The current work integrates cell-cycle dynamics occurring in the bone marrow compartment as a key element in the structure of a semimechanistic pharmacokinetic/pharmacodynamic model for neutropenic effects, aiming to describe, with the same set of system- and drug-related parameters, longitudinal data of neutropenia gathered after the administration of the anticancer drug diflomotecan (9,10-difluoro-homocamptothecin) under different dosing schedules to patients (n = 111) with advanced solid tumors. To achieve such an objective, the general framework of the neutropenia models was expanded, including one additional physiologic process resembling cell cycle dynamics. The main assumptions of the proposed model are as follows: within the stem cell compartment, proliferative and quiescent cells coexist, and only cells in the proliferative condition are sensitive to drug effects and capable of following the maturation chain. Cell cycle dynamics were characterized by two new parameters, FProl (the fraction of proliferative [Prol] cells that enters into the maturation chain) and kcycle (first-order rate constant governing cell cycle dynamics within the stem cell compartment). Both model parameters were identifiable as indicated by the results from a bootstrap analysis, and their estimates were supported by date from the literature. The estimates of FProl and kcycle were 0.58 and 1.94 day−1, respectively. The new model could properly describe the neutropenic effects of diflomotecan after very different dosing scenarios, and can be used to explore the potential impact of dosing schedule dependencies on neutropenia prediction.
Several pharmacokinetic (PK)/pharmacodynamic models have been published over the last decade describing myelosuppression response occurring during cancer treatment with chemotherapy agents (Minami et al., 1998; Zamboni et al., 2001; Friberg et al., 2002; Krzyzanski and Jusko, 2002; Panetta et al., 2003, 2008). The most used and accepted model was developed by Friberg et al. (2002), hereafter the reference model, which has demonstrated consistency among a wide variety of anticancer agents (Latz et al., 2006; Fetterly et al., 2008; Soto et al., 2010b) and has been used to describe neutropenic effects after drug combinations (Sandstrom et al., 2005; Soto et al., 2010a) and predict human hematologic toxicity from laboratory animal data (Friberg et al., 2010).
The aforementioned models are considered semimechanistic and are capable of discriminating between system- and drug-related parameters. The system-related parameters include those accounting for baseline condition, cell proliferation/maturation/degradation, and rebound, whereas drug-related effect parameters are represented, for example, by IC50, the drug concentration in plasma eliciting half of the maximal reduction of the cell proliferation process. However, there are some examples in the literature for antitumor drugs where a change in the drug-related effect parameters has been reported for anticancer drugs when the drug was given through different routes and/or different dosing schedules (Soto et al., 2011). In the case of topotecan, the drug-related effect parameter was estimated to be 43% lower after oral administration using a different dosing schedule compared with the intravenous administration (Leger et al., 2004). Those findings suggest that there might be aspects beyond the proliferation, maturation, degradation, and rebound processes that also have to be considered (Steimer et al., 2010).
Diflomotecan (9,10-difluoro-homocamptothecin) is a homocaptothecin, and its mechanism of antitumoral action is related to the inhibition of topoisomerase I, a nuclear enzyme involved in the replication process. The recommended and maximal tolerated doses as well as its pharmacokinetic and neutropenic profiles under single dosing schedules have been previously reported (Troconiz et al., 2006; Soto et al., 2011), using the reference model for neutropenia (Friberg et al., 2002).
The aim of the current work was to describe the neutropenic effects of diflomotecan administered under different dosing schedules to patients with advanced solid tumors involved in different phase I clinical trials, using the same set of system- and drug-related parameters. To achieve such an objective, the general framework of neutropenia models had to be expanded with an additional physiologic process resembling cell cycle dynamics.
Materials and Methods
Patient Population and Study Design
Data from five phase I clinical trials in advanced malignant tumors, including 111 patients, were available. All participants provided written informed consent consistent with the International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use–Good Clinical Practice and local legislation, once the nature and the intention of the investigation were fully explained. The studies were performed in accordance with the Declaration of Helsinki and were approved by the institutional review board of the ethics committee at each study site. Supplemental Table 1 lists the characteristics of the patient population.
A total of 111 patients were enrolled in five different clinical studies. In all studies, on day 1 of the first cycle of treatment, patients received diflomotecan as an intravenous infusion over 20 minutes. Additionally, 1) a 20-minute intravenous infusion was administered on days 7 and 14 in study B (n = 15 patients), 2) five consecutive oral daily administrations were given on days 14–18 in studies C (n = 24) and E (n = 18), or 3) four intravenous doses were administered between days 2 and 5 in study D (n = 30). Patients in study A (n = 24) received only the intravenous infusion over 20 minutes on day 1. Subsequent cycles in studies C–E lacked an intravenous infusion over 20 minutes on day 1 of the new cycle.
