Till Pontus & Alicia
List of Papers
This thesis is based on the following papers, which are referred to in the text by their Roman numerals.
I Hansson E.K., Wallin E.J., Lindman H., Sandström M., Karlsson M.O., Friberg L.E. Limited inter-occasion variability in relation to inter-individual variability in chemotherapy-induced myelosuppression. Cancer Chemother Pharmacol.(2010) 65:839–848
II Hansson E.K., and Friberg L.E. The shape of the myelosuppression time profile is related to the probability of developing neutropenic fever in patients with docetaxel-induced grade IV neutropenia. Cancer Chemother Phamcol.(2011) Nov 5, [Epub ahead of print],
III Hansson E.K., Amantea M., Westwood P., Milligan P.A., Houk B.E., French J., Karlsson M.O., Friberg L.E. Pharmacokinetic- pharmacodynamic modeling of VEGF, sVEGFR-2, -3 and sKIT as predictors of tumor dynamics and overall survival following sunitinib treatment in GIST. In manuscript
IV Hansson E.K., Ma G., Amantea M., French J., Milligan P.A., Friberg L.E., Karlsson M.O. PKPD modeling of predictors for side effects and overall survival in sunitinib treated patients with gastro intestinal stromal tumor. In manuscript
Reprints were made with permission from Springer Science and Business Media.
Contents
Introduction ... 11
Pharmacometrics ... 11
Mixed Effects Modeling ... 12
Myelosuppression in Anticancer Treatment ... 13
Febrile Neutropenia ... 13
Models for Myelosuppression ... 14
Dose Individualization based on Myelosuppression ... 16
Sunitinib ... 16
Biomarkers ... 17
Biomarkers in Anti-angiogenic Treatment ... 18
PKPD Modeling of Biomarkers in Oncology ... 19
Aims ... 20
Patients and Methods ... 21
Description of Data ... 21
Hematological Toxicity Data ... 21
GIST Data ... 23
Model Building ... 25
Analysis of Hematological Toxicity Data ... 25
Integrated Modeling Framework ... 26
Data Analysis ... 29
Results ... 31
Variability in Myelosuppression Model Parameters ... 31
Relationship between Neutropenia and FN ... 33
Integrated Modeling Framework ... 35
Discussion ... 43
Hematological Toxicity ... 43
Integrated Modeling Framework ... 45
Conclusions ... 47
Acknowledgements ... 49
References ... 51
Abbreviations
ANC Absolute neutrophil count ANC0 Baseline neutrophil count AUC Area under the curve
BM Biomarker
BSA Body surface area
CL Clearance
CTCAE Common terminology criteria for adverse events CV Coefficient of variation
CWRES Conditional weighted residuals dBP Diastolic blood pressure
EC50 Drug concentration producing 50% of Emax
Emax Maximum effect
ET The epirubicin-docetaxel regimen
FEC The 5-fluorouracil-epirubicin- cyclophosphamide regimen FN Febrile neutropenia
FOCEI First order conditional estimation with interaction G-CSF Granulocyte colony stimulating factor
GIST Gastrointestinal stromal tumor HFS Hand-foot syndrome
Hill Sigmoidicity factor characterizing the steepness of the concentration- effect relationship
i.v. Intravenous
IIV Inter-individual variability IOV Inter-occasion variability Kin Formation rate constant Kout Degradation rate constant MBDD Model based drug development MRT Mean residence time
MTT Mean transit time
n Number
NA Not available
OFV Objective function value OS Overall survival
PD Pharmacodynamics PK Pharmacokinetics
qd Once daily
RECIST Response evaluation criteria in solid tumors RSE Relative standard error
SCM Stepwise covariate model building SE Standard error
SE Standard error sKIT Soluble KIT
SLD Sum of longest diameters SLOPE Drug efficacy parameter
sVEGFR-2 Soluble vascular endothelial growth factor receptor-2 sVEGFR-3 Soluble vascular endothelial growth factor receptor-3 TKI Tyrosine kinase inhibitor
VEGF Vascular endothelial growth factor
VEGFR Vascular endothelial growth factor receptor VPC Visual predictive check
γ Feedback factor in myelosuppression model
ε Difference between individual prediction and observation, residual error
η Difference between population and individual parameter estimate κ Difference in individual parameter estimate between occasions θ Typical population value
Introduction
Drug development in oncology is a great challenge because of the large heterogeneity and complexity of the disease. The research area has been struggling with a large proportion of drugs failing in late phases of development due to unacceptable toxicity or lack of efficacy. Only 5% of drugs proceed from first in human to marketing approval [1] and a change in the drug development process is needed.
One initiative is the application of model based drug development (MBDD), recognized by the FDA as a methodology to increase the productivity [2]. The approach involves the development of mathematical and statistical models to quantify the pharmacokinetic (PK) and pharmacodynamic (PD) properties of a drug.
Until now, the main focus in oncology MBDD has been building models for prediction and prevention of side effects [3] e.g. hematological toxicity [4]. New approaches to characterize and quantify the effect of treatment would also be of value. If valid biomarkers are identified prediction of safety and overall survival, based on data in early phases of development is enabled [5]. Applied in a model-based framework, biomarkers may increase trial efficiency, allowing more accurate dose selection and treatment individualization [6].
Besides their application in drug development, model-based techniques could be used to optimize treatment of already approved anticancer drugs.
For many drugs in oncology, large variability between individuals with regard to toxicity and treatment outcome are observed. Traditionally most attempts to account for the differences between individuals have been to adjust the individual dose level based on body surface area (BSA), this despite being shown to be of limited value in reducing the variability in PK [7]. Alternatively, if the individual dose was determined by taking into account differences in PK and PD, efficacy and safety may be optimized.
Pharmacometrics
Pharmacometrics has been defined as “the science of developing and applying mathematical and statistical methods to characterize, understand, and predict a drug’s PK, PD, and biomarker-outcome behavior” [8]. Pharmacometrics is applied with the goal of a more efficient drug development and drug usage and includes a large variety of applications. The developed models may e.g. be used for prediction of untested conditions, evaluation of dosing strategies, designing studies and performing simulations of (pre-) clinical trials.
