Abstract
Purpose: To develop and validate a population pharmacokinetic model for troxacitabine, a novel lnucleoside analogue, administered by short infusion; to characterize clinical covariates that influence pharmacokinetic variability; and to design a dosage rate for continuous infusion administration to achieve low micromolar concentrations, which may be more efficacious than shorter infusions.
Experimental Design: Plasma samples from 111 cancer patients receiving troxacitabine (0.1212.5 mg/m^{2}) as a 30minute infusion in phase I trials were used to develop the model with NONMEM. Clinical covariates evaluated included creatinine clearance, body surface area, age, and sex. From the model, a troxacitabine dosage rate of 2.0 to 3.0 mg/m^{2}/d was expected to achieve a target concentration of 0.1 μmol/L; plasma samples were obtained during the infusion from eight patients receiving troxacitabine as a 3day infusion.
Results: Troxacitabine pharmacokinetics were characterized by a threecompartment linear model. The mean value for systemic clearance [interindividual variability (CV%)] from the covariatefree model was 9.1 L/h (28%). Creatinine clearance and body surface area accounted for 36% of intersubject variation in clearance. Troxacitabine 2.0 mg/m^{2}/d (n = 3) and 3.0 mg/m^{2}/d (n = 5) for 3 days produced mean ± SD end of infusion concentrations of 0.12 ± 0.03 and 0.15 ± 0.03 μmol/L, respectively.
Conclusions: Renal function and body surface area were identified as sources of troxacitabine pharmacokinetic variability. The population pharmacokinetic model model–derived dosage rates for continuous infusion administration successfully achieved predetermined target plasma concentrations. The present model may be used to optimize treatment with troxacitabine by developing a dosing strategy based on both renal function and body size.
 Troxacitabine
 Lnucleoside analogue
 population pharmacokinetics
Troxacitabine, (−)2′deoxy3′oxacytidine (Fig. 1 ), is a novel unnatural lnucleoside analogue with in vitro and in vivo antitumor activity against human leukemias and a variety of solid tumors, including hepatocellular, ovarian, prostate, and renal carcinomas (1–7). Like the related natural dnucleoside analogues cytarabine and gemcitabine, troxacitabine requires phosphorylation to its active triphosphate form by intracellular kinases, including deoxycytidine kinase (1, 2, 8). Troxacitabine produces cytotoxic activity through incorporation of the triphosphate anabolite by DNA polymerases, complete DNA chain termination, and inhibition of DNA replication (9, 10). Unlike the natural dnucleoside analogues, troxacitabine's lconfiguration is resistant to catabolism by cytidine deaminase, which represents an inactivation step for other nucleoside analogues (2, 8, 9, 11). Troxacitabine is removed intracellularly by apurinic/apyrimidinic endonuclease (APE1), an enzyme responsible for DNA repair and regulation of gene expression (2, 8, 9, 11). Nucleoside transporters are involved in the cellular uptake of cytarabine and gemcitabine, whereas troxacitabine seems to accumulate intracellularly by passive diffusion (9).
In phase I and II trials, troxacitabine given as an i.v. infusion for 30 minutes daily for 5 days showed significant antineoplastic activity in patients with relapsed myeloid leukemias, with the principal toxicities being grade 3 or 4 stomatitis, handfoot syndrome, and skin rash (12–14). Troxacitabine was also evaluated as a 30minute infusion in patients with advanced solid malignancies on various administration schedules, including daily for 5 days every 3 to 4 weeks, weekly for 3 of 4 weeks, and once every 21 days, where the doselimiting toxicity was neutropenia, and the most frequent nonhematologic toxicities were skin rash and handfoot syndrome (15–17).
In phase I studies, the pharmacokinetic behavior of troxacitabine was characterized by a mean plasma clearance of 10 L/h, with ∼3fold variability between patients, and renal excretion resulting in the elimination of 61% to 77% of the given dose as unchanged drug (15–17). Plasma exposure toxicity assessments in patients with refractory leukemia receiving 30minute infusions showed that elevated troxacitabine plasma area under the concentrationtime curve was related to the severity of mucositis and handfoot syndrome (13).