A single infusion or infusions given on days 1, 7, and 14 within a cycle were denoted as dosing schedule I, whereas the consecutive once-daily administrations were referred to as dosing schedule II. Dosing schedule II corresponds to oral solution, intravenous infusion, and oral capsules in studies C, D, and E, respectively. Cycle duration varied from the planned 28 days based on the recovery from the neutropenic toxicity.
Figure 1 summarizes the dosing scheme for all studies (studies A–E) and provides detailed information on the dose levels administered in cycle 1 together with the number of patients allocated to each dose group. Diflomotecan concentrations were collected during the administration days, and absolute neutrophil counts were measured in peripheral blood every 3–7 days. The total number of absolute neutrophil counts was 1865, and 789 (42%) were obtained during the first cycle of treatment.
Data were analyzed using the population approach with NONMEM version 7.2 (Bauer, 2011). Parameter estimation was performed based on the first-order conditional estimation method together with the INTERACTION option. Both types of data, diflomotecan concentrations and neutrophil counts, were logarithmically transformed. Interindividual variability was described exponentially, and residual error was accounted for using a combined error model on the logarithmic scale. The model-building process was performed sequentially. First, the empirical Bayes estimates of the individual PK parameters were obtained from a previous published population PK model (Soto et al., 2011), and were incorporated to the data set containing the neutrophil counts information. Given the change in the dosing paradigms from cycle 1, and the fact that data were more sparse in terms of number of patients and measurements, the model-building process was performed using only data from the first treatment cycle.
Model selection was mainly based on the log-likelihood ratio test [for two nested models, a decrease of 3.84 points in −2× log(likelihood) (−2LL) for an extra added parameter was considered significant at the 5% level] and visual exploration of goodness-of-fit plots.
Model evaluation was performed through prediction-corrected visual predictive checks (pc-VPC) (Bergstrand et al., 2011). For each study design, 1000 simulated data sets were generated. At specific sampling time periods, the 2.5th, 50th, and 97.5th percentiles of the simulated data were calculated. Then, the 95% prediction intervals of the 2.5th, 50th, and 97.5th percentiles were computed and displayed graphically together with the experimental data. Additionally, parameter precision was evaluated from the analysis of 500 simulated bootstrap data sets.
For graphical and statistical analysis, the R software (version 2.6.0; http://cran.r-project.org) was used. Pc-VPC and bootstrap analysis were performed using Perl-speaks-Nonmem (PsN) (Lindbom et al., 2005) and Xpose version 4.5.3 (Jonsson and Karlsson, 1999).
The population PK model for diflomotecan consisted of a three-compartment model with first-order absorption and elimination processes. The population pharmacokinetics of diflomotecan were previously studied (Soto et al., 2011).
The semimechanistic model for chemotherapy-induced myelosuppression previously published by Friberg et al. (2002) was fitted to the absolute neutrophil count versus time data obtained during schedule I. Linear, Emax, and sigmoidal Emax models were used to describe the drug effects on the first-order rate constant of proliferation, kprol. Then, the outcome during dosing scenario II was predicted by generating individual profiles using the individual Bayes parameter estimates obtained from the schedule I data fit. As is illustrated in Fig. 2, B and C, the neutrophil profiles corresponding to schedule II were not well described, and values of neutrophils at the nadir were in general overpredicted [not in the case of the data obtained from schedule I (Fig. 2A)].
A semimechanistic model considering the dynamics of a simplified cell cycle including just the proliferative and quiescent sates was proposed and fitted to all cycle I data obtained from the five clinical studies. This model, represented in Fig. 3, assumes the following: within the stem cell compartment, proliferative (Prol) and quiescent (Qc) cells coexist, and cell cycle dynamics are described by first-order processes governed by kcycle (first-order rate constant governing cell cycle dynamics within the stem cell compartment); quiescent cells comprise two compartments (Qc1 and Qc2); and only cells in the proliferative condition are sensitive to drug effects and capable of either following the maturation chain or passing to the quiescent state.
The rest of the model assumptions are equal to those presented in the original reference model (Friberg et al., 2002).
The dynamics in the stem cell compartment are given by the following set of equations:(1)(2)(3)where FProl is the fraction of Prol cells that enters into the maturation chain and kTR is the first-order rate constant controlling the transfer through the maturation chain. In the model, kTR is defined as (n + 1)/MTT, with n, the number of maturation compartments, and MTT, the mean transit/maturation time. Circ0 and Circ represent the absolute neutrophil counts at baseline and at any time after the start of the study, respectively. The parameter γ modulates the magnitude of the feedback mechanism.