Pharmacometrics may also be utilized to find strategies for treatment individualization, both in drug development and for existing therapies.
Mixed Effects Modeling
Non-linear mixed effects modeling (population modeling) is often applied in pharmacometrics. The approach involves simultaneous characterization of the typical individual (the mean) as well as the variability components of the data in the studied population [9]. Separation of different types of variability is possible, which usually is quantified in terms of the difference between individuals (inter-individual variability) and the difference between observations and individual predictions (residual variability). Additionally, the variability within an individual between occasions may be characterized [10].
The general structure of the mixed effects model is expressed in Eq. 1 where observation j in individual i is described by a linear or nonlinear function f(…) with independent variables xij (time, dose) and parameter vector Θi.
ij
ij i ij ij 2
y = f ( x ,Θ ) ε+ ε ~ N(0,σ ) (1) εij is the random effect variable describing residual variability, the difference between the individual prediction and the measurement. Quantification of the residual variability is often referred to as the error model, which commonly is described as additive, proportional (to the individual prediction), or a combination of the two [11]. The parameter value in individual i (Pi) is often assumed to be log-normally distributed around the typical parameter value (θ) (Eq. 2).
ηi 2
i i
P θ e= ⋅ η ~ N(0,ω ) (2)
The difference between the individual and typical parameter estimate is described by the random effect ηi. Some of the variability between individuals can often be explained by individual characteristics, covariates (e.g. kidney function, weight)
Myelosuppression in Anticancer Treatment
Classical cytotoxic anticancer agents act by non-specifically killing rapidly dividing cells. Both malignant and healthy somatic cells, e.g. in the bone marrow, are affected. Treatment with cytotoxic agents thereby results in a temporarily suppressed hematopoietic system with decreased production and lower levels of circulating blood cells.
Neutropenia, defined as low neutrophil counts in blood, is the most common and often dose limiting side effect in cytotoxic treatment [12]. In oncology, the severity of side effects are classified according to the common terminology criteria for adverse events (CTCAE), constituting five different grades [13]. Grade 5 represents death related to the adverse event and grade 4 an event with potentially life-threatening consequences. For neutropenia, grade 4 corresponds to an absolute neutrophil count (ANC) < 0.5∙109 cells/L.
To allow recovery of the hematopoietic system in patients that develop grade 4 neutropenia during chemotherapy, the next dose is often reduced and/or delayed. The reduction in dose intensity [dose delivered per time (mg/m2 per week)] may however compromise the long-term clinical outcome [12]. Several studies in e.g. breast cancer have reported a correlation between the maintenance of high dose intensity and improved treatment outcome in terms of overall survival [14-15].
Treatment with the more specifically acting anticancer agents, such as the vascular endothelial growth factor (VEGF) inhibitor and VEGF receptor (VEGFR) tyrosine kinase inhibitors (TKIs), also results in a suppressed bone marrow, but to a lesser extent [16]. Neutropenia has especially been reported in treatment with the TKIs sorafenib and sunitinib which act on multiple targets, including the stem cell factor c-kit, and inhibits processes involved both in angiogenesis and tumor proliferation. Whether neutropenia is caused by the inhibition of VEGF or some other factor is not known [16].
Febrile Neutropenia
Neutrophils serve as the first line of defense against infections in the body.
Consequently neutropenia increases the patient's susceptibility to the development of infections, with the extent and duration of neutropenia determining the risk [17]. Fever during neutropenia, i.e. febrile neutropenia (FN), is often the first and only sign of infection and may indicate a life- threatening condition, requiring hospitalization and treatment with i.v.
antibiotics [12]. In this work, FN was defined according to the classification used by e.g. the Infectious Disease Society America (IDSA) and the European Organization for Research and Treatment of Cancer (EORTC), as grade 4 neutropenia concurrent with fever (body temperature > 38.5 °C) [18-19].
The risk of developing FN can be reduced by prophylactic treatment with granulocyte stimulating factors (G-CSF) and antibiotics [20-21]. Their use in
routine clinical practice has however been questioned due to the emergence of antibiotic resistance, the high cost of G-CSF treatment and its associated risk of acute myeloid leukemia [22]. Guidelines for the use of prophylactic treatment have been developed to help identifying patients at high risk of FN [18-19, 23]. These risk factors include cancer type, chemotherapy regimen and patient specific risk factors such as age (> 65 years), female gender, advanced disease, previous episodes of FN, poor performance status, hemoglobin level (< 12 g/dL) and liver, renal or cardiovascular disease.
Also, numerous risk models for FN have been proposed [24-25].
Even though an increased knowledge about the risk factors for FN has emerged over the past years, FN remains a common side effect. For docetaxel treated patients (100 mg/m2) up to 85% develop grade 4 neutropenia (which may be necessary for a good treatment effect) and 12%
experience FN [26]. A better understanding of why some individuals develop FN is of importance to improve dosing strategies and to avoid unnecessary treatment interruptions/dose reductions, thereby increasing the probability of a successful treatment.
One aspect that has not yet been fully elucidated is the relationship between the myelosuppression response and FN. The duration and extent of myelosuppression are already known to be important predictors of FN [17]
but the shape of the neutrophil time-course may also be informative for the risk of FN [27]. Using PKPD modeling, the full time-course of myelosuppression can be described and thereby provide insight into what role the shape of the profile plays. Patient specific risk factors can also be identified. As grade 4 neutropenia is a criterion in the diagnosis of FN, an investigation of risk factors for FN would need to focus on a population of patients suffering from grade 4 neutropenia.
Models for Myelosuppression
Numerous models, ranging from empirical to more mechanism based, have been proposed for the prediction of hematological toxicity in anticancer treatment [28-29]. Myelosuppression has in the past often been described in terms of summary variables such as nadir, grade 4 neutropenia, relative change in cell count and time to nadir. However, with the use of summary variables for neutropenia, important information is often lost as the risk of infections depends on both the extent and duration of neutropenia. A more accurate description of myelosuppression is utilizing information from the whole neutrophil time-profile of hematological toxicity [17, 28-29].
