Abstract
Background and Objectives
Lisocabtagene maraleucel (lisocel) is a CD19directed, defined composition, 41BB chimeric antigen receptor (CAR) Tcell product administered at equal target doses of CD8^{+} and CD4^{+} CAR^{+} T cells. Large betweensubject variability has been noted with CAR Tcell therapies; patient characteristics might contribute to CAR Tcell expansion variability. We developed a population cellular kinetic model to characterize the kinetics of the lisocel transgene, via quantitative polymerase chain reaction assessment after intravenous infusion of lisocel, and to understand covariates that might influence lisocel kinetics in individual patients.
Methods
We employed nonlinear mixedeffects modeling to develop a population cellular kinetic model for lisocel. The population cellular kinetic analysis was performed using 2524 postinfusion transgene observations from 261 patients with relapsed/refractory large Bcell lymphoma who were treated with a single dose of lisocel in TRANSCEND NHL 001. Covariates for the analysis included baseline intrinsic factors such as age, baseline disease characteristics, and lisocel and coadministration factors.
Results
Lisocel cellular kinetics were well described by a piecewise model of cellular growth kinetics that featured lag, exponential growth, and biexponential decay phases. Population means (95% confidence interval) of lag phase duration, doubling time, time to maximum levels, initial decline halflife, and terminal halflife were 3.27 (2.71–3.97), 0.755 (0.667–0.821), 9.29 (8.81–9.70), 5.00 (4.15–5.90), and 352 (241–647) days, respectively. The magnitude of effect on lisocel expansion metrics demonstrated that the covariate associations were smaller than the residual betweensubject variability in the population.
Conclusions
The covariates tested were not considered to have a meaningful impact on lisocel kinetics.
Clinical Trial Registration
NCT02631044.
A population cellular kinetic model of lisocabtagene maraleucel (lisocel), a CD19directed chimeric antigen receptor Tcell product, was developed to characterize the kinetics of the lisocel transgene in relapsed/refractory large Bcell lymphoma. 
Lisocel cellular kinetics were well described by a piecewise model of cellular growth kinetics that featured lag, growth, and biphasic decay phases. 
The covariates tested were not considered to have a meaningful impact on lisocel kinetics. 
Introduction
Lisocabtagene maraleucel (lisocel; JCAR017) is a CD19directed, genetically modified, defined composition, autologous cellular immunotherapy administered at equal target doses of CD8^{+} and CD4^{+} chimeric antigen receptor (CAR)positive T cells [1]. The CAR comprises an FMC63 monoclonal antibodyderived singlechain variable fragment, immunoglobulin G4 hinge region, CD28 transmembrane domain, 41BB (CD137) costimulatory domain, and CD3ζ activation domain [2]. In addition, lisocel includes a nonfunctional truncated epidermal growth factor receptor that is coexpressed on the cell surface with the CD19specific CAR and can serve as a surrogate for CAR expression [3,4,5]. CAR binding to CD19 expressed on the cell surface of tumors and normal B cells induces activation and proliferation of CAR T cells, release of proinflammatory cytokines, and cytotoxic killing of target cells [6].
TRANSCEND NHL 001 (TRANSCEND; NCT02631044) is a multicenter, multicohort, openlabel, seamless design (i.e. consisting of dosefinding, doseexpansion, and doseconfirmation phases) study to determine the safety, antitumor activity, and cellular kinetics of lisocel in patients with relapsed/refractory large Bcell lymphoma (LBCL; LBCL cohort) and mantle cell lymphoma (mantle cell lymphoma cohort). TRANSCEND is the largest clinical study reported to date of CD19directed CAR Tcell therapy in relapsed/refractory LBCL [1, 3, 7,8,9]. Eligible patients underwent leukapheresis for collection of autologous peripheral blood mononuclear cells for manufacture of lisocel followed by lymphodepleting chemotherapy (LDC; fludarabine 30 mg/m^{2} and cyclophosphamide 300 mg/m^{2} for 3 days) [1]. During the lisocel manufacturing process (between leukapheresis and LDC), bridging therapy with systemic and/or radiation therapy was allowed at the discretion of the treating physician. Lisocel was administered as two sequential infusions of CD8^{+} and CD4^{+} CAR^{+} T cells at one of three dose levels (50 × 10^{6}, 100 × 10^{6}, or 150 × 10^{6} CAR^{+} T cells). The 269 patients who received lisocel had a median age of 63 years and a median of three previous lines of systemic therapy; 67% had chemotherapyrefractory disease, 33% had previous autologous hematopoietic stem cell transplantation (HSCT), and 59% received bridging therapy. In efficacyevaluable patients (n = 256), treatment with lisocel resulted in a high rate of durable complete response (CR), with an objective response rate of 73%, CR rate of 53%, and an estimated duration of CR at 1 year of 65% [1]. Lisocel treatment was associated with a low incidence of severe cytokine release syndrome (CRS; 2%) and neurological events (NEs; 10%). CRS of any grade was reported in 42% of patients, with median time to onset of 5 days and median time to resolution of 5 days. NEs of any grade were reported in 30% of patients, with median time to onset of 9 days and median time to resolution of 11 days. Additional safety outcomes of interest included severe neutropenia (60%), anemia (37%), and thrombocytopenia (27%), with prolonged cytopenia (not resolved at Day 29) in 37% of patients. Severe infections, including bacterial, fungal, and viral, were reported in 12% of patients.
