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© 2000 American Society for Clinical Oncology Population Pharmacokinetic Model for Topotecan Derived From Phase I Clinical TrialsFrom the Department of Pharmacology, Fox Chase Cancer Center, Philadelphia, PA; Cancer Therapy and Research Center, Institute for Drug Development, San Antonio, TX; and National Cancer Institute, Cancer Therapy Evaluation Program, Bethesda, MD. Address reprint requests to James M. Gallo, PhD, Department of Pharmacology, Fox Chase Cancer Center, 7701 Burholme Ave, Philadelphia, PA 19111; email jm_gallo{at}fccc.edu
PURPOSE: To characterize the pharmacokinetics of topotecan in a population model that would identify patient variables or covariates that appreciably impacted on its disposition. PATIENTS AND METHODS: All data were collected from 82 patients entered in four different phase I trials that were previously reported as separate studies from 1992 to 1996. All patients received topotecan as a 30-minute constant-rate infusion on a daily-times-five schedule and were selected for this study because their daily dose did not exceed 2.0 mg/m2. Among the 82 patients were 30 patients classified as having renal insufficiency and 13 patients with hepatic dysfunction. The population pharmacokinetic model was built in sequential manner, starting with a covariate-free model and progressing to a covariate model with the aid of generalized additive modeling. RESULTS: A linear two-compartment model characterized total topotecan plasma concentrations (n = 899). Four primary pharmacokinetic parameters (total clearance, volume of the central compartment, distributional clearance, and volume of the peripheral compartment) were related to various combinations of covariates. The relationship for total clearance (TVCL [L/h] = 32.0 + [0.356(WT - 71) + 0.308(HT - 168.5) - 8.42(SCR - 1.1)] x [1 + 0.671 sex]) was dependent on the patients’ weight (WT), height (HT), serum creatinine (SCR), and sex and had a moderate ability to predict (r2 = 0.64) each patient’s individual clearance value. The addition of covariates to the population model improved the prediction errors, particularly for clearance. Removal of 10 outlying patients from the analysis improved the ability of the model to predict individual clearance values (r2 = 0.77). CONCLUSION: A population pharmacokinetic model for total topotecan has been developed that incorporates measures of body size and renal function to predict total clearance. The model can be used prospectively to obtain a revised and validated model that can then be used to design individualized dosing regimens.
THE TOPOISOMERASE I inhibitor, topotecan (Hycamtin; SmithKline Beecham, King of Prussia, PA), was introduced as an anticancer agent in 1989 and approved for the treatment of ovarian cancer in 1996. It has recently received regulatory approval for treatment of patients with recurrent and refractory epithelial ovarian carcinoma and small-cell lung carcinoma. It, along with other campthothecin analogs, is used in a variety of other solid tumors, as well as hematologic malignancies.1 Numerous clinical studies have been conducted to characterize the pharmacokinetic and pharmacodynamic properties of topotecan.2-8 For the most part, the pharmacodynamic investigations of topotecan have focused on its dose-limiting toxicity of myelosuppresion, particularly neutropenia. Topotecan is chemically a lactone species that, through a reversible pH-dependent equilibrium, coexists with an inactive open-ring or hydroxyacid form.9 This chemical attribute has precluded the use of a single assay for measurement of topotecan in patient plasma samples and has allowed investigators the option to base their analyses on plasma concentrations of the lactone form or total topotecan, the sum of both the lactone and hydroxyacid forms. Regardless of the measured species, the relative pharmacokinetic behavior is analogous and can be described as a linear two-compartment model.9 Pharmacodynamic analyses of topotecan in the clinic have essentially relied on establishing relationships between a pharmacokinetic end point, such as a steady-state plasma concentration or area under the drug plasma concentration–time curve (AUC), and an index of myelosuppresion, such as the percentage decrease in absolute neutrophil count (ANC) at the nadir.3,5-7,10 It has been observed that such pharmacodynamic correlations have been equal or slightly improved when the pharmacokinetic end point is based on total topotecan concentrations.1 Given the large quantity of pharmacokinetic information that has been compiled for topotecan, it is of interest that a population pharmacokinetic analysis has yet to be completed. A population model is a means for incorporating patient variables or covariates that impact on drug disposition into a single comprehensive pharmacokinetic model. Ultimately, these models may lead to drug-dosing algorithms that can individualize a patient’s dose, thereby maximizing the therapeutic index. In cancer chemotherapy, a growing number of population pharmacokinetic models have been developed with this potential in recent years.11-13 Topotecan does undergo significant renal excretion (approximately 50%), and thus a patient’s renal function is expected to affect clearance of topotecan. A population model for topotecan would yield a formula relating renal status to topotecan clearance that, given a patient’s measure of renal function, can be used to individualize topotecan dosing. The effects of renal function and other patient variables on topotecan’s disposition have not yet been evaluated by a population modeling approach. The goal of the current investigation was to apply a population pharmacokinetic approach to topotecan plasma concentration data that had been previously acquired in different phase I trials.5-7,14,15