Edrug represents drug effects which were described as a linear or nonlinear (i.e., sigmoidal Emax model) function of the predicted plasma (or effect site) concentrations of diflomotecan.
The remaining compartments of the model were characterized as follows:(4)(5)(6)(7)where TR1–3 correspond to immature neutrophil levels in each of the maturation compartments, and kcirc is the first-order rate constant representing neutrophil degradation. The last three differential equations are common to the reference model (Friberg et al., 2002).
Therefore, in the current models, the typical system-related parameters to be estimated by the model are Circ0, FProl, kcycle, MTT, and γ.
The initial conditions of the system are represented by the following expressions:
kTR = kcirc, implying that TR1 = TR2 = TR3 = Circ0.
Prol0, the level of proliferative cells at baseline, is given by the Circ0/FProl ratio.
Qc1 = Qc2 = (1 − FProl) × Prol0, and therefore, kProl = kTR × FProl.
During the model development process, other alternatives were also considered assuming that diflomotecan can also exert an effect on the Qc cells, or the inclusion of an effect compartment as suggested by Hing et al. (2008).
Results of the population PK model are shown in the Supplemental Material. Supplemental Figure 1 shows the results of the pc-VPC, indicating the population PK model provides a proper description of the drug concentration data. Population pharmacokinetics estimates are listed in Supplemental Table 2. All parameters in the model were estimated with good precision based on the values of the results from the bootstrap analysis.
Modeling Absolute Neutrophil Counts
Data obtained during dosing schedule I were fitted using the reference model for neutropenia. The Emax model provided a better fit than the linear model; however, the precision of the IC50 parameter was poor. To improve parameter precision, the Emax model was reparameterized (Schoemaker et al., 1998), where IC50 is expressed as Emax/θSlope, and θSlope is an estimated model parameter together with Emax (the maximum attainable effect that diflomotecan can exert on kProl). Model parameter estimates are shown in Table 1. Estimates showed consistency with those obtained in previous studies (Soto et al., 2011).
Figure 2A shows that nadir concentrations from schedule I were well described, whereas nadir levels from schedule II simulated according to parameters obtained from the analysis of the schedule I data were not adequately captured (Fig. 2B). This result reveals model mis‐specifications reflected as an underprediction of neutropenic effects at the nadir (Fig. 2B) and on the overall neutrophil versus time profile (Fig. 2C showing nine patients only).
The previously described model provided a good description of the data regardless of the type of dosing scenario, as can be seen in Fig. 4A. The model properly predicted the nadir concentrations from individuals from schedules I and II. Figure 4B shows the model performance evaluated as pc-VPC including all individuals from the five clinical studies, where both the general tendency and the dispersion of the neutrophil data were well described. In this case, Edrug was best characterized by a linear model of the form SLP × CP, where the slope (SLP) parameter drives the relationship between the parameter kProl and the plasma concentrations of diflomotecan (CP). Better fit was obtained with two Qc compartments with respect to a single Qc compartment. Increasing the number of Qc compartments did not improve data description. Table 2 lists the population parameter estimates of the selected model incorporating cell cycle dynamics. All parameters were estimated with good precision, as indicated by the bootstrap analysis where none of the 2.5–97.5th percentiles included the null value, and the parameter values estimated are within the 2.5–97.5th percentiles from the bootstrap analysis. Figure 4C shows that, for the nine selected patients included in Fig. 2C, the current model provides a good description of the individual profiles in both dosing scenarios. The three panels in Fig. 4 show slight trends suggesting some degree of model mis-specification. Models incorporating an effect compartment or considering quiescent cells also sensitive to drug effects did not provide a better description of the data.
Figure 5 summarizes the results of Figs. 2C and 4C with a focus on the degree of neutropenia at the nadir after the administration of schedule II. For half of the selected patients, the reference model predicted grade III neutropenia, whereas raw data indicated grade IV. The new model provided a 100% match between raw and predicted degree of neutropenia at the nadir. Both the reference and the current models show very similar estimates of the parameters Circ0 and MTT (see Tables 1 and 2). The FProl parameter was estimated as 0.58, indicating that, at any time, approximately more than half of the proliferative cells follow the maturation chain, and slightly fewer than half transit to a quiescent state. The turnover process within the stem cell compartment is 2.5-fold faster than the maturation process, as indicated by the difference between the median cell cycle time (calculated as 3/kcycle) and MTT (1.6 vs. 3.8 days).