Cellular kinetics of two other CAR Tcell therapies (tisagenlecleucel and axicabtagene ciloleucel [axicel]) were characterized in Bcell acute lymphoblastic leukemia (BALL; tisagenlecleucel) [10,11,12] and relapsed/refractory LBCL (tisagenlecleucel [13] and axicel [8]). These CAR Tcell therapies generally showed rapid in vivo expansion within 2 weeks postinfusion followed by subsequent biexponential decline [8, 12]. In TRANSCEND, median time to lisocel peak expansion was 12 days, and higher lisocel expansion was associated with higher rates of CR and partial response (maximum transgene levels [C_{max}], 3.55fold) and higher incidence of CRS (C_{max}, 2.29fold) and NEs (C_{max}, 3.34fold) in patients with relapsed/refractory LBCL [1]. Lisocel was present in peripheral blood for up to 2 years [1]. Large betweensubject variability (BSV) was noted in all three CAR Tcell therapies (e.g. percentage coefficient of variation [%CV] of > 100% for tisagenlecleucel) [12, 13], as expected for biologic products that expand in vivo; patient characteristics might also contribute to the variability of CAR Tcell expansion. Tisagenlecleucel expansion was lower in LBCL than BALL [13]. Patient demographics such as age and sex had no significant impact on the expansion of both tisagenlecleucel and axicel [14, 15]; however, these findings might be because of the relatively small sample size given the large BSV. TRANSCEND is the largest clinical study among CD19directed CAR Tcell therapies, and in this study the association of baseline intrinsic and disease factors with lisocel kinetics was investigated. This study describes a population cellular kinetic model of lisocel that was developed to characterize the kinetics of the lisocel transgene in relapsed/refractory LBCL, as assessed by quantitative polymerase chain reaction (qPCR) after intravenous infusion of lisocel, and to understand covariates that might influence lisocel kinetics in individual patients.
Methods
Clinical Study Data
The population cellular kinetic analysis was performed using data from the LBCL cohort of TRANSCEND for three dose levels (50 × 10^{6}, 100 × 10^{6}, or 150 × 10^{6} CAR^{+} T cells) on a singledose schedule [1]. Based on doselimiting toxicities and activity observed during the dosefinding and doseexpansion phases, dose level 2 (100 × 10^{6} CAR^{+} T cells) was selected for evaluation during the doseconfirmation phase. For patients who were on a singledose schedule and received retreatment with or additional cycles of lisocel, data after retreatment or additional cycles (maximum, two cycles) were excluded from the analysis. Followup for the TRANSCEND LBCL cohort was ongoing as of 12 August 2019, the data cutoff date used for this analysis. The study was conducted in accordance with the Declaration of Helsinki, International Conference on Harmonisation Good Clinical Practice guidelines, and applicable regulatory requirements. Institutional Review Boards approved the study protocol and amendments at participating institutions. All patients provided written informed consent.
Bioanalytical Methods
Blood samples for determination of the lisocel transgene were collected at preinfusion and 1, 3, 7, 10, 14, 21, and 28 days and 2, 3, 6, 9, 12, 18, and 24 months postinfusion. Lisocel transgene levels in peripheral blood were measured using a validated realtime qPCR assay, which is an accepted approach for evaluating cellular kinetics of CAR Tcell therapies. Lisocel vector copy number was determined through the quantification of two genes: (1) woodchuck hepatitis virus posttranscriptional regulatory element (WPRE), a posttranscriptional regulatory element present in the lentiviral vector used to transduce the gene that encodes for lisocel into cells; and (2) human albumin, a housekeeping gene used to normalize genomic DNA for each sample. DNA was extracted from cells after the removal of plasma using QIAamp DNA Isolation Kits, quantified, and stored until analysis. Samples were analyzed in a duplex reaction at a DNA input of 200 ng per reaction using a proprietary assay that quantifies WPRE and albumin. Results were reported as WPRE copies/μg of DNA, which was determined based on the number of WPRE copies normalized to the number of albumin copies/reaction (assuming 2 albumin copies/genome and 6.6 pg DNA/genome). The limit of detection of WPRE was determined to be 5 copies/reaction. Inter and intraassay precision was evaluated using prepared quality control samples. The interassay precision (%CV) was ≤ 30% for albumin and ≤ 25% for WPRE, while the intraassay precision for WPRE and albumin was ≤ 20% for all levels, except at the lower limit of quantification where it ranged from 3% to 57%.