Recent preclinical data suggest that troxacitabine given as a continuous infusion may be more efficacious than intermittent infusions. In a HT29 human xenograft model, prolonged exposure to low micromolar concentrations (≥0.1 μmol/L) of troxacitabine for 3 to 5 days leads to superior growth inhibition compared with single highdose bolus infusions (18). Based on this data, troxacitabine given by continuous infusion is being evaluated in patients with refractory acute myeloid leukemia (19). The starting dosage rate was 10.1 mg/m^{2}/d, which was determined using the present population pharmacokinetic model to achieve a minimum target plasma concentration of 0.4 μmol/L. The initial infusion duration was 3 days with an increase in infusion to 5 to 6 days. In the first 13 patients treated, two complete responses were observed. With these promising results, accelerated development of continuous infusion troxacitabine is planned. A parallel phase I study of continuous infusion troxacitabine is being done in patients with advanced solid malignancies. In this study, the starting dosage rate was 2.0 to 3.0 mg/m^{2}/d for 3 days, which was expected to reach a lower target plasma concentration of 0.1 μmol/L (20).
Population pharmacokinetic analysis is a useful tool for identification of sources of pharmacokinetic variability during anticancer drug development and can aid in the design of alternative dosing regimens to enhance their efficacy and safety (21). The objective of this study was to develop and validate a population pharmacokinetic model for troxacitabine to characterize clinical covariates that influence troxacitabine pharmacokinetics and to design a continuous dosing regimen to achieve a target plasma concentration of 0.1 μmol/L for phase I evaluation in patients with advanced solid malignancies.
Materials and Methods
Patient population and plasma troxacitabine levels
Troxacitabine plasma concentration versus time data from 111 patients with cancer from four separate phase I studies were used (12, 15–17). Ninetytwo (83%) had advanced solid tumors, and 19 (17%) had advanced leukemia. All concentration versus time data were obtained after a single i.v. dose of troxacitabine (0.1212.5 mg/m^{2}) given as a 30minute infusion. All patients provided written informed consent, and the study protocols were approved by the investigational review boards from the respective institutions.
Four covariates were considered in the analysis, including continuous [age, body surface area (BSA), and creatinine clearance] and categorical (sex) variables. BSA was calculated using Mosteller's formula: BSA = [height (cm) × weight (kg) / 3,600]^{0.5} (22). Creatinine clearance was estimated using the Crockcroft and Gault method and expressed in units of mL/min; entrance criteria to the clinical protocols included an estimated creatinine clearance of ≥45 mL/min (23). Plasma sampling was extensive; a mean of 12.6 samples (range, 916 samples) per patient were obtained between 4 minutes to 168.5 hours after the start of infusion. Troxacitabine was quantitated in plasma using a method involving highperformance liquid chromatography with tandem mass spectrometry detection and calibration curves ranging from 0.6 to 99.9 ng/mL, as previously described (12, 15, 16), and all concentrations were measured in the same laboratory.
Pharmacokinetic model
The population pharmacokinetic model for troxacitabine was developed in two steps: (a) covariatefree (base) model development and (b) covariate model development. Pharmacokinetic models were fitted to the data using the computer software programs NONMEM version V, level 1.1 (GloboMax LLC, Hanover, MD) and PDx POP version 1.1 (Globomax LLC). Xpose 3.1/SPLUS 6.0 (Insightful Corporation, Seattle, WA) was used for graphical diagnostics and covariate screen.