Patient Population and Data Collection Eighty-two patients were selected from 117 patients that participated in four phase I studies of topotecan.5-7,14,15 The 82 patients were chosen for population analysis because their daily doses did not exceed 2.0 mg/m2/d of topotecan and thus would be most representative of current dosing practices. The mean topotecan dose was 1.12 ± 0.48 mg/m2/d (dose range, 0.45 to -2.0 mg/m2/d). Table 1 lists the patient covariates that were evaluated and their values. Thirteen covariates were considered in the analysis, including both continuous (age, serum albumin [ALB], ALT, AST, body surface area [BSA], creatinine clearance [CRCL], height [HT], serum creatinine [SCR], total bilirubin [TBIL], weight [WT] and categorical (performance status [PS], prior therapy [PT], sex) variables. Of the 82 subjects, 13 were classified as having hepatic dysfunction (serum total bilirubin > 1.2 mg/dL; range, 0.2 to 6.9 mg/dL), and 30 patients possessed various degrees of renal dysfunction based on creatinine clearances of less than 60 mL/min (range, 16.3 to 220 mL/min) estimated by the method of Cockcroft and Gault.16 The greatest number of patients (55) were obtained from two phase I studies5,6 that included the hepatic and renal dysfunction patients. Fifteen patients were entered from a phase I trial14 evaluating sequences of topotecan and cisplatin; however, for the purposes of this investigation, all topotecan plasma concentrations were obtained before cisplatin administration. Of the remaining patients (12 of 82), six participated in the first phase I trial7 of topotecan, and six were entered from a study using granulocyte colony-stimulating factor.15
Each patient received topotecan as a 30-minute constant-rate infusion daily for 5 days every 3 weeks. As is consistent with most phase I studies, blood sampling for measurement of topotecan plasma concentration was intensive, with samples collected on the first day of drug administration from the start of the infusion until approximately 8 hours postinfusion. Nineteen patients also had blood samples collected between 8 and 24 hours postinfusion. The mean number of samples per patient was 11, with a total of 899 observed topotecan concentrations in the population. Total topotecan plasma concentrations were quantitated by a high-performance liquid chromatography method previously reported17 and modified as described in each study.5-7,14,15
Pharmacokinetic Model
Step 1: development of the covariate-free model.
The goal of this step was to define the best structural pharmacokinetic model for topotecan that would consist of the compartmental and statistical models. The best-fit pharmacokinetic model would delineate the number of compartments and whether drug disposition was linear or nonlinear and provide estimates for the parameters associated with each model. The statistical model characterizes the unknown intersubject and intrasubject variability and defines the number and form of the Step 2: GAM. GAM analysis was completed to determine which covariates (Table 1) are significantly related to each pharmacokinetic parameter and whether this relationship is linear or nonlinear. The individual Bayes parameter estimates generated in step 1 from the best structural model are entered into the GAM analysis along with the covariates from all of the patients. At each step in the GAM analysis, individual covariates are added, deleted, or replaced in the regression model using Akaike’s information criterion23 until a final model is obtained. The final model indicated a set of candidate covariates for each pharmacokinetic parameter that were further evaluated in step 3. Case deletion diagnostics can be performed in conjunction with any GAM analysis to identify individual patients who have a large influence on the particular GAM model.20,24 Studentized residuals and Cooks distances are diagnostic tests performed within Xpose that indicate which patients may have a significant influence on the GAM and covariate structure. These diagnostic evaluations were performed before development of the final covariate model and with the final model (after step 3). In the latter scenario, the analysis indicated the extent to which each patient influenced the final covariate model and facilitated a subsequent analysis to determine if any covariate may have entered the final model inappropriately. Step 3: development of the covariate model. Each candidate covariate identified in step 2 was entered into the population pharmacokinetic model derived in step 1. All continuous covariates were centered on their median values. In some cases, covariates not identified in step 2, yet barring a logical relationship to a pharmacokinetic parameter, were also evaluated in the population model. For example, both BSA and WT were evaluated as covariates for clearance even though they were not identified as candidate covariates by GAM analysis in step 2. The forward-addition and backward-deletion strategies were used to evaluate each set of covariates within the population pharmacokinetic model. Covariates were selected for the final population pharmacokinetic model if they produced a minimum reduction of four in the LLF and a reduction in the variability, assessed by the percentage coefficient of variation, of the associated pharmacokinetic parameter.18,19 As mentioned in step 2, case deletion diagnostics were performed to ensure that individual patients did not cause a covariate to enter into the final model.