Population Cellular Kinetic Modeling Analysis
Overall, 2524 postinfusion transgene observations from 261 patients were used in the population cellular kinetic analyses. Of these, 394 (16%) were below the limit of detection and were flagged as missing. This primarily occurred in the extreme end of posttreatment followup. Population cellular kinetic models were developed using a nonlinear mixedeffect modeling approach, as implemented in NONMEM version 7.3.0 (ICON Development Solutions, Ellicott City, MD, USA) and PerlspeaksNONMEM [16]. Data management and graphical evaluations were performed in R version 3.3.2 (The R Foundation, Vienna, Austria).
First, the firstorder conditional estimation with etaepsilon interaction (FOCEI) method was used to approximate the objective function value (OFV). The FOCEI OFV is a linear approximation of the true OFV. Next, the final parameter values from the FOCEI step were used as starting values for the importance sampling method to further refine the solution and response surface without OFV approximation [17]. The variance–covariance matrix was derived from the importance sampling step, and parameter relative standard error estimates were produced without OFV linearization. Finally, 500 replicate bootstrap data sets were generated using sampling without replacement to produce the 2.5th and 97.5th percentiles of the parameters.
Structural Model
Systemic disposition of CAR Tcell therapies such as lisocel have been previously described by a piecewise model embodying an initial cellular expansion phase followed by a biphasic contraction phase based on theoretic work by De Boer and Perelson [10, 18, 19]. The specific form was taken from the case where vigorous immune responses are evoked (e.g. in the presence of a rapidly replicating pathogen). Under these circumstances, Tcell proliferation is triggered rapidly and not limited by antigens, leading to all T cells proliferating at their maximal rate for some period. After this time, all T cells enter a contraction phase, where activated T cells either rapidly die out or transition to longerlived memory T cells. This structural model was used as the starting model and was refined as necessary to adequately describe the data among patients. The model was fit to logarithmically transformed lisocel transgene levels. Adequacy of the model to describe the data was evaluated using standard goodnessoffit criteria, including observations versus population and individual predictions and conditional weighted residuals (CWRES) versus population predictions and time.
The exponential model was used for the description of BSV in cellular kinetic parameters. BSV on model parameters was introduced in terms of random betweensubject effects as follows (Eq. 1):
where θ_{k} denotes the typical population parameter estimate for the kth parameter, θ_{k,i} denotes the parameter estimate for the kth parameter in the ith subject, and η_{k,i} denotes the betweensubject random effect for the ith subject, where η_{k,i} is assumed to have a mean of 0 and an estimated variance of ω^{2}. BSV on a model parameter was retained if supported by the data (i.e. if estimates did not cause model instability and shrinkage was < 30%) [20]. A logittransformed parameter was used to introduce BSV in the case of parameters with domain [0,1] (i.e. when describing the fraction of activated T cells that transition to memory T cells). However, BSV for this parameter was dropped because of poor estimate quality for this BSV term. The inclusion of offdiagonal elements was investigated but was not supported based on pairwise plots of individual η estimates. Additive error models were used to describe residual variability after the model predictions were logarithmically transformed. The statistical model was assessed with the diagnostic plots, including histograms of η estimates and pairwise plots of individual η estimates.
Covariate Model
Covariate modeling focused on identifying and quantifying covariates that explain BSV in cellular kinetic parameters among patients. Covariates for the analysis included:

Baseline intrinsic factors: age, body size (by body weight and body mass index), sex, race, ethnicity, creatinine clearance by Cockcroft–Gault equation, alanine aminotransferase, aspartate aminotransferase, and left ventricular ejection fraction (≥ 40% to < 50% or ≥ 50%).

Baseline disease factors: lactate dehydrogenase (LDH) before LDC, sum of the product of perpendicular diameters (SPD) per Independent Review Committee (IRC) before LDC, Creactive protein, LBCL subtype, secondary central nervous system lymphoma, Eastern Cooperative Oncology Group performance status at screening, prior lines of systemic therapy, prior response status, prior chemotherapy response status, and prior HSCT.

Lisocel and coadministration factors: administered dose of lisocel, bridging therapy after leukapheresis, and tocilizumab and/or corticosteroid use for CRS or NE treatment.
Covariate inclusion in the model was guided by the following considerations: graphical exploration against random effects in the model, clinical and physiological considerations, and results of the prespecified covariate search applied to noncompartmental analysis results. Missing covariates were imputed as the median value in the study population.
A forwardaddition and backwardselimination stepwise covariate modeling approach was used to add covariates to the model based on these considerations. The likelihood ratio test was used to evaluate the statistical significance of incorporating or removing each respective covariate in the model. For forward addition and backward elimination, significance levels (α) of 0.01 and 0.001, respectively, were employed.
Continuous covariates were centered on a typical value (e.g. median of the study population). Relationships between cellular kinetic parameters and continuous covariates were described as a linear model as follows (Eq. 2):
where P_{k,i} is the individual value of the cellular kinetic parameter k, P_{k} is the typical value of the cellular kinetic parameter k, cov_{i} is the individual covariate value, med_{cov} is the median covariate value of the study population, and θ is the scaling parameter for the range of the covariate. All covariates (except age) were logtransformed; thus, this linear model formulation was equivalent to a power model formulation for these covariates.