Drug effects were best characterized with a linear model in the case of the new proposed model. The slope parameter showed large differences between the two models (1.5 versus 9.5 ml/ng), which might at least partly explain the underprediction of neutropenic effects after administration of schedule II, when using the empirical Bayes individual parameters obtained from the analysis of the schedule I data.
The estimate of the interindividual variability in the slope parameter was 108%. There is the possibility that individual pharmacokinetic data were not sufficiently informative, and so pharmacokinetic variability has been assigned to pharmacodynamics. To test that possibility, a simultaneous fit was attempted, but we could not achieve convergence, and all additional models were terminated without providing parameter estimates. On the other hand, in a previous analysis (Troconiz et al., 2006) performed with only part of the data included in this study (study A), an estimate of interindividual variability of 61% was already obtained. It is expected that by pooling data from additional individuals with advanced cancer from other studies, the magnitude of interindividual variability increases.
As a final modeling exercise, the reference model was also fit to all data (schedules I and II), and a significant decrease in −2LL was found in favor of the proposed model (Δ−2LL = 5.2; P < 0.05). However, the main difference in model performance as shown in Figs. 2C and 4C is at the level of the nadir, which has a profound impact on adverse effect characterization but, in our case, less impact on −2LL.
Figure 6 explores how the model behaves. In Fig. 6A, the typical profiles in each compartment for the reference and current proposed models after a 20-minute intravenous infusion of 0.5 mg/m2 on day 1 (schedule I) followed by five consecutive 20-minute intravenous infusions of 0.1 mg/m2 given once daily, starting at day 14, are shown. After a single drug infusion, both models behaved very similarly. However, after consecutive administrations and due to the turnover dynamics in the stem cell compartment, the absolute depletion of the proliferative cells is increased in the current model, eliciting higher neutropenic effects. The schedule dependency seen for diflomotecan is caused possibly by the fast decline of its drug concentrations. After a short intravenous infusion, proliferative cells are affected, but by the time the quiescent cells are converted into proliferative cells, most of the drug has been eliminated from the body. In Fig. 6B, we explored the differences in the overall neutrophil profiles between the two models corresponding to different scenarios where the total plasma clearance of the drug was reduced (half-life was augmented). The prediction discrepancy between the two models diminished as the plasma clearance was reduced. Figure 6C shows the typical plasma drug concentration profiles for each of the PK scenarios, highlighting the median cell cycle time of 1.58 days.
In the current work, a model describing the neutropenic effects of diflomotecan administered under different dosing schedules involving either a short (20 minutes) intravenous infusion or five daily intravenous or oral administrations within a cycle of chemotherapy has been developed.
The proposed model was built from the physiologic platform of the reference model of neutropenia (Friberg et al., 2002). In addition to the proliferation, maturation, rebound, and degradation processes, cell cycle dynamics occurring within the stem cell compartment were incorporated. Such an extra physiologic element in the model was represented by two new parameters, FProl and kcycle, the first accounting for the fraction of the proliferative cells that enter into the maturation chain, and the latter quantifying the dynamic of the transit between the different cells’ status. Both model parameters were identifiable, as indicated by the results from the bootstrap analysis. It should be noted that the identifiability of those two parameters could only be obtained when data of the two types of schedules were analyzed together; otherwise, the current model collapsed to the reference model (i.e., FProl = 1) with a smaller estimate of the slope parameter associated with the schedule I data. An attempt was made to fit all available data (all treatment cycles) using the proposed model; however, it was not possible to get precise and reliable estimates for Fprol and kcycle, due to the sparse nature of the data (samples were recorded at times far from the nadir, usually at the end of each treatment cycle) and the fact that the number of subjects providing data after the first cycle of treatment decreased by at least half. This result stresses the need of rich data to apply the model proposed in the current work, which is generally the case of phase I studies at least during the very first cycles of treatment.
The FProl and kcycle estimates obtained in this work are in accordance with values obtained from literature data (Reddy et al., 1997; Quesenberry et al., 2015). Proliferative cells are able to replicate into new stem cells, which might remain as the same cell type or differentiate into a new one along the maturation chain compartments. These mechanisms are controlled by different biochemical and cell cycle checkpoint signals (Pietras et al., 2011), which might increase or reduce cell differentiation and/or stem cell growth. The cell growth rate estimated in the current model (kProl = kTR × FProl = 0.6 day−1) is in accordance with the cell growth rate values of 0.56 day−1 published elsewhere (Clairambault and Fercoq, 2012). On the contrary, higher cell growth rate values were estimated using the reference model (0.83 day−1). This discrepancy might be explained because, at any time, two pools of stem cells are present in the quiescent compartments and, because of the cell cycle turnover process, lower cell growth rates are needed to satisfy circulating neutrophil demand. The cell cycle duration in the current model (3/kcycle) was 37.9 hours, indicating a physiologic resemblance with the published cell cycle duration window for hematopoietic stem cells (Reddy et al., 1997; Pietras et al., 2011).