Step 1: covariatefree (base) model development. The troxacitabine population pharmacokinetic model was built using two drug input methods: (a) actual dose (mg/h; model A) and (b) dose normalized to BSA (mg/m^{2}/h; model B). Model B was explored because the dose of troxacitabine given was normalized to a patient's individual BSA. This approach would provide an independent assessment of the contribution of BSA to interindividual variability on troxacitabine clearance when compared with the covariatefree model for model A. The best structural pharmacokinetic model for troxacitabine was defined by fitting the data to predefined pharmacokinetic models provided in the NONMEM library. Linear compartmental pharmacokinetic models were evaluated because linear pharmacokinetic characteristics were noted in previous phase I trials (12, 15, 16). The pharmacokinetic model incorporated unknown intersubject and intrasubject variability and defined the number and form of η, a measure of intersubject variability, and ε_{ij}, a measure of intrasubject or residual variability. Intersubject variability for each pharmacokinetic variable was modeled with the exponential function. Residual error models of the additive, proportional, exponential, and combination methods were evaluated for the best structural pharmacokinetic model. The computational, intense, firstorder conditional estimation method with or without interaction (FOCE + INTER) was used (24, 25).
For model discrimination, the NONMEM objective function (−2 times the loglikelihood function or −2 loglikelihood) was used to calculate the Aikake Information Criterion = (−2 loglikelihood) + 2p, for each nonhierarchical model, where 2p is twice the number of pharmacokinetic variables appearing in the model. Diagnostic plots for observed versus predicted plasma concentrations, residuals versus predicted concentrations, and weighed residuals versus predicted concentration were also considered during model discrimination.
Step 2: covariate model development. Covariate models were developed separately for models A and B as described above. Each candidate covariate identified from the screen was evaluated for inclusion to the selected structural pharmacokinetic model in a stepwise fashion by adding covariates in the order of highest to lowest level of significant correlation. General additive models and tree models were used in this analysis as implemented in the Xpose software (26).
Continuous variables were evaluated with the following models on pharmacokinetic variables as described in the manual for the software program PDx Pop: linear additive effect, normalized by median weight, centered on median weight, and power or allometric. The order of selecting pharmacokinetic variables for covariate model building was systemic clearance, volumes of distribution, and then intercompartmental clearance constants. Covariates were included into the model provided that the run resulted in successful minimization and covariate run status, a minimum reduction in objection function value of 3.875 (χ^{2} distribution for 1 degree of freedom with α = 0.05), and a reduction in the intersubject variance of the associated pharmacokinetic variable, and the %RSE (relative SE of estimation) associated with each variable estimate was <50%.
A stepwise backward deletion procedure was done for both full covariate models. Covariates remained in the final population pharmacokinetic model when the removal of the covariate resulted in a ≥10.828 increase in the objective function (χ^{2} distribution for 1 degree of freedom with α = 0.001). The final covariate models were run with the FOCE + INTER method.
Statistical assessment of final population pharmacokinetic models
To determine the influence of covariates on model prediction, a predictive performance evaluation was done for pharmacokinetic variables derived from both group I and II final population models as described previously (27, 28). Briefly, prediction errors (bias) were determined for pharmacokinetic variables estimated by the covariatefree (PEN) and the final covariate (PE) models. For all models, percentage prediction error (PE_{j} or PEN_{j}) was calculated as (TVPK_{j} − PK_{j}) / TVPK_{j} × 100, where TVPK_{j} is the typical (population) value for the pharmacokinetic variable for patient j, and PK_{j} is the true value for the pharmacokinetic variable for patient j. The individual calculated PE_{j} and PEN_{j} of the pharmacokinetic variable was compared to see if the final population pharmacokinetic model had improved on predicting the respective pharmacokinetic variable. An improvement was defined as having the absolute value of PE_{j} to be less than the absolute value of PEN_{j}.
Validation of final population pharmacokinetic models
Validation of the final population pharmacokinetic models was undertaken using internal crossvalidation techniques as recommended by the guidance document from the U.S. Department of Health and Human Services Food and Drug Administration Center for Drug Evaluation and Research Center for Biologics Evaluation and Research, Guidance for industry: population pharmacokinetics, February 1999 (http://www.fda.gov/cder/guidance/1852fnl.pdf) and described previously by Vozeh et al. (29).