Binary categorical covariates were incorporated into the model as index variables described as follows (Eq. 3):
where cov_{i} is the individual covariate value for a binary covariate with possible values of 0 and 1. Categorical covariates with multiple values were implemented as products of the binary covariate model.
Model Evaluation
A final NONMEM model was expected to meet the following criteria: (1) a ‘minimization successful’ statement by the NONMEM program; (2) three or more significant digits for all parameters; (3) parameter estimates that were judged to be clinically meaningful and not close to a boundary; and (4) good agreement between observations and predictions in standard goodnessoffit plots. Bootstrap resampling techniques were used to evaluate the stability of the final model and to estimate confidence intervals (CIs) for the model parameters. The predictive performance of the model was assessed by a visual predictive check. Observed data and 500 replicate simulations from the final model were summarized by median and 5th/95th percentiles, respectively.
Simulations
The final population cellular kinetic model was used to simulate individual lisocel cellular kinetic parameters: C_{max}, time to maximum transgene levels (T_{max}), and area under the curve for transgene levels from 0 to 28 days postinfusion (AUC_{0–28d}). Covariate values in the model were given by observed values in TRANSCEND, thus preserving any collinearity between covariates. Random effects were sampled from the estimated variance–covariance matrices 300 times for each of the 261 patients, yielding 78,300 simulated patients. Fixed effects were given from the population estimates. Forest plots were used to explore the impact of significant covariates on lisocel expansion metrics. Stochastic simulations using the final population cellular kinetic model were performed to show the expected impact on lisocel expansion in subpopulations of interest.
Results
Patients
The population cellular kinetic data set included data from 261 patients in TRANSCEND. Table 1 shows the patients’ demographic and clinical characteristics that were included as covariates of the patient data set. Median age was 63 years (range 18–86). Twentyeight percent of patients received either tocilizumab or corticosteroids, or both, for the treatment of CRS and/or NEs.
Structural Population Cellular Kinetic Model of Lisocel
A piecewise model embodying an initial cellular expansion phase, followed by a biphasic contraction phase, was fit to the lisocel transgene data. Notable discrepancies in the first 3 days postinfusion were observed. Specifically, the modelpredicted expansion phase overpredicted early time points and transgene levels near their peak values. The model was expanded to include four classical phases of cellular growth: lag, growth, stationary, and decay [21]. Adding a lag phase to the initial cellular expansion phase improved model fit. The addition of a stationary phase did not improve model fit and was discarded.
Figure 1 shows the final form of the structural model for lisocel transgene levels. After infusion (t = 0), lisocel transgene levels were stationary during the lag phase. The duration of the lag phase was defined as T_{lag}, during which time lisocel levels were constant initial transgene levels (C_{0}). During the lag phase, lisocel transgene levels were given as (Eq. 4):
which is a simple rearrangement of the C(t) expression below, substituting t = T_{max} = T_{lag} + T_{gro} and C(t) = C_{max}. After the lag phase (t = T_{lag}), lisocel transgene levels doubled every interval (T_{dbl}) during the growth phase, reflecting doubling of infused T cells bearing lisocel transgene by mitotic cell division. The duration of the growth phase was defined as T_{gro}, at which time (T_{max} = T_{lag} + T_{gro}) lisocel transgene levels reached C_{max}. During the growth phase, lisocel transgene levels were given as (Eq. 5):
After the growth phase (t = T_{max} = T_{lag} + T_{gro}), lisocel transgene levels declined in a biphasic manner during the decay phase. A fraction of lisocel transgene signal at C_{max} that appears in the β or terminal phase with halflife HL_{β} was F_{β}. One minus that fraction appeared in the α phase with halflife HL_{α}. During the decay phase, lisocel transgene levels were given as (Eq. 6):
Random effects for T_{gro}, F_{β}, and HL_{β} were removed from the model because the η shrinkage exceeded 30%. The remaining random effects were centered around 0, normally distributed, and showed little correlation, except for the random effects for C_{max} and T_{dbl} that had a correlation coefficient of r = − 0.459. This would suggest that patients with high C_{max} (maximal lisocel transgene levels after expansion) have a short T_{dbl} (doubling time of lisocel transgene levels during expansion). However, the correlation coefficient dropped to r = − 0.352 after additions of all covariates in the final model, suggesting a weak correlation after covariate addition. Thus, a diagonal variance–covariance matrix structure was selected.
