitations. The DV vs. PRED plot showed a clear trend, not visible in the DV vs. IPRED plot. This trend resulted from the mathematical definition of the baseline T cell count and the covariate effect on kin. Estimation of the baseline T cell count was necessary because the actual baseline T cell count was often lower than the repopulated T cell counts, which resulted in model miscalibration. End‐stage kidney disease is known to decrease the number of circulating lymphocytes, ⁴⁰ , ⁴¹ , ⁴² which could explain this discrepancy. With the current definition, the turnover model could adequately handle repopulation despite the low, observed baseline counts. The resulting trends in the GOF plots were accepted because the population‐predicted baseline values were deemed less important for the model purpose.

The observed baseline cell count was included in the model as a positively correlated covariate on kin, which was expected considering both the physiologic and the applied mathematical relationship between the two. More surprising was the negative correlation between the baseline T cell count covariate and EC50. This effect of baseline cell count was not found with other alemtuzumab PK‐PD models, ¹⁶ , ³⁵ or a similar PK‐PD model of ATG. ¹⁸ It could be explained by differences in T cell subsets between patients with high and low baseline cell counts, as some T cell subsets have been shown to be more sensitive to alemtuzumab. ²⁹ , ⁴³ , ⁴⁴

The CWRES over time, VPC plot, and NPDE plot over time also showed a slight overestimation of the T cell count 1 year after alemtuzumab administration. Incomplete recovery of T cells after lymphocyte‐depleting therapy is a known phenomenon and results from a diminished cytokine‐induced homeostatic proliferation. ²⁸ , ²⁹ T cell production and turnover are very low but increase after cell depletion. ⁴⁵ In order to model this dynamic, we included a feedback mechanism that would allow for a variable repopulation rate. ¹⁷ This feedback mechanism helped to correctly estimate the initial, steep recovery of T cells but did not adequately describe the reduction of the recovery rate at later times. Because the aim of the model was to reliably estimate cell depletion and early recovery, and not the cell count at 1 year, the slight overprediction was accepted.

In conclusion, a population PK‐PD model was developed that adequately describes the depletion and recovery of T cells after alemtuzumab induction therapy in adult kidney transplant recipients. We show that halving the current 30 mg alemtuzumab induction dose can improve T cell recovery while maintaining complete T cell depletion for at least 4 weeks. These findings can be used to inform future dose optimization studies.

FUNDING

No funding was received for this work.

CONFLICT OF INTEREST

D.A. Hesselink has received lecture fees and consulting fees from Astellas Pharma, Astra Zeneca, Chiesi Pharma, Medincell, Novartis Pharma, Sangamo Therapeutics and Vifor Pharma. He has received grant support from Astellas Pharma, Bristol‐Myers Squibb and Chiesi Pharma (paid to his institution). D.A. Hesselink does not have employment or stock ownership at any of these companies, and neither does he have patents or patent applications. AdV received lecture and consulting fees from Astellas, Astra Zeneca, Aurinia, Chiesi, CSL Behring, Hansa, Neovii, Novartis, Sangamo Therapeutics, Sanofi, Takeda all of which went to his institution and none to personal bank accounts. All other authors declared no competing interests for this work.

AUTHOR CONTRIBUTIONS

L.K.V., T.C.Z., S.B., S.H., M.E.J.R., D.A.H., A.P.J.V., B.C.M.W., and D.J.A.R.M. wrote the manuscript. T.C.Z., M.E.J.R., and D.J.A.R.M. designed the research. L.K.V., T.C.Z., B.C.M.W., and D.J.A.R.M. performed the research. L.K.V., T.C.Z., D.J.A.R.M., and S.B. analyzed the data.

Supporting information

Data S1