Internal crossvalidation. Briefly, 20 different data sets were generated by randomly removing the observed plasma concentrations of five to six subjects in each data set from the entire data set of 111 subjects, where data from each subject was removed only once. Each of the 20 data sets were then fitted with the final population pharmacokinetic models to provide individual predicted plasma concentrations from which an individual's standardized mean prediction error was calculated as previously described (29). The mean and 95% confidence interval for standardized mean prediction error were assessed; the model was considered to provide unbiased estimates for predicting troxacitabine plasma concentrations if the 95% confidence interval included 0.
Application of population pharmacokinetic model for the design of a continuous infusion regimen. One objective of the present study was to develop a population pharmacokinetic model to design a continuous dosing regimen to sustain a troxacitabine plasma concentration of 0.1 μmol/L for 3 days. Based on the final population pharmacokinetic models, a continuous infusion of troxacitabine 2.0 to 3.0 mg/m^{2}/d was estimated to achieve a minimum target plasma concentration of 0.1 μmol/L, which is being evaluated in patients with advanced solid tumors (20). In this study, plasma samples were obtained at 4 hours after the start of infusion then daily at 24hour intervals, with a final sample immediately before termination of the infusion, to determine if the target concentration of 0.1 μmol/L was achieved. Plasma troxacitabine concentrations for this study were measured using the same assay and laboratory used for the phase I studies (12, 15–17).
Results
The population distributions of values for the patient covariates evaluated in the pharmacokinetic models are summarized in Table 1 . All but three patients had adequate renal function defined as calculated creatinine clearance of >45 mL/min.
Step 1: covariatefree (base) model development
The best structural (covariatefree) pharmacokinetic model that described troxacitabine concentrations was a threecompartment linear model (NONMEM ADVAN 11 with TRANS4 translator subroutines) with a combination residual error model. Results of the covariatefree models are summarized in Tables 2 and 3 , where the mean (interindividual variability, CV%) values for systemic clearance were 9.09 L/h (28%) and 4.78 L/h/m^{2} (24%) for models A and B, respectively. Based on assessment of interindividual variability between the two models, normalization of drug dose to BSA reduced variability on troxacitabine clearance by 14%.
Step 2: covariate model development
During the covariate screen for model A, where drug input was the actual dose in units of mg/h, creatinine clearance and BSA were identified as two significant covariates for troxacitabine clearance, and BSA was identified as a covariate for the variables V_{1}, V_{2}, and Q_{3}. During the model building process, the addition of creatinine clearance as a covariate on troxacitabine clearance decreased interindividual variability (CV%) on this variable from 28% to 21% (Fig. 2A ), representing ∼25% of intersubject variance. The further addition of BSA as a covariate on clearance decreased the CV% from 21% to 18%, indicating that BSA accounted for 14% of interindividual variability on troxacitabine clearance. These results are consistent with those obtained from the base models, where interindividual variability on clearance was decreased by 14% when drug in put was based on drug normalized to BSA (model B) compared with drug input based on the actual dose (model A). The objection function value continued to decrease with the successive addition of BSA on V_{1}, V_{2}, and Q_{3}, but interindividual variability for clearance and other variables were not reduced (Fig. 3A ). The stepwise backward deletion process resulted in the removal of no covariates from the covariate model.
Table 2 presents troxacitabine typical population pharmacokinetic variables for the base model and final model for model A using the more computationally intense FOCE + INTER estimation method. From base to final model, the value for objection function value decreased by 144 (from 8,210 to 8,066), and the addition of covariates (creatinine clearance and BSA) accounted for 36% of unexplained variation on clearance (CV% decreased from 28% to 18%). The goodness of fit between observed and final modelpredicted troxacitabine concentrations are shown in Fig. 3A (R^{2} = 0.8918).