Statistical Assessment of the Population Pharmacokinetic Model
Similarly, the percentage naive prediction error (PE-Nj) was calculated by replacing TVPKj with the mean of the individual Bayes estimates for the pharmacokinetic parameter in the covariate-free model in the above equation. Thus, comparison of PEj to PE-Nj and their distribution indicated the influence of the covariate(s) on the model predictions. Typical value parameters reflect the influence of the associated covariates on the model predictions, whereas the true value is the individual Bayes parameter estimate. Typical value parameters are those determined from the population mean parameters and could be used in the prospective design of drug dosing regimens. The so-called true parameters are based on both the population parameters and the individual’s measured drug concentration–time data. Model performance was also assessed by an analysis of residuals, the difference between observed and model-predicted topotecan concentrations.25
Pharmacodynamic Model–Based Dosing
The patient population characteristics (Table 1) were consistent with those commonly seen in phase I trials of cytotoxic agents in patients with advanced malignancies. Development of the structural pharmacokinetic model indicated that a linear, open two-compartment model best fit the observed total topotecan concentration–time data. In this best-fit structural model, interpatient variability was modeled using an exponential function to relate the TVPKj to the PKj as follows: 
 jPK is a measure of the jth patient difference in TVPKj and PKj. Parameters (PKj) in this model were total systemic clearance (CL), volume of the central compartment (V1), volume of the peripheral compartment (V2), and distribution clearance between compartments 1 and 2 (Q). jPK was modeled as a random variable with a mean of zero. Each PKj is an empirical Bayes estimate of the jth individual true parameter based on the population parameters and the jth individual’s observed concentrations. This estimation step is implemented in NONMEM as the POSTHOC option.
Residual or intrapatient variability ( In step 2 of model development, GAM analysis identified a set of candidate covariates (Table 2) that were further evaluated in the covariate population model or step 3. Additional covariates were also included in the final stage of analyses. In the GAM regression procedure, different sets of entered covariates can produce different sets of candidate covariates. This was highlighted in the identification of covariates influencing CL. Entering both CRCL and SCR in the GAM analysis on CL caused CRCL to replace HT and SCR in the list of candidate covariates (Table 2). All candidate covariates listed in Table 2 were entered into the best GAM models linearly with one exception. The relationship between CL and SCR in the GAM model was nonlinear and exponential in nature; however, in the final population model, only an inverse linear relationship could be supported.