Final Population Cellular Kinetic Model of Lisocel
Population cellular kinetic parameters for the final model are listed in Table 2. Population means (95% CIs) of cellular kinetic parameters in a typical patient were T_{max} (T_{lag} + T_{gro}) 9.29 (8.81–9.70) days; doubling time (T_{dbl}) 0.755 (0.667–0.821) days; C_{max} 23,600 (18,900–29,900) copies/µg; initial decline halflife (HL_{α}) 5.00 (4.15–5.90) days; terminal halflife (HL_{β}) 352 (241–647) days; and fraction of C_{max} that appears in the β or terminal phase (F_{β}) 0.659 (0.529–0.820) percent. The final model included the following covariates: age on C_{max} and T_{dbl}; SPD per IRC before LDC on HL_{α}; tocilizumab and/or corticosteroid use (for the treatment of CRS and/or NEs) on C_{max}, HL_{α}, and T_{lag}; and LDH before LDC on T_{lag}. Covariate effects on model parameters are given as foldchange in Table 2. In patients aged 18 and 86 years, C_{max} was altered 2.49fold and 0.24fold, respectively, and T_{dbl} was altered 0.70fold and 1.15fold, respectively, relative to the median age of 63 years. In patients treated with tocilizumab and/or corticosteroids, C_{max} was 1.67fold higher, HL_{α} was 2.31fold longer, and T_{lag} was altered 0.62fold, compared with patients who received neither tocilizumab nor corticosteroids. HL_{α} was altered 1.55fold and 0.37fold in patients with SPD per IRC of 419 cm^{2} and 0.8 cm^{2}, respectively, relative to the median SPD per IRC of 22.5 cm^{2}. T_{lag} was altered 2.12fold and 0.74fold in patients with LDH of 11,900 U/L and 112 U/L, respectively, relative to the median LDH of 269 U/L.
Figure 2 shows the populationpredicted and individualpredicted lisocel transgene levels versus observed lisocel transgene levels for the final model. Data pairs (predicted, observed) that lie on the line of unity denote agreement between the model and observations. The model adequately captured the observations. Improvement in the populationpredicted concurrence with the observed data is noted and expected due to the introduction of model covariates. Figure 2 also shows CWRES versus populationpredicted and time after dose for the final model, which were acceptable and similar to results from the base model. Generally, no values fell outside CWRES > 5, indicating that no data points were classified as outliers. The residuals showed no trend by populationpredicted or time, indicating no systemic biases in model fit in these dimensions. Figure 3 shows a visual predictive check between modelpredicted and observed lisocel transgene levels versus time after dose. The median and 5th/95th percentiles of the 500 replicate simulations were superimposed with the observation summaries. These simulations demonstrated that the model adequately captured the central tendency and variability in the observed data.
Simulations
Figure 4 shows the simulated AUC_{0–28d}, C_{max}, and T_{max} values from the final model, conditioned on the observed patient covariates in the data set and summarized over 300 replicate simulation studies. Median (5th–95th percentile) values across the simulations were 214,000 (26,100–1,560,000) day*copies/μg for AUC_{0–28d}, 27,300 (4260–146,000) copies/μg for C_{max}, and 9.00 (6.96–14.5) days for T_{max}. Covariates associated with C_{max} were also associated with AUC_{0–28d}. Both C_{max} and AUC_{0–28d} increased with decreasing patient age. Both C_{max} and AUC_{0–28d} tended to increase with increasing SPD per IRC before LDC. Furthermore, both C_{max} and AUC_{0–28d} were higher and T_{max} was slightly shorter in patients receiving tocilizumab and/or corticosteroids. T_{max} tended to be longer with increasing LDH before LDC. The magnitude of effect on lisocel expansion metrics demonstrated that the covariate associations were smaller than the residual BSV in the population.
Discussion
Unlike systemic therapies, CAR Tcell therapies are administered once and the kinetics depend on CAR Tcell expansion, contraction, and persistence after infusion into the patient. Patient and disease characteristics are anticipated to play a role in the variability of cellular kinetics observed with CAR Tcell therapy. Lisocel transgene observations were well described by a piecewise model of cellular growth kinetics that featured lag, exponential growth, and biphasic decay phases in treated patients. Unless otherwise specified, the following summaries are for a typical patient who was 63 years of age, had SPD before LDC (per IRC) of 22.5 cm^{2}, had LDH before LDC of 269 U/L, and did not use tocilizumab and/or corticosteroids for the treatment of CRS and/or NEs. Lisocel transgene levels were stable during the lag phase (T_{lag}) and doubled approximately eight times during the growth phase (T_{gro}), reaching a C_{max} of 23,600 copies/μg (91.5% BSV) at 9.29 days (T_{max} = T_{lag} + T_{gro}). After peak levels, the lisocel transgene decay phase was biphasic, with αphase (HL_{α}) and βphase (HL_{β}) halflife estimates of 5.00 (97.7% BSV) and 352 days, respectively. The fraction of peak lisocel transgene levels appearing in the βphase (F_{β}) was estimated at 0.659%. In this empirical cellular kinetic model, the fractions of αphase and βphase were assumed as effector and memory T cells, respectively.