Both empirical [30] and semi-mechanistic models have been developed to describe the full time course of myelosuppression [31-34]. Generally, mechanism-based models are preferred since they allow extrapolation outside the studied conditions [4, 35]. In a mechanism based model the underlying hematological system is considered when characterizing the onset, duration
and severity of myelosuppression. These models can also serve as a modeling platform, to which other components may be added to improve the knowledge of the system e.g. incorporation of G-CSF treatment effects on myelosuppression [36].
Semi-mechanistic myelosuppression model
The currently most widely used semi-mechanistic model for the prediction of chemotherapy induced hematological toxicity was proposed by Friberg et al. in 2002 [34]. The model has been applied in various settings; to describe and predict myelosuppression following combination treatment [36-37]; to identify patients at a higher risk of neutropenia [38-41]; to optimize doses [42]; and to support drug development [43-45]. The model has also been proven useful for interspecies scaling of drug-induced myelosuppression from rat to human [46].
The model is composed of one compartment representing drug sensitive proliferating progenitor cells in the bone marrow, three transit compartments mimicking the non-mitotic maturation of cells, and one compartment of circulating cells in the blood (Figure 1). A feedback mechanism is also incorporated in the model representing the effect of endogenous growth factors such as G-CSF which increase the proliferation rate when neutrophil levels in the blood are low. In the model the drug is assumed to act by reducing the proliferation rate/induce cell kill.
The model consists of system- and drug-related parameters and is semi- mechanistic in the sense that it describes the main physiological processes determining the number of neutrophils in the circulation. The estimated parameters associated with the hematopoietic system are the baseline neutrophil count (ANC0), the mean transit time through the maturation chain (MTT) and the feedback factor gamma (γ). MTT is defined as n + 1/ktr, in which rate constants (ktr) between the n transit compartments are assumed equal. The model parameter SLOPE, or alternatively Emax and EC50, are drug dependent and describe the drug effect.
Figure 1. Schematic illustration of the semi-mechanistic myelosuppression model
Dose Individualization based on Myelosuppression
Traditionally, most attempts to account for differences between individuals in treatment with antineoplastic agents have been to adjust the individual dose level based on body surface area. However, the BSA based dosing strategy has been shown to be of limited value in reducing the large variability in exposure and drug sensitivity [7]. For most cytotoxic drugs, new alternatives would be of value.
Several studies have reported a favorable treatment outcome in terms of overall survival in patients experiencing grade 2-3 neutropenia compared to patients with less toxicity [47-50]. Some patients may thus benefit from an increased dose. Dose escalations are however seldom performed outside clinical trials. One approach to identify underexposed patients is to utilize neutrophil counts as a biological marker to guide dose adjustments and thereby ensure sufficient exposure in every individual [51]. Moreover may neutrophil counts be applied to guide dose reductions indicated due to hematological toxicity. Not all patients will benefit from the same relative dose reduction, but today the same decrease is often applied to all individuals.
A model based tool for feedback dose individualization using neutrophil counts as a guide has been proposed [52]. The tool is based on the semi- mechanistic myelosuppression model and uses a maximum a posteriori (Bayesian) approach to calculate a suitable dose (lower or higher) for the next cycle aiming at a pre-specified treatment target:
To judge the value of the dose individualization tool more information is needed about the variability in myelosuppression. A high inter-occasion variability (IOV) may limit the usefulness of the approach, as the next treatment course is less predictable based on information from the previous cycle [10]. Consistency in system-related model estimates and in the magnitude of IIV across drugs has been observed in myelosuppression model parameters [34, 38], whereas the information about IOV is limited.
Sunitinib
Sunitinib malate (Sutent®, Pfizer Inc) is an oral multitargeted tyrosine kinase inhibitor approved for the treatment of advanced renal cell carcinoma (RCC), imatinib resistant gastrointestinal stromal tumor (GIST), and pancreatic neuroendocrine tumor (pNET). Sunitinib acts by inhibition of e.g.
vascular endothelial growth receptors (VEGFR-1, -2 and -3), platelet- derived growth factor receptors (PDGFR-α and -β) and the stem cell factor receptor (c-KIT) [53-54]. Inhibition of VEGFR and PDGFR is believed to mediate the anti-angiogenic effect, whereas inhibition of c-KIT (relevant in
GIST where a gain in function is acquired in c-KIT) results in decreased tumor proliferation [55].
Sunitinib is metabolized primarily by CYP3A4 to the equipotent metabolite SU12662 with a 21% conversion fraction (preclinical data).
Sunitinib and SU12662 have similar PK properties with an estimated terminal half-life of 69 and 80 hours, respectively [56].
A recommended starting dose of sunitinib in RCC and GIST is 50 mg qd for 4 weeks followed by a 2-week rest period to give a complete cycle of 6 weeks while in pNET the recommended dose is 37.5 mg daily in a continuous treatment regimen. Doses are adjusted in steps of 12.5 mg when required due to safety and tolerability. Most frequently observed side effects are fatigue, hypertension, diarrhea, neutropenia, elevated lipase levels and hand-foot syndrome [57].
Biomarkers
According to the Biomarkers Definitions Working Group (BDWG), a biomarker is defined as “a characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacological responses to a therapeutic intervention” [5].
A valid biomarker should have biological plausibility and correlate with and accurately capture changes in the response parameter [5]. Additionally, assays for the biomarker should also meet acknowledged analytical standards in terms of sensitivity, specificity, precision and reproducibility [8].
Identification of valid biomarkers provide possibilities of getting safe and effective drugs to the market faster and can aid in the drug development process in a variety of ways. For example, biomarkers can contribute knowledge about clinical pharmacology, serve as proof-of-concept (POC) in early phases of drug development, and be used to guide dose selection.
Biomarkers may also act as an indicator of safety issues and ultimately improve efficiency of clinical trials if the biomarker is validated as a surrogate endpoint. Furthermore, biomarkers may be helpful in clinical practice as a diagnostic tool, to assess the disease process, monitor response to treatment and for dose individualization [5].
Biomarkers are often distinguished into being prognostic or predictive.