Table 2 also lists the final set of covariates obtained via step 3 using forward-addition and backward-deletion strategies. There was not uniform agreement in the covariate sets identified in GAM and the final sets used in the population model. The greatest discrepancy was in the covariates affecting V1. GAM analysis revealed three candidate covariates, yet these were found not to significantly minimize the LLF. The final population pharmacokinetic model for topotecan was as follows: TVCL (L/h) = 32.0 + [0.356(WT - 71) + 0.308(HT - 168.5) - 8.42(SCR - 1.1)] x (1 + 0.671 sex) TVV1(L) = 36.5 + 1.22(HT - 168.5) TVQ (L/h) = 263 + 185(BSA - 1.85) TVV2 (L) = 83.6 + 37.3 sex + 28.0(ALB - 3.9) For each pharmacokinetic parameter, the constant immediately to the right of the equal sign is the population mean value. Sex is defined to have a value of 1 for male patients and 0 for female patients. Each patient will have a set of typical values (ie, TVCL, TVV1, TVQ, TVV2) distributed around the mean values depending on that patient’s covariates. A number of alternate parameter-covariate relationships, particularly for CL, were tried; however, the equations above best described the data based on producing the lowest LLF. The prediction errors associated with both the covariate (PE) and covariate-free (PE-N) population models are listed in Table 3. Also listed in Table 3 are the percentages of patients whose predictions were improved or worsened by the covariate model compared with the covariate-free model or naive predictor. Addition of covariates to the model reduced the SD of the prediction errors or increased the precision of the predicted pharmacokinetic parameters. The bias as indicated by the mean prediction errors is analogous for both the covariate and covariate-free model. Of the four primary pharmacokinetic parameters, CL was most influenced by the covariates. This is illustrated in Fig 1, in which the distribution of prediction errors is compared for the final (covariate) model and the covariate-free (naive-predictor) model. Addition of the covariates reduced both the magnitude (unsigned mean PE = 23.2% v PE-N = 39.0%) and variability of the prediction error. The influence of the covariates on prediction errors of V1, V2, and Q was not as great as on CL yet, particularly for V2, reduced interpatient variability (Table 3). For all pharmacokinetic parameters, addition of the covariates improved the model predictions in more than 50% of the patients (range, 56% to 70%; Table 3).
Model performance can also be evaluated by a comparison of observed and predicted total topotecan plasma concentrations (Fig 2). The residuals, or the difference between the observed and final model-predicted concentrations, had a mean (± SD) value of 0.027 ± 5.8 ng/mL, with 90% of the residuals ranging from -5.8 ng/mL to 5.4 ng/mL. Elimination of 20 concentrations (2.2% of 899 concentrations), based on a criteria of an outlier as equal to the mean residual plus three times the SD or 17.4 ng/mL, resulted in a greater correspondence between observed and predicted total topotecan concentrations (r2 = 0.70). Because CL, and specifically TVCL, is the most valuable parameter in designing dosing regimens, Fig 3 indicates the correlation between the TVCL and the true clearance (CL) for the covariate model. Elimination of 10 patients with the greatest divergence (absolute value of PE > 50%) between TVCL and CL, consistent with the case-deletion diagnostics, appreciably improved the correlation between TVCL and CL (r2 = 0.78; Fig 3). These 10 patients yielded the highest Studentized residuals, indicating that they had the largest influence on the GAM models. This suggests that one or more of these patients may have skewed the final covariate model. However, this was not the case, as deletion of these patients from the NONMEM analysis did not alter the final covariate structure. There were no distinguishing characteristics of these patients in terms of their covariate profile, and thus the cause for their high PE remains unknown.
The potential impact of a population model for topotecan was illustrated with two examples, one using a pharmacokinetic end point and the other a pharmacodynamic end point. In the first case, individualized doses were generated from each patient’s TVCL value under the assumption that a target AUC of 47.0 µg · h/L · m2 was desired. This would be the predicted AUC for a typical patient (ie, a male or female patient possessing median HT, WT, and SCR values) receiving a naive dose of 1.5 mg/m2/d, a standard topotecan dose. Figure 4A shows a histogram of model-predicted doses needed to reach this hypothetical target AUC. The doses ranged approximately six-fold from 0.5 to 3 mg/m2/d.
In the second example, pharmacodynamic-based dosing was evaluated under the assumption that a target ANCn of 50%, 75%, or 90% was desired (see Methods). Figure 4B illustrates the dose adjustment factors for each desired target nadir. Regardless of the desired target nadir, a relatively broad range of doses is suggested, in addition to the fact that patients may require both decreases and increases from the typical 1.5 mg/m2/d dosing. Moreover, the inference is that without inclusion of covariates in the model, there is minimal capability of standard topotecan dosing to achieve desired target pharmacokinetic and pharmacodynamic end points.