A covariate search using stepwise forward addition (α = 0.01) and backward elimination (α = 0.001) demonstrated that baseline age, SPD per IRC before LDC, LDH before LDC, and the use of tocilizumab and/or corticosteroids for the treatment of CRS and/or NEs were associated with lisocel kinetics. Univariate effect sizes should be interpreted with caution as the covariates may be correlated. Therefore, the association of patient covariates was instead assessed by simulation of C_{max}, T_{max}, and AUC_{0–28d} using the final model. Observed patient covariates were used to condition these simulations, thus preserving any collinearity in the covariates. Treatment with tocilizumab and/or corticosteroids was associated with higher C_{max} and AUC_{0–28d}. Higher C_{max} and AUC_{0–28d} were also associated with CRS and/or NEs [1], which triggered the therapeutic intervention with tocilizumab and/or corticosteroids. In TRANSCEND, the median time to onset of CRS and NEs was 5.0 and 9.0 days, respectively [1], and the median time from onset of CRS to first administration of tocilizumab was 1.5 days [1]. Therefore, the relationship of tocilizumab/corticosteroid use with cellular kinetic parameters should be interpreted with caution. Examination of these cellular kinetic parameters across the covariate range (quartiles, in the case of continuous covariates) showed the expected association pattern described in Fig. 4. The magnitude of effect on expansion metrics demonstrated that the covariate associations were smaller than the residual BSV in the population. Particularly, BSV not explained by covariates for C_{max} was estimated as 91.5%. Thus, the covariate effects were not considered meaningful.
Recent work with physiologically based pharmacokinetic models of exogenous Tcell administration found that the administered dose did not contribute to initial Tcell blood concentrations [22]. In this effort, a similar lack of dose dependence was noted with lisocel transgene levels. Dose was examined as a covariate on model parameters but was not found to be statistically significant. This suggests that the dose was not associated with expansion quantities in the tested administered dose range (44–156 × 10^{6} CAR^{+} T cells). Thus, no dose adjustment is recommended in specific populations [23]. Tisagenlecleucel also exhibited a flat relationship between dose and the cellular kinetic parameters (0.2–5.0 × 10^{6} CAR^{+} T cells/kg in patients weighing ≤ 50 kg, and 0.1–2.5 × 10^{8} CAR^{+} T cells in patients weighing > 50 kg) [12].
Finally, these results can be compared with similar analyses conducted for tisagenlecleucel in pediatric and young adult patients with BALL [10] and axicel in adult patients with LBCL [19]. Prior literature reports for CAR Tcell therapies were based on a theoretic model developed by De Boer and Perelson [18] describing the murine immune response to an infection by Listeria monocytogenes or lymphocytic choriomeningitis virus. Findings from this present analysis are aligned with previous analyses conducted for other CAR Tcell therapies (expansion of CAR T cells postinfusion followed by biphasic decline). Two new concepts were introduced by this analysis: the introduction of the novel lag phase and the parameterization of the lisocel transgene population cellular kinetic model. First, previous reports in the literature for CAR Tcell therapies did not report a lag phase after administration, but the general concept of a lag phase as living cells acclimatize to a new environment is well established [21, 24]. Parameterization of the population cellular kinetic model reported here differs from previous efforts, posing the model in more readily interpretable (but still interconvertible) terms. For example, exponents of base 2 were used (instead of base e), reflecting the underlying biology of mitotic doubling of cell populations. Furthermore, the doubling time of CAR T cells is expressed in this model instead of a foldexpansion from baseline ratioed to time to maximum lisocel transgene levels. The model parameterizations are interconvertible with the previous formulation using the following relationships: fold_{x} = C_{max}/C_{0}; ρ = log(fold_{x})/T_{gro}; α = log(2)/HL_{α}; β = log(2)/HL_{β} (definition of terms is available in the study by Stein et al. [10]). Doubling time, T_{max}, HL_{α}, and HL_{β} of tisagenlecleucel were 0.78, 9.3, 4.3, and 220 days, respectively [10], while doubling time, T_{max}, HL_{α}, and HL_{β} of axicel were 0.87, 4.9, 3.3, and 173 days, respectively [19]. Doubling time and HL_{α} of other CD19directed CAR Tcell therapies were consistent with lisocel kinetic parameters. T_{max} of axicel was earlier than that of tisagenlecleucel and lisocel. HL_{β} of lisocel was longer than that of tisagenlecleucel or axicel (352 vs. 220 or 173 days, respectively), which might be due to longer followup with lisocel; however, the interpretation of these comparisons requires caution because of the limitations of the current analysis stated below.