As discussed earlier, cell cycle dynamics could only be detected and modeled when data from the two schedules were fitted simultaneously. Then, for a particular anticancer drug under investigation or in clinical use, and in the case of neutrophil data available only under the same or similar schedules, the question of how to anticipate relevant dosing schedule dependency limiting the prediction of neutropenic effects after different dosing scenarios remains open.
In Fig. 6, B and C, we showed that the greater the remaining area under the plasma drug concentration versus time curve outside the time corresponding to the estimated cell cycle duration, the lower the differences between the neutrophil profiles predicted by the two models (suggesting a lack of impact of predicting neutropenia when ignoring cell cycle dynamics). However, we have not formally explored the relationship between, for example, the percentage of total area under the plasma drug concentration versus time curve predicted over the duration of the cell cycle and the degree of discrepancy between the two models; other factors, such as drug potency, might play a role.
We propose the following workflow to explore the potential impact of dosing schedule dependencies on neutropenia prediction. Taking advantage of the fact that the system-related parameters of the reference model have shown repeated consistency across drugs, and that FProl and kcycle are supported by the literature, neutrophil data obtained after administration of one schedule were analyzed under 1) the reference model estimating the full set of parameters, and 2) the current model fixing FProl and kcycle to the estimates obtained in the current evaluation, and the rest of parameters to be estimated. Then simulations are performed under different scenarios to evaluate discrepancies in the outcome (i.e., percentage of patients experiencing grade 4 neutropenia) of the two models.
When that approach was performed on the data from schedule I in the current work, we found that after the administration of 0.2 mg/m2 on day 1 and five consecutive oral doses of 0.35 mg on days 14–18, the median simulated percentage of patients showing grade 4 neutropenia receiving diflomotecan was 77% and 94% using the parameters obtained from the reference and currently developed models, respectively.
To summarize the results from the current investigation, a model describing the neutropenic effects after administration of diflomotecan following two different dosing administration schemes was developed, incorporating cell cycle dynamics in addition to the proliferation, maturation, degradation, and rebound processes described in previously published semimechanistic models. The new model accounted for the schedule-dependent parameters obtained when the reference model was applied. Cell cycle dynamics were characterized by new parameters, FProl and kcycle, the first accounting for the fraction of proliferative cells following the maturation chain, and the latter quantifying the dynamic of the transit between the different cells’ status. Both model parameters were identifiable, and their estimates were supported by literature data.
Performed data analysis: Mangas-Sanjuan, Buil-Bruna, Garrido, Soto, Trocóniz.
Wrote or contributed to the writing of the manuscript: Mangas-Sanjuan, Buil-Bruna, Garrido, Soto, Trocóniz.
- Received February 16, 2014.
- Accepted May 5, 2015.
V.M.-S. received a predoctoral grant from the Ministry of Education and Science of Spain and Miguel Hernandez University [Grant FPU AP2010-2372]. N.B.-B. was supported by a predoctoral fellowship from the Asociación de Amigos de la Universidad de Navarra. This work was supported by the Innovative Medicines Initiative Joint Undertaking under grant agreement No. 115156, the resources of which are composed of financial contributions from the European Union's Seventh Framework Programme (FP7/2007-2013) and European Federation of Pharmaceutical Industries and Associations companies’ in kind contribution. The Drug Disease Modeling Resources project is also supported by financial contribution from academic and Small and Medium-sized Enterprises partners. This work does not necessarily represent the view of all DDMoRe partners.
Part of this work was presented at the following meeting: Mangas-Sanjuan V, Buil-Bruna N, Soto E, Garrido MJ, and Troconiz IF (2014) Semi-mechanistic cell cycle PKPD model of chemotherapy-induced neutropenia. Population Approach Group of Europe Meeting; 2014 Jun 10–13; Alicante, Spain.
- 2× log(likelihood)
- mean transit/maturation time
- prediction-corrected visual predictive checks
- proliferative cells
- quiescent cells
- Copyright © 2015 by The American Society for Pharmacology and Experimental Therapeutics