Population approaches to pharmacokinetic modeling have become increasingly used and promoted in the area of clinical pharmacology of anticancer drugs.11-13,27 Their appeal is multifactorial and includes the ability to analyze sparse and dense data sets, quantitatively assess the influence of patient covariates on drug disposition, and ultimately provide dosing regimen algorithms for optimal individualized dosing. Clearly this latter attribute creates added incentives for the population approaches for the highly toxic anticancer drugs. These formidable advantages to the population modeling technique have been met with moderate success, given that there are only a handful of reports of anticancer agents that highlight the full potential of the methodology.11-13,27 The imbalance between expectations and fulfillment may equilibrate as the methodologies are improved and large databases of pharmacokinetic data are sought prospectively. Given the narrow therapeutic index of topotecan, a population model could be beneficial to its use through the design of individualized dosing regimens. From previous studies (see review in Herben et al1) it is known to undergo appreciable renal elimination (approximately 50%) and low plasma-protein binding (approximately 50%). There have been no previous reports that have integrated how demographic variables or other covariates could influence the disposition of topotecan. The general features of the population model agree with previously reported attributes, being a linear two-compartment model. Further, the population mean values for clearance (ie, 32 L/h) and the volume of distribution at steady-state (ie, V1 + V2; 120.1 L) agree with those previously reported (see review in Herben et al1). The analysis of topotecan’s pharmacokinetic parameter–covariate relationship initiated with GAM reduced the total number of covariates from 13 to no more than four (Table 2) for any parameter. Other than the single nonlinear relationship it suggested between CL and SCR, GAM found all other covariates to be linearly related to the corresponding pharmacokinetic parameter. At this stage, the GAM step fulfilled its expectations by greatly reducing the number of covariates to be further evaluated in NONMEM. Although there was not an exact correspondence between covariates identified by GAM and those entered into the final population model, the speed and ease of conducting GAM make it a valuable model development tool. Covariates for Q and V2 nearly agreed between GAM and the final model, although the basis for these specific sets of covariates is not readily forthcoming. It can be inferred that body size parameters (ie, BSA, HT, and WT) and definitely protein binding are related to the volume of distribution, and both V1 and V2 were found to be influenced by such variables. However, because of the relatively low plasma-protein binding of topotecan, it was unexpected to find ALB as a covariate on V2. Because the analysis was based on total topotecan concentration, differential protein binding of the lactone or hydroxyacid could provide a partial explanation for the potential influence of ALB on V2; however, such a phenomenon does not exist for topotecan, as has been reported for camptothecin.28 Of the three covariates (BSA, SCR, and TBIL) suggested by GAM for V1, none entered the final population model because neither produced a significant reduction in the LLF. A clear rationale for a relationship between V1 and SCR and TBIL is also absent. In addition to BSA, other body size variables (HT and WT) were examined as covariates for V1. The final population model did identify HT as the only size covariate that caused a significant reduction in the LLF, yet the improvement in the PE for V1 is modest, and V1 still exhibits the greatest interpatient variability of all the pharmacokinetic parameters. The covariate structure for clearance has the greatest importance because of its possible role in dosage regimen design and prompted the evaluation of other covariates that were not identified in GAM. Both the GAM and final population model agreed that HT, SCR, and sex were important covariates, yet ALB was eliminated from the NONMEM model on the basis of the LLF criteria. The importance of renal function to topotecan clearance is accepted,6 and methods to assess glomerular filtration rate, traditionally considered the best overall index of renal function, have spawned recent investigations.29 Through studies characterizing carboplatin pharmacokinetics,11 it has been shown that renal function is more accurately determined by chromium-51 EDTA or technetium-99m DTPA clearances as opposed to the Cockcroft-Gault formula or variants that calculate CRCL. At the time when the current phase I trials were performed, the radioisotopic-based clearance methods were unavailable; therefore, an analysis of estimated CRCL as a covariate on topotecan clearance was fostered. It was found that the combination of HT, SCR, sex, and WT yielded the greatest reduction in the LLF and improved the PE compared with covariate structures that included CRCL. Although three of the covariates (WT, SCR, and sex) are component variables for estimated CRCL formulas, their independence is an advantage that allows direct measurement of the variables and eliminates a singular measure of renal function. Age, another determinant of renal function, was of borderline significance as a covariate on clearance, producing a reduction in the LLF of three. Thus the effect of age on topotecan clearance was measurable but not highly contributory. The fact that HT entered the final model stimulated an interest to examine if BSA could replace HT and WT because BSA can be calculated from these parameters.30 However, BSA did not produce the extent of reduction in the LLF as did the combination of HT and WT. It should