This analysis was limited by the following factors. Random effects for T_{gro}, F_{β}, and HL_{β} were not estimated in the cellular kinetic model of lisocel due to their high η shrinkage. T_{max} (T_{lag} + T_{gro} = 9.29 days) in this lisocel model was slightly earlier than T_{max} reported by noncompartmental analysis (12 days) [1]. This discrepancy might be in part due to misspecification of the cellular kinetic model by no random effect of T_{gro}. Furthermore, HL_{β} had slightly high relative standard error (23.0%). Furthermore, the evaluation period (2 years for lisocel and 1 year for tisagenlecleucel and axicel) was approximately two HL_{β}, which is relatively short for the robust estimation of HL_{β}. Therefore, the abovementioned comparison of HL_{β} among CD19directed CAR T cells should be interpreted with caution. The following differences among CAR Tcell therapies should also be noted for the comparison of cellular kinetic parameters: defined composition (lisocel) versus undefined composition (tisagenlecleucel and axicel); LBCL (lisocel and axicel) versus BALL (tisagenlecleucel); and 41BB (lisocel and tisagenlecleucel) versus CD28 (axicel) costimulatory domain. Earlier T_{max} of axicel compared with tisagenlecleucel and lisocel might be explained in part by the finding that CD28 and 41BB costimulatory domains are associated with effector Tcell like phenotype and memory Tcell like phenotype, respectively [25]. No apparent relationship has been observed between the CD8^{+}:CD4^{+} ratio and cellular kinetic parameters of tisagenlecleucel in LBCL and BALL [12, 13], suggesting that defined versus undefined composition might not be a crucial factor to determine cellular kinetics. The eligibility criteria in TRANSCEND is broad and aligns with recommendations for clinical trials of CAR Tcell therapies to maximize generalizability [26]; however, the findings cannot be extrapolated to the broader population (e.g. pediatric patients and patients with severe renal impairment). Nonetheless, the population cellular kinetic model of lisocel adequately captured the central tendency and variability in observations from patients in TRANSCEND and indicated no systemic biases in model fit in the dimensions of time or predicted values.
Conclusion
Observed lisocel transgene levels were well described by a piecewise model of cellular growth kinetics that featured lag, growth, and biphasic decay phases in treated patients. Covariates tested were not considered to have a meaningful impact on lisocel kinetics.
Change history
03 July 2021
A Correction to this paper has been published: https://doi.org/10.1007/s40262021010555
References
 1.
Abramson JS, Palomba ML, Gordon LI, Lunning MA, Wang M, Arnason J, et al. Lisocabtagene maraleucel for patients with relapsed or refractory large Bcell lymphomas (TRANSCEND NHL 001): a multicentre seamless design study. Lancet. 2020;396(10254):839–52.
 2.
Teoh J, Johnstone T, Christin B, Yost R, Haig N, Mallaney M, et al. Lisocabtagene maraleucel (lisocel) manufacturing process control and robustness across CD19+ hematological malignancies [abstract]. Blood. 2019;134(Suppl 1):593.
 3.
Turtle CJ, Hanafi LA, Berger C, Hudecek M, Pender B, Robinson E, et al. Immunotherapy of nonHodgkin's lymphoma with a defined ratio of CD8+ and CD4+ CD19specific chimeric antigen receptormodified T cells. Sci Transl Med. 2016;8(355):355ra116.
 4.
Paszkiewicz PJ, Fräßle SP, Srivastava S, Sommermeyer D, Hudecek M, Drexler I, et al. Targeted antibodymediated depletion of murine CD19 CAR T cells permanently reverses B cell aplasia. J Clin Invest. 2016;126(11):4262–72.
 5.
Wang X, Chang WC, Wong CW, Colcher D, Sherman M, Ostberg JR, et al. A transgeneencoded cell surface polypeptide for selection, in vivo tracking, and ablation of engineered cells. Blood. 2011;118(5):1255–63.
 6.
Maus MV, Levine BL. Chimeric antigen receptor Tcell therapy for the community oncologist. Oncologist. 2016;21(5):608–17.
 7.
Kochenderfer JN, Somerville RPT, Lu T, Shi V, Bot A, Rossi J, et al. Lymphoma remissions caused by antiCD19 chimeric antigen receptor T cells are associated with high serum interleukin15 levels. J Clin Oncol. 2017;35(16):1803–13.
 8.
Neelapu SS, Locke FL, Bartlett NL, Lekakis LJ, Miklos DB, Jacobson CA, et al. Axicabtagene ciloleucel CAR Tcell therapy in refractory large Bcell lymphoma. N Engl J Med. 2017;377(26):2531–44.
 9.
Schuster SJ, Bishop MR, Tam CS, Waller EK, Borchmann P, McGuirk JP, et al. Tisagenlecleucel in adult relapsed or refractory diffuse large Bcell lymphoma. N Engl J Med. 2019;380(1):45–56.
 10.
Stein AM, Grupp SA, Levine JE, Laetsch TW, Pulsipher MA, Boyer MW, et al. Tisagenlecleucel modelbased cellular kinetic analysis of chimeric antigen receptorT cells. CPT Pharmacometrics Syst Pharmacol. 2019;8(5):285–95.
 11.
Mueller KT, Maude SL, Porter DL, Frey N, Wood P, Han X, et al. Cellular kinetics of CTL019 in relapsed/refractory Bcell acute lymphoblastic leukemia and chronic lymphocytic leukemia. Blood. 2017;130(21):2317–25.