Prognostic biomarkers correlate with treatment outcome independent of treatment whereas predictive biomarkers reflect the impact of the treatment [58]. Biomarkers can also be divided into biomolecular (soluble proteins, blood glucose) or clinical biomarkers (blood pressure, tumor size) [59].
Biomarkers in Anti-angiogenic Treatment
Today, the newly developed targeted anticancer therapies call for the use of biomarker based strategies in drug development as well as in clinical use.
One of the applications is to improve dose selection. The dose level for cytotoxic drugs is usually set by the concept of maximum tolerated dose (MTD), since it is believed that maximum exposure is associated with maximum clinical benefit. For the target-specific anticancer agents such as angiogenesis inhibitors, it is unclear whether the MTD is the most effective dose level [60]. Maximum target inhibition may be reached before toxicity arises and a well defined rather than empirically selected dose may avoid unnecessary toxicity.
Another application of biomarkers is the establishment of objective measures of response to treatment. Tumor response is often evaluated based on tumor shrinkage and response rate according to the standard Response Evaluation Criteria in Solid Tumors (RECIST) [61]. Anti-angiogenic drugs are however typically cytostatic in their mechanism of action and stabilize the tumor rather than reduce the size. Consequently tumor shrinkage will be an insensitive estimate of efficacy [60].
Also, biomarkers for treatment individualization would be of value in anti-angiogenic treatment, both to identify patients that will benefit from treatment (personalized medicine) and/or to guide dosing within each individual. One class of drugs that may benefit from dose individualization is the tyrosine kinase inhibitors (TKIs). They are currently administered at fixed dosing across patients, which may result in suboptimal therapy and toxicity, considering the high variability in PK [62].
Biomarkers in sunitinib treatment
When trying to identify valid biomarkers in anti-angiogenic therapy the focus has been on circulating proteins reflecting the angiogenesis, circulating endothelial cells and vascular imaging [60, 63]. In sunitinib treatment the vascular endothelial growth factor (VEGF) and soluble fragments of the VEGF receptors-2 and -3 (sVEGFR-2, -3) have been identified as biomarker candidates. Several reports have been published on their consistent change in response to treatment. The levels of VEGF were reported to increase with treatment whereas sVEGFR-2 and sVEGFR-3 decrease, all in a cyclic manner returning to near baseline levels during off-treatment periods [64-67]. Also, a soluble form of the c-Kit receptor (sKIT) has been identified as a possible predictor of survival in sunitinib treated GIST. Decreasing levels with treatment were observed in responding patients [64, 68].
The mechanisms behind the treatment induced biomarker modulations are however not well known. The increased levels of VEGF may result from treatment induced hypoxia, alterations in VEGF clearance from blood or release of VEGF from existing pools [69]. The reduced levels of circulating
soluble receptor VEGFR-2 has been indicated to result from VEGF mediated down regulation of VEGFR-2 [70] and the decreased sKIT levels may reflect the reduced number of viable tumor cells in GIST treated patient, which dominantly are c-Kit positive [64].
Easily measured clinical biomarker candidates have also been evaluated in sunitinib treatment with the potential to be used for treatment individualization. Increased blood pressure (hypertension) is a frequent side- effect for anti-angiogenic drugs [16] and the degree of hypertension has been shown to correlate with improved clinical outcome in sunitinib treatment [71-72]. The hypertension is hypothesized to result from a decreased production of nitric oxide and vascular rarefaction due to VEGF blockade, both inducing vasoconstriction and hypertension [16]. Also the degree of neutropenia has been reported to correlate with improved survival in sunitinib treatment and may be a valid biomarker [73].
PKPD Modeling of Biomarkers in Oncology
The use of PKPD modeling may increase the information gained from biomarkers by enabling a quantitative characterization of the link between exposure, biomarker concentrations and outcome (e.g. survival or adverse events) by taking the complete time-course of biomarker changes into account. An established relationship may be used for prediction of changes in biomarker concentration and the resulting outcome under a variety of conditions to evaluate e.g. new study designs, dose levels and strategies [8].
Several examples are available on how model based analyses of biomarker data can support the drug development process of anti-cancer drugs [6]. One concept that has proved useful is the prediction of phase III survival data based on the model predicted change in tumor size in phase II [74-76]. The concept is built on a drug specific tumor growth inhibition model coupled with a survival model using baseline tumor size and the relative change in tumor size at week 7 as predictors. The change in tumor size at a specific time point could be seen as a biomarker of drug effect which may be useful when comparing expected clinical response to reference compounds and support end of phase II decisions.
A similar approach was proposed by Wang et al. [77] who developed a disease specific outcome model for non small cell lung cancer (NSCLC) using tumor and survival data from nine different treatment regimens.
Observed relative change in tumor size at week 8, performance status and baseline tumor size were predictors of survival. This model may also be used for early estimation of expected treatment outcome, but not to perform dose- response simulations as drug effects not were incorporated in the model.
Aims
The general aim of the thesis was to develop pharmacometric models for characterization and quantification of relationships between drug exposure, biomarkers, side effects and efficacy in order to identify predictors of clinical response in anti-cancer drug therapy.
Relationships considered:
Patients and Methods
Description of Data
The data included in this work derive from previously performed prospective clinical trials for the treatment of various types of cancer. All trials were conducted according to the Declaration of Helsinki and approved by local ethics committees. Signed informed consent was obtained from all patients before enrollment.
Hematological Toxicity Data
To characterize the variability in myelosuppression (paper I), neutrophil counts and dosing history were available following therapy with docetaxel, paclitaxel, epirubicin-docetaxel, 5-fluorouracil-epirubicin-cyclophosphamide, topotecan and etoposide. The relationship between the shape of the myelosuppression time-course and the probability of FN (paper II) was characterized in the docetaxel treated patients.
Data from treatment cycles in which patients were known to have received G-CSF therapy were excluded.
Docetaxel
Data from 244 patients treated with docetaxel for metastatic breast cancer (2262 observations, median 4 treatment cycles) were analyzed [78]. The patients were part of the active control group in a phase III trial studying the effect and tolerability of combined capecitabine/docetaxel therapy. Initial dose level was 100or 75 mg/m2 (if mild hepatic impairment)of docetaxel infused intravenously over 1-hour every third week. Dose reductions were based on hematological and non-hematological toxicity and resulted in a final dose range of 50-100 mg/m2.