During the covariate screen for model B, where drug input was dose normalized to BSA in units of mg/m^{2}/h, creatinine clearance was identified as a covariate for troxacitabine clearance. The addition of creatinine clearance on troxacitabine clearance decreased interindividual variability (CV%) for this variable from 24% to 20% (Fig. 2B). Subsequent models included the addition of AGE on V_{1}, creatinine clearance on Q_{2}, and BSA on Q_{3}, with a significant reduction in the objective function, but provided no further explanation of interindividual variability on troxacitabine clearance (Fig. 2B). In addition, when AGE was added as a covariate on V_{1}, the %RSE for V_{1} increased from 10% to 55% and increasingly worsened with addition of covariates on other variables. Likewise, with the addition of creatinine clearance on Q_{2}, the %RSE for Q_{2} increased from 13% to 42%, and the %RSE for interindividual variability on this variable increased from 20% to 250%. Similarly, the addition of BSA to Q_{3} resulted in worsened %RSE (>100%) for this variable.
Table 3 presents troxacitabine typical population pharmacokinetic variables for the base model and final model for model B. From base to final model, the value for objection function value decreased by 32 (from 8,104 to 8,072), and the addition of creatinine clearance as a covariate accounted for 18% of unexplained variation on clearance (CV% decreased from 24% to 20%). The goodness of fit between observed and final modelpredicted troxacitabine concentrations are shown in Fig. 3B (R^{2} = 0.8823).
Statistical assessment of final population pharmacokinetic models
Table 4 summarizes the prediction errors associated with pharmacokinetic variables estimated from the covariatefree (PEN) and two final covariate (PE) population models, and the percentage of patients whose pharmacokinetic variable value predictions were improved by the covariate models. Addition of covariates reduced the prediction error and the SD for all pharmacokinetic variables and similar prediction errors were noted for both covariate models. Predictions were improved for clearance in >50% of patients for both models A and B.
Validation of final population pharmacokinetic models
Internal crossvalidation. The mean (95% confidence interval) standardized mean prediction error for the final covariate model B was 0.0508 (−0.0553 to 0.157), suggesting that this covariate model provides unbiased estimates for predicting troxacitabine plasma concentrations (95% confidence interval contains 0). The correlation (R^{2}) between observed and final modelpredicted concentrations was 0.8775. Convergence was not achieved during internal cross validation of final covariate model A. Model A incorporated more variables than model B (13 versus 9), and overparameterization may have precluded convergence of model A.
Application of population pharmacokinetic model for the design of a continuous infusion regimen. Eight patients received troxacitabine 2.0 mg/m^{2}/d (n = 3) for 3 days or 3.0 mg/m^{2}/d for 3 days (n = 5). At 2.0 mg/m^{2}/d, observed mean ± SD concentrations at 4, 24, 48, and 72 hours (end of infusion) were 0.06 ± 0.002, 0.10 ± 0.006, 0.10 ± 0.01, and 0.12 ± 0.03 μmol/L, respectively; at 3.0 mg/m^{2}/d, concentrations were 0.08 ± 0.01, 0.13 ± 0.02, 0.15 ± 0.04, and 0.15 ± 0.03 μmol/L, respectively. Assessment of end of infusion concentrations show that the minimum target concentration of 0.1 μmol/L was achieved in all patients with the starting dose of 2.0 to 3.0 mg/m^{2}/d, which was derived from the described population pharmacokinetic model.
Discussion
This report provides the first description of a population pharmacokinetic model for troxacitabine, a novel unnatural lnucleoside analogue, and the influence of clinical covariates on drug disposition. Renal function, assessed by calculated creatinine clearance, had the most significant effect on troxacitabine clearance. BSA, which is currently used to normalize troxacitabine dose, was also found to be an independent covariate on drug clearance. Creatinine clearance and BSA combined accounted for 36% of intersubject variance in troxacitabine clearance. Because elevated troxacitabine plasma exposure has been related to the severity of toxicities in phase I and II trials, including neutropenia, mucositis, and handfoot syndrome, the described model has potential for optimization of troxacitabine therapy.