be appreciated that the covariates that do influence topotecan clearance do not only account for changes in renal function but rather physiologic variables that reflect alterations in any mechanism of topotecan clearance. Because assessment of hepatic function is complex and prohibits a single measure of predictive value, it may not be overly surprising that TBIL, ALT, and AST, covariates associated with hepatic function, did not enter the population model. Moreover, hepatic metabolism is not the dominant pathway of topotecan elimination. On the basis of various objective indices of model performance, the current population model for topotecan has appreciably reduced interpatient variability. It can be further seen that the patient covariates identified in this model have a large impact on dosage regimen design (Fig 4) in which wide ranges of daily doses were required to achieve a target AUC (six-fold dose range) or target reduction in the percentage decrease in ANCn (approximately eight-fold dose ranges). It is acknowledged that this latter illustration of pharmacodynamic-based dosing would be enhanced by choosing time-dependent end points, such as the time below a set ANC value, that require the development of time-dependent pharmacodynamic models.31,32 Nonetheless, regardless of the particular pharmacodynamic end point that might be used for individualized dosing, the analysis demonstrates the impact of patient variables on the design of topotecan dosing regimens. Achievement of all of the goals of population pharmacokinetic modeling, such as dosage regimen design, requires model validation. Just as the steps or criteria of covariate acceptance into a model are nonstandard, so too are the means to stamp a model as valid. Issues of concern are the number of patients on which the models should be based, how well the model should predict the desired end point, and whether model simulations serve as a valuable tool for validation. There is some consensus that model validation should consider both index and validation data sets, yet the nature of the validation may differ depending on how the population model may be applied to drug therapy.33 A population pharmacokinetic model could be used to identify patients who are at increased risk of over- or underdosing, design a priori drug dosing regimens, and estimate individual pharmacokinetic parameters, including drug concentration–time curves. A general approach to model validation would use the index data set (ie, patient population 1) as the initial means to build the population model that is then used to generate Bayes parameter estimates for a new validation data set (ie, patient population 2) that can also provide independent estimates of model parameters. Agreement of model predictions derived from patient populations 1 and 2 validates the model, whereas disagreement would most likely cause the original model to be revised with a new index data set formed by combining patient populations 1 and 2. In reference to the current population model for topotecan, the 82 patients served as an index data set that has highlighted a number of characteristics relevant to the disposition of topotecan. Clearly, patients with compromised renal function require a different dose than patients with normal renal function. A patient’s size and sex are also factors that bear consideration in designing dosing regimens. The current model will require validation and potential revisions depending on its predictive performance with new data sets. There seem to be some limitations in the current predictive performance given the moderate correlation between TVCL and CL (r2 = 0.64; Fig 3A). The roots of these limitations are unknown but may partially reside in the retrospective nature of the analysis and the inclusion of outlying patients (r2 = 0.77 with their removal; Fig 3B). As the current model undergoes prospective validation, it will be important to compare and contrast characteristics of this patient population with new ones and their impact on the pharmacokinetic model. The current model was derived from a heterogeneous group of phase I trial patients, whereas a validation population of patients is apt to consist of ovarian cancer and small-cell lung cancer patients. In designing prospective investigations, limited blood sampling strategies and the resultant topotecan plasma concentrations can be used in conjunction with the current population model to revise and validate the model. In this scenario, a priori predictions of the pharmacokinetic parameters (TVCL, and so on) are made and then compared with Bayes-predicted parameters on the basis of each patient’s limited topotecan concentration–time data. Agreement between these two sets of pharmacokinetic parameters validates the model, whereas disagreement initiates the iterative process of redefining the index population and pharmacokinetic model followed by another validation protocol. In conclusion, the current population model for topotecan has identified a set of patient variables and pharmacokinetic relationships that will foster further analyses leading to a validated model.
Supported in part by grant no. CA76254 from the National Institutes of Health, Bethesda, MD.
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ABSTRACT
INTRODUCTION
ij, a measure of the residual or intrasubject variability. In development of the best covariate-free model, alternate statistical models, such as additive, constant coefficient of variation, and exponential, were evaluated. Identification of the best structural model was based on the NONMEM objective function (-2 times the log likelihood function [LLF]), SEs of the estimated parameters, diagnostic plots, and agreement between the mean of the individual Bayesian (ie, POSTHOC step in NONMEM) parameter estimates and the population mean estimates. 