Neutrophil counts (n=820) from patients with observed grade 4 neutropenia (n =140, 57%) during the first course of docetaxel treatment were included in the development of the FN model. Twenty-six of the patients with grade 4 neutropenia (19%) experienced FN. Median (range) time to FN was 7 (6-9) days after treatment and the duration 7 (3-11) days.
The neutrophil data for all patients in the first treatment cycle was also characterized for comparison.
Paclitaxel
The paclitaxel data included neutrophil counts (523 observations, median 3 treatment cycles) from 45 patients with different types of cancer [79]. The initial dose was 175 mg/m2administered as a 3-h infusion every third week.
Doses were adjusted based on hematological and non-hematological toxicity resulting in a final dose range of 110-232 mg/m2.
Epirubicin-docetaxel (ET)
Neutrophil counts (659 observations, median 4 cycles) sampled from 41 patients with advanced breast cancer treated with the ET regimen were available [37]. The treatment was administered every third week as a 1-hour i.v. infusion of epirubicin followed by a 1-hour free interval and then a 1- hour infusion of docetaxel. Initial doses were 75/70 mg/m2 for epirubicin and docetaxel, respectively, followed by escalated/reduced doses in subsequent cycles based on the resulting leukocyte and platelet counts according to a predefined dosing scheme.
5-Fluoriuracil-epirubicin-cyclophosphamide (FEC)
Sixty breast cancer patients treated with either standard or tailored FEC were included in the analysis (1196 neutrophil observations, median 7 cycles) [36]. The treatment was administered every third week as a 15 minute i.v.
infusion of cyclophosphamide followed by an i.v. bolus dose of 5- fluorouracil and a bolus or 1-hour infusion of epirubicin. The initial doses of 5-fluorouracil, epirubicin and cyclophosphamide were in the first treatment cycle for standard FEC 600/60/600 mg/m2, respectively,and for the tailored therapy 600/75/900 mg/m2, respectively. Doses in the tailored therapy were stepwise escalated or decreased based on the observed nadir and the dosing day leukocyte/platelet count according to a dose escalation/reduction protocol.
Topotecan
The topotecan dataset included neutrophil counts (501 observations, median 2 cycles) from single agent topotecan treatment in 26 patients with various types of solid tumors [80]. The initial dose level was 6 mg/m2 administered as 24-h intravenous infusion every third week.
Etoposide
Neutrophil counts (583 observations) from 44 patients with solid tumors and hematological malignancies who received two treatment courses of a 3-day continuous infusion of etoposide were analyzed [81-82]. The patients were randomized to receive either the standard dose (total dose of 375 mg/m2) or concentration guided dosing (total delivered dose 225-789 mg/m2)in a 28 day cycle.
GIST Data
To develop an integrated modeling framework identifying predictors of clinical response (paper III and IV), data was pooled and analyzed from four phase I-III clinical trials of single agent sunitinib in imatinib resistant GIST [83-86]. Data on soluble biomarkers (VEGF, sVEGFR-2, sVEGFR-3 and sKIT), tumor size, treatment-related side effects (i.e. fatigue, hand-foot syndrome, neutropenia and hypertension) and overall survival were available. Only patients with biomarker, tumor and survival data reported were included in the analysis, in total 303 patients (Table 1).
Sunitinib was administered in one of four different treatment schedules including the 4/2, 2/2, 2/1 (weeks on/weeks off treatment) schedule and continuous treatment, with doses ranging from 0 to 75 mg orally once daily.
Patients randomized to receive placebo treatment (n=47) in the placebo- controlled trial were offered sunitinib upon disease progression as defined by the response evaluation criteria in solid tumors (RECIST) [87].
When available, empirical Bayes estimates of PK parameters were used to describe the PK of sunitinib. In patients with missing PK data (n=57) population estimates of PK parameters from a previously developed model [56] were utilized.
Table 1. Summary of GIST data included in the development of the integrated modeling framework Parameter (unit)Study 1004Study 1047Study 1045Study 013 ReferenceDemetri et al. [83]George et al. [84]Shiaro et al. [85]Maki et al. [86] n 202 active Initially 47 placebo133652 Biomarkers measuredVEGF, sVEGFR-2, sVEGFR-3, sKIT VEGF, sVEGFR-2, sVEGFR-3, sKIT VEGF, sVEGFR-2, sKIT VEGF, sVEGFR-2, sKIT Tumor size at baseline (mm)a 194 (35-822)108 (29-191)166 (31-644)255 (55-687) Hand-Foot Syndrome (%)b0: 83 1: 4.9 2: 6.9 3: 5.4 4: 0
0: 100 1: 0 2: 0 3: 0 4: 0
0: 14 1: 20 2: 34 3: 32 4: 0
0: N.A 1: N.A 2: N.A 3: N.A 4: N.A Fatigue (%)b0: 30 1: 33 2: 25 3: 11 4: 1.0
0: 54 1: 23 2: 23 3: 0 4: 0
0: 31 1: 39 2: 19 3: 8.3 4: 2.7
0: 12 1: 48 2: 33 3: 5.7 4: 1.9 Absolute neutrophil counts (∙109 cells/L)c 3.1 (0.080-20) 1.8 (0.010-7.5)2.1 (0.28-12)2.6 (0.16-15) Diastolic blood pressure (mmHg)c 80 (20-120)78 (40-120)79 (40-120)80 (50-130) Survival (weeks)a 61 (4-226)31 (81-15)37 (27-48)39 (4-96) N.A: Not available,a Median (range), b Highest observed severity within an individual, c Median (range) response during treatment
Model Building
Analysis of Hematological Toxicity Data
The time-course of hematological toxicity following anticancer drug therapy was described using a semi-mechanistic myelosuppression model [34]. The original model structure was modified by fixing the half-life of circulating neutrophils to the literature value of 7 hours [88] instead of modeling the half-life as dependent on the MTT estimate. The neutrophil data was also Box-Cox transformed with λ=0.2 (Eq. 3) prior to the analysis as this has been shown to result in approximately normally distributed residuals [33, 89].