Troxacitabine is eliminated principally via renal excretion. During model development, it was anticipated that creatinine clearance would be a covariate explaining a significant percentage of interindividual variability in drug clearance. The addition of BSA as an independent, significant covariate on clearance is generally consistent with the correlation of body size with glomerular filtration rate (30) and supports the calculation of troxacitabine dose based on BSA. During covariate screening, age was not selected as a significant covariate on clearance. Because age was included in the formula for calculated creatinine clearance, inclusion of this variable may have accounted for agerelated decline in renal function. Perhaps the inclusion of younger pediatric and older geriatric patients into the population may have resulted in retaining age into the final model. Sex was not included into the model most likely due to the predominance of male subjects (80%).
Both final models, one where drug input was the actual dose (model A) and one where drug input was the dose normalized to BSA (model B), equally accounted for a significant percentage of interindividual variability for troxacitabine clearance. Final estimates for interindividual variability were 18% and 20% for models A and B, respectively. SEs (%RSE) on variable estimates and predictive performance were similar for models A and B.
Recent preclinical data suggest that prolonged troxacitabine exposure at low micromolar concentrations (≥0.1 μmol/L) was superior to bolus infusion administration, and that a 3 to 5day infusion achieved optimal efficacy (18). Troxacitabine penetrates into cells via passive diffusion, which may explain, in part, why troxacitabine showed enhanced cytotoxicity with prolonged versus bolus administration. To optimize the therapeutic potential of troxacitabine, several phase I trials were designed to evaluate prolonged infusion schedules (19, 20). The population pharmacokinetic model was used to derive a starting dosage rate to achieve a target troxacitabine plasma concentration of 0.1 μmol/L in patients with advanced solid malignancies, and the target plasma concentration was achieved in all patients receiving 2.0 to 3.0 mg/m^{2}/d, albeit with accompanying intersubject pharmacokinetic variability. The equations for troxacitabine clearance as described in Tables 2 and 3 (final models), could be used to individualize the dosage rate for continuous infusion administration. For example, an individualized dose could be determined using values for creatinine clearance and BSA and the clearance equation in Table 2 according to the following equation: dose (μg/h) = [(4.8 × creatinine clearance^{0.431}) + (BSA − 1.95) × 2.84] × target C_{ss} (μg/L). If the target C_{ss} is 0.1 μmol/L (21 μg/L), the individualized dosage rate for an individual with a BSA of 1.80 m^{2} and creatinine clearance of 45 mL/min (2.7 L/h) would be 146 μg/h (3.5 mg/d); the individualized dosage rate for an individual with the same BSA but a creatinine clearance of 100 mL/min (6.0 L/h) would be 209 μg/h (5.0 mg/d). If both patients received the same dose normalized to their BSA (e.g., 2.0 mg/m^{2}/d or 3.6 mg/d), the patient with the higher creatinine clearance may have been undertreated. The clinical applicability and safety of the proposed dosing strategy would require prospective evaluation compared with the currently used BSAbased dosing.
In conclusion, a population pharmacokinetic model has been developed that accounted for 36% of unexplained intersubject variance for troxacitabine clearance using measures of renal function (calculated creatinine clearance) and body size (BSA). Further refinement of dosing strategies to decrease pharmacokinetic variability will likely include more accurate assessment of glomerular filtration rate and renal function. In addition, the population pharmacokinetic model was used to determine a dosage rate for continuous infusion administration that achieved predetermined target plasma concentrations. The present analysis shows that population pharmacokinetic modeling can be incorporated in the drug development process to identify sources of pharmacokinetic variability, aid in the design of alternative dosing regimens, and optimize therapy.
Footnotes

Grant support: Shire Pharmaceuticals.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Conflict of interest statement: S.D. Baker and M. Hidalgo received research funding from Shire Pharmaceuticals.
 Accepted January 17, 2006.
 Received October 17, 2005.
 Revision received December 15, 2005.