 12.
Mueller KT, Waldron E, Grupp SA, Levine JE, Laetsch TW, Pulsipher MA, et al. Clinical pharmacology of tisagenlecleucel in Bcell acute lymphoblastic leukemia. Clin Cancer Res. 2018;24(24):6175–84.
 13.
Awasthi R, Pacaud L, Waldron E, Tam CS, Jäger U, Borchmann P, et al. Tisagenlecleucel cellular kinetics, dose, and immunogenicity in relation to clinical factors in relapsed/refractory DLBCL. Blood Adv. 2020;4(3):560–72.
 14.
YESCARTA (axicbatagene ciloleucel) [summary of product characteristics]. Amsterdam, The Netherlands: Kite Pharma EU B.V.; 2018.
 15.
KYMRIAH (tisagenlecleucel) [summary of product characteristics]. Dublin: Novartis Europharm Limited; 2018.
 16.
Lindbom L, Pihlgren P, Jonsson EN. PsNToolkit—a collection of computer intensive statistical methods for nonlinear mixed effect modeling using NONMEM. Comput Methods Programs Biomed. 2005;79(3):241–57.
 17.
Bauer R. NONMEM Users Guide. Introduction to NONMEM 7.4.1. 2017. https://nonmem.iconplc.com/nonmem741. Accessed 30 Apr 2020.
 18.
De Boer RJ, Perelson AS. Quantifying T lymphocyte turnover. J Theor Biol. 2013;327:45–87.
 19.
US Food and Drug Administration. Pharmacometric review of axicabtagene ciloleucel. 2017. https://www.fda.gov/media/109140/download. Accessed 5 May 2020.
 20.
Savic RM, Karlsson MO. Importance of shrinkage in empirical Bayes estimates for diagnostics: problems and solutions. AAPS J. 2009;11(3):558–69.
 21.
Madigan M, Martinko J, Parker J. Brock biology of microorganisms. 8th ed. London: Prentice Hall, Inc.; 1997.
 22.
Khot A, Matsueda S, Thomas VA, Koya RC, Shah DK. Measurement and quantitative characterization of wholebody pharmacokinetics of exogenously administered T cells in mice. J Pharmacol Exp Ther. 2019;368(3):503–13.
 23.
BREYANZI (lisocabtagene maraleucel) [prescribing information]. Princeton, NJ: Bristol Myers Squibb; 2021.
 24.
Zwietering MH, Jongenburger I, Rombouts FM, van 't Riet K. Modeling of the bacterial growth curve. Appl Environ Microbiol. 1990;56(6):1875–81.
 25.
Salter AI, Ivey RG, Kennedy JJ, Voillet V, Rajan A, Alderman EJ, et al. Phosphoproteomic analysis of chimeric antigen receptor signaling reveals kinetic and quantitative differences that affect cell function. Sci Signal. 2018;11(544):eaat6753.
 26.
Jaggers JL, Giri S, Klepin HD, Wildes TM, Olin RL, Artz A, et al. Characterizing inclusion and exclusion criteria in clinical trials for chimeric antigen receptor (CAR) Tcell therapy among adults with hematologic malignancies. J Geriatr Oncol. 2021;12(2):235–8.
Acknowledgements
The authors are grateful for the support of their colleagues at Bristol Myers Squibb, with special thanks to Kathryn Newhall for guidance and support and Changpin Huang for data validation. All authors contributed to and approved the manuscript; writing and editorial assistance were provided by Amy Agbonbhase, Ph.D., of The Lockwood Group (Stamford, CT, USA), and was funded by Bristol Myers Squibb.
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This study was funded by Juno Therapeutics, a BristolMyers Squibb Company.
Conflict of interest
Ken Ogasawara, Timothy Mack, James Lymp, Justine Dell’Aringa, and Jeff Smith are employees of Bristol Myers Squibb and hold stock in Bristol Myers Squibb. Michael Dodds is a consultant for Bristol Myers Squibb.
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The research was conducted within all the appropriate ethical and legal guidelines.
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For investigations involving human patients, informed consent was obtained from the participants involved.
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Bristol Myers Squibb policy on data sharing may be found at https://www.bms.com/researchersandpartners/independentresearch/datasharingrequestprocess.html.
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KO and MD contributed to the study design and data analysis and interpretation. TM, JL, JD, and JS contributed to data acquisition and interpretation. KO drafted the manuscript. All authors critically reviewed the draft manuscript, approved the final version to be published, and agree to be accountable for all aspects of the work.
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The original Online version of this article was revised: The corresponding author's affiliation has been incorrectly published.
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Ogasawara, K., Dodds, M., Mack, T. et al. Population Cellular Kinetics of Lisocabtagene Maraleucel, an Autologous CD19Directed Chimeric Antigen Receptor TCell Product, in Patients with Relapsed/Refractory Large BCell Lymphoma. Clin Pharmacokinet (2021). https://doi.org/10.1007/s40262021010395
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