λ
transformed ANC 1
ANC λ
= − (3)
The drug effect was originally described as being a linear or Emax function of the drug concentration. For the characterization of the variability, a linear model was assumed and in the development of the FN model linear, Emax and sigmoidal Emax drug-effect relationships were evaluated.
Characterization of variability in myelosuppression model parameters The significance and magnitude of variability in myelosuppression model parameters were evaluated and compared across six different treatments including docetaxel, paclitaxel, ET, FEC, topotecan and etoposide.
For consistency, IIV was included for the model parameters ANC0, MTT and SLOPE in all datasets and IOV was evaluated for statistical significance (P < 0.001) for these parameters, using OFV in the likelihood ratio test. One occasion was defined as one treatment course with the nominal cycle length of 21 or 28 (etoposide) days. To exclude the possibility of time-dependent and non-random variability between occasions, linear changes in model parameters with time were evaluated and CWRES [90] was graphically assessed for time dependent changes.
The contribution of IOV to the variability in myelosuppression in relation to total IIV was evaluated by simulations of 1000 time-courses of hematological toxicity for each of the six datasets including IIV only, IOV only and both IOV and IIV.
Relationship between the time-course of neutropenia and FN
The relationship between the shape of the myelosuppression time-course and the probability of FN was characterized by the development of a logistic regression model. The time-course of hematological toxicity following the first cycle of docetaxel treatment was described for individuals with grade 4 neutropenia (scenario b), by applying the myelosuppression model, and linked to the probability of FN using a sequential [91] modeling approach.
Only patients with grade 4 neutropenia were included in the analysis in an attempt to distinguish risk factors for FN from risk factors for grade 4 neutropenia. The neutrophil data in all patients (scenario a) were also characterized for comparison.
The myelosuppression model parameters (ANC0, MTT, SLOPE and γ) and myelosuppression descriptors (nadir and duration of grade IV neutropenia) were assessed as predictors of FN in the logistic regression model. Linear, Emax, sigmoidal Emax and power functions were evaluated to link the predictors to the probability of FN. Also, earlier proposed risk factors [19, 23] (age > 65 years, performance status, haemoglobin level <12 g/dL, and liver function) were explored as potentially being related to the probability of FN using the automated stepwise covariate model building method (SCM) in PsN (p < 0.05 forward inclusion, p < 0.01 backward exclusion).
Integrated Modeling Framework
An integrated modeling framework linking biomarkers, tumor dynamics, side- effects and overall survival in a unified structure, was developed sequentially with the goal of identifying predictors of clinical response in sunitinib treated GIST (Figure 2).
Figure 2. Investigated relationships for the identification of predictors for clinical response in sunitinib treated GIST.
Biomarker models
The changes in biomarker concentrations over time were related to sunitinib exposure (dose or AUC calculated as dose/CL/F) using indirect response models with linear, inhibitory Emax (Imax) and sigmoid Imax drug effect relationships [92]. Biomarker modulations in placebo patients due to the natural history of the disease were characterized using linear or non-linear disease progression models. Modeling was performed on log transformed biomarker data. Models for each of the biomarkers were initially developed separately and combined into a joint model to explore correlations between the biomarkers and to reduce the model structure.
The relationships between sunitinib exposure, the biomarkers, tumor size and side effects were assessed by investigating how well measures of the model predicted biomarker concentrations, alone or in addition to drug exposure, could describe the longitudinal data. Baseline concentrations and absolute and relative change in biomarker levels over time were linked to tumor size and side effects in a similar fashion as drug exposure. Competing models were discriminated by using OFV in the likelihood ratio test.
Tumor model
The change in tumor size, i.e. the sum of longest diameters (SLD) of target lesions according to RECIST [87], as a function of time, was described by applying a longitudinal model for tumor growth inhibition [74]. The model accounts for the underlying tumor growth dynamics (KG), exposure driven drug effect (KDrug) and resistance development/tumor regrowth [R(t)] (Eq. 4).
In the current analysis the observed tumor size at baseline (y0) was incorporated as a covariate acknowledging residual error (ε) in the measurement [93]. The time-course of the different biomarkers [BM(t)] were evaluated to describe the tumor response with KBM representing the tumor size reduction rate constant related to biomarker response (Eq.4).
( ) ( ( ) ) ( ) ( )
G BM DRUG
dy K y t K BM t K AUC R t y t
dt = ⋅ − ⋅ + ⋅ ⋅ ⋅
( ) λ t
R t =e− ⋅ (4)
( ) o
y 0 = y +ε
To accurately depict simulation results, the frequency and time-course of patient dropout from tumor measurements had to be taken into account. A logistic regression model for the probability of dropout over time was developed and applied in the simulations. AUC, time, progressive disease, SLD at dropout, baseline SLD and relative change in SLD since start of
Models for side effects Hematological toxicity
The time-course of sunitinib induced neutropenia was described by a semi- mechanistic model for myelosuppression [34]. The original model was applied with the earlier described modifications (see analysis of hematological toxicity data). Linear, Emax, and sigmoid Emax models were evaluated to link drug exposure (dose and AUC) and biomarkers to decreased proliferation/induce cell kill.
Hypertension
Changes in diastolic blood pressure (dBP)following sunitinib and placebo treatment were described with an indirect response model with stimulation of the zero-order production rate (Kin) [94]. Also the alternative model with inhibition of the first-order elimination rate constant (Kout) was assessed.
Baseline (dBP0) and Kout (reported as MRT = 1/Kout) were estimated (Eq. 5).
Linear, Emax and sigmoid Emax-models were evaluated to describe the drug/biomarker effect relationships.
( ) ( )
in Drug effect out
ddBP K 1 dBP AUC K dBP t
dt = ⋅ + ⋅ − ⋅
in 0 out
K =dBP K⋅ (5)
( ) 0
dBP 0 =dBP
Fatigue and hand-foot syndrome
The severity of fatigue and hand-foot syndrome (HFS) were assessed on a daily basis throughout the studies and reported according to the National Cancer Institute (NCI) common toxicity criteria (CTCAE) [13] as different grades (i.e. 0 = no adverse event, 4 =life-threatening). Grade 4 was only reported in a few patients (for fatigue 1% and for HFS 0%) and was consequently grouped with grade 3 into one category.
A first order Markov model was used to describe the probability and severity of fatigue and HFS over time [95-96]. The Markov model conditions the probability of a transition between different severities on the preceding one, accounting for that the scores are not independent. Here, transitions between all the different grades were considered, in total 16 transitions. The probability of a transition from grade a to grade b for the ith individual at the jth observation was described according to Eq. 6. fb|a wasa function of baseline transition probabilities (Bb|a) and covariate effects g(xi).
Inter-individual random effect around parameter Bb|a for subject i (ηi) was assumed to be normally distributed. Three probabilities for each grade were
directly estimated and the fourth probability (P0|0, P0|1, P0|2 and P0|3) was expressed as one minus the sum of the associated probabilities.
Time, drug exposure and absolute/relative changes in biomarker concentrations over time were assessed to describe the probability and severity of fatigue and HFS. Linear and non-linear relationships were evaluated. The addition of an effect compartment to account for a delay in the drug distribution was also assessed [97].
|
| |
|
( ijb a) ln ijb a b a i
ijb a
Logit P P f n
= 1 P = +
− (6)
| | ( )
b a b a i
f =B +g x Overall survival model
The relationships between the four biomarkers, tumor size, side effects and overall survival (OS) were explored by a parametric survival (time-to-event) model. The underlying survival distribution was assessed by comparing exponential, Weibull, log-logistic, extreme value and Gompertz probability density functions. Drug exposure (dose and AUC), model predicted (using AUC as predictor), baseline values and absolute and relative changes over time in biomarkers, tumor size, neutropenia and hypertension were evaluated as predictors of OS. The predictors were extrapolated based on developed models until time of death/censoring assuming dosing and schedule according to protocol. For fatigue and HFS the observed severity scores (last observation carried forward) were evaluated as predictors of OS by including each observed score as a predictor. Also, point estimates of the relative change in tumor size and biomarkers at treatment week 6 or 12 were assessed for the relationship to OS.
Data Analysis
Software
Modeling and simulations were performed using the non-linear mixed effects modeling approach implemented in NONMEM (version VI and 7) [98]. The first-order conditional estimation method with interaction (FOCEI) was used for parameter estimation of continuous data, and the Laplacian estimation method with the likelihood option for categorical type data.
The R-based software Xpose (version 4) [99] was applied to create graphical diagnostics and the PsN toolkit (version 3) [100-101] was utilized for execution of models, covariate model building (SCM), non- parametric bootstraps, log-likelihood profiling, and simulations and calculations for visual predictive checks (VPCs).
Models for random effects
Random inter-individual variability (IIV) in model parameters was assumed to be log-normally distributed around the population mean and modelled in terms of eta (η) variables. A normal distribution (on the logit scale) of the IIV was assumed for the fatigue and HFS-models (paper IV).
IOV (evaluated in paper I) was described by the kappa (κ) parameter and included in the same manner as IIV assuming constant variances across all occasions as previously described [10]. The ηs and κs were assumed to be normally distributed parameters with mean zero and estimated variances ω2 and π2, respectively.
Random residual variability was explored using additive, proportional and combined (additive + proportional) error models. For the hematological toxicity data, an additive (on Box-Cox scale) residual error was applied.
Model selection
Model selection was based on graphical assessment of goodness of fit plots, comparison of the objective function value (OFV) provided by NONMEM in the likelihood ratio test, plausibility, and precision in parameter estimates.
Simulation properties were also considered.
Model evaluation
The final models were evaluated by internal validation procedures. Model robustness was judged by relative standard errors (RSE) of the model parameter estimates obtained by non-parametric bootstrapping with 200 samples (n=100 in paper II). For the models developed for the evaluation of IOV in myelosuppression (paper I), standard errors were obtained from the S matrix (R matrix for topotecan) in NONMEM because of long run times.
The predictive performance of the final models was assessed by simulation based diagnostics. Models for continuous data were evaluated by standard visual predictive checks (VPCs) [102] and prediction-corrected visual predictive checks (pcVPCs) [103]. Prediction intervals with 95%
confidence intervals were derived from 500 simulated datasets and graphically compared with the corresponding percentiles for the observed data (normalized to the typical population prediction for the pcVPCs).
Models for categorical type data were assessed by an adapted version of the VPC [104]. The observed data and 95% prediction interval for the simulated fraction of observations for each category were plotted versus an independent variable and compared. Also, summary statistics such as the observed and median number of simulated events and transitions between different severity scores were compared for consistency.
Drop-out and time-to-event type data was evaluated by creation of Kaplan-Meier plots of observed data overlaid with a 95% confidence interval calculated from 200 simulations.
Results
Variability in Myelosuppression Model Parameters
A semi-mechanistic model for myelosuppression adequately characterized the neutrophil-time course following single-agent and combination therapy for all the investigated datasets. The system-related parameters and IIV estimates were in agreement with previously reported results [34, 38].
For all the investigated treatments, except topotecan, IOV in the myelosuppression model parameter MTT was significant and of similar magnitude. For docetaxel and etoposide IOV in SLOPE was in addition also significant. Only IOV in SLOPE was significant for topotecan (Table 2).
Inclusion of IOV decreased the residual errors by an average of 21% with the highest decrease observed for the paclitaxel and etoposide datasets (Table 2).
No significant time-dependent trends were identified in the parameters with IOV included, indicating that the estimated variability was random.
In all the six analyzed data sets, the contribution of IOV to the variability in nadir was clearly lower than IIV as shown in Figure 3. This is also illustrated by the relative impact of total IIV and IOV on the variability in the myelosuppression time-course for 20 simulated individuals (Figure 4).
Table 2. Estimated IIV and IOV (relative SE %) for the six analyzed datasets.
IIV CV% IOV CV%
ANC0 MTT SLOPE ANC0 MTT SLOPE Δ Residual Error % Docetaxel 33 (5.9) 9.0 (19) 37 (7.0) - 16 (4.8) 19 (12) -17 Paclitaxel 36 (13) 17 (22) 39 (20) - 16 (8.5) - -41
ET 37 (15 12 (21) a22 (23) - 8.0 (20) - -17
FEC 28 (15) 16 (13) a23 (14) - 7.5 (11) - -7.0 Topotecan 32 (27) 15 (34) 62 (45) - - 28 (39) -3.3 Etoposide 47 (15) 23 (24) 28 (42) - 12 (39) 39 (24) -38 CV: Coefficient of variation
Δ Residual Error; relative change in residual error after inclusion of IOV
aCommon IIV parameter for the component drugs
Figure 3. Box-plots of nadir distributions from 1000 simulated patients using the final models including IOV and IIV, only IIV or only IOV. The solid circle corresponds to the median, the top and bottom of the box the 25th and 75th
percentiles and the whiskers to the maximum and minimum of the simulated nadir counts.
Figure 4. Twenty individual time-courses of myelosuppression simulated using the final models including IIV only, IOV only or both IIV and IOV for all the six investigated datasets.
Relationship between Neutropenia and FN
The neutrophil time-course following the first cycle of docetaxel treatment in all patients (a) and in the subpopulation that developed grade 4 neutropenia (b) was well characterized by a semi-mechanistic myelosuppression model (Table 3). The drug effect was described by a sigmoidal Emax-function which significantly improved the model fit, especially around nadir. The myelosuppression model parameter estimates were as expected somewhat different for the cohort of patients with grade 4 neutropenia (b). The parameter MTT was shorter, EC50 was lower and Emax was higher in grade 4 neutropenia individuals, compared to when data for the full population was described (Table 3).
Evaluating the model by simulating 500 replicates of the data, using parameter estimates from scenario a, showed that the model accurately predicted the number of patients with grade 4 neutropenia. The median simulated number of individuals (n=136) were well in agreement with the observed (n=140). Also, the predictive performance of the final myelosuppression models was adequate as illustrated by VPCs (Figure 5).
Table 3. Final model parameter estimates (relative SE %) for the myelosuppression model and the logistic regression model.
Myelosuppresion model FN model
(a) All patients (b) Grade 4 patients
Parameter (unit) Estimate IIV CV% Estimate IIV CV% Parameter Estimate ANC0 (∙109cells/L) 4.65 (3.4) 32 (8.6) 4.65 (1.7) 32 (5.3) θ1 -0.360 (32) MTT (hours) 86.5 (3.6) 19 (9.2) 78.3 (2.1) 12 (5.5) θEC50 -0.160 (21) γ 0.159 (3.7) 20 (12) 0.155 (3.2) 24 (8.1) HillEC50 7.76 (11)
Emax 91.3 (6.6) - 95.1 (4.9) - θMTT -0.122 (43)
EC50 (mg/L) 1.50 (8.4) 68 (7.4) 1.39 (10) 36 (9.4) HillMTT 25.4 (8.3)
Hill 1.64 (9.9) - 1.45 (10) -
Residual errora 0.497 (5.5) - 0.468 (5.1) -
aadditive error on Box-Cox scale
EC50 50
Hill 50 EC 50
50
f ( EC ) θ EC
TVEC
=
HillMTT
MTT MTT
f ( MTT ) θ
TVMTT
= (7)
[ ]
[
1 1 5050]
exp θ f ( EC ) f ( MTT ) P 1 exp θ f ( EC ) f ( MTT )
+ +
= + + +
Figure 5. VPC of the final myelosuppression models including all patients (a, left) and only patients with grade 4 neutropenia (b, right). Observed neutrophil data (o), median (—) and the 5th and 95th percentiles (---) of the observed data. Shaded area is the 95% confidence intervals based on the simulated data (n=500) for the corresponding percentiles.
The drug potency parameter (EC50) and mean transit time (MTT) were both significantly related to the probability of FN via a power function in a logistic regression model. The power function included the constant parameters (θEC50,θMTT, and HillEC50,HillMTT) and the individual parameter estimates were normalised to the typical value in the population (TVEC50
and TVMTT) (Eq. 7, Table 3).
The results indicate that patients with high drug sensitivity (low EC50) and a fast decline of neutrophils (short MTT) are more likely to develop FN.
None of the evaluated risk factors such as age, performance status and liver function were significantly related to the probability of FN when EC50 and MTT had been included in the model. Neither was predicted nadir or duration of grade IV neutropenia.
The evaluation of the logistic regression model shows a satisfactory predictive performance as depicted by a categorical VPC (Figure 6). The model also accurately simulates number of FN events as the observed number (n=26) were within the 90th prediction interval of the simulated number of FN events (median n=21).
Figure 6. VPC of the final FN model. The solid line represents the predicted fraction and the shaded area the 95% confidence interval for the simulated fraction of MTT and EC50 estimates for individuals with and without an episode of FN.
Integrated Modeling Framework
Biomarker models
The changes in biomarker levels with time [BM(t)] were described using indirect response models with inhibitory sigmoid Imax (VEGF, sVEGFR-2) or Imax (sKIT, sVEGFR-3) drug effect relationships with Imax fixed to 1.
Changes in sVEGFR-2, -3 and sKIT due to sunitinib treatment were described with models with a decreased zero-order production rate (Kin) (Eq. 8) and VEGF with an inhibited degradation rate (Kout) (Eq. 9). A linear disease progression model characterized the increase of VEGF and sKIT over time (Eq. 10). The final models were reduced to include a common drug effect parameter (IC50) for the four biomarkers and a common disease progression parameter (DPSlope) for sKIT and VEGF. IC50 was highly correlated (75-92%) for VEGF, sVEGFR-2 and -3 and the magnitude of IIV in mean residence time (MRT=1/Kout) for VEGF, sVEGFR-2 and -3 was quantified using a common variability term (Table 4).
Data on sVEGFR-3 was not available for two of the studies, in total 69 patients. sVEGFR-2 and -3 were however highly correlated in IC50 (92%) and 100% correlated in MRT which contributed to the information about the sVEGFR-3 response in individuals with missing data. The predictive performance of the final biomarker models as illustrated by VPCs (Figure 7) shows an adequate description of the biomarker data.
