Population pharmacokinetic (PK) analysis of laromustine, an emerging alkylating agent, in cancer patients.

Abstract 1. Alkylating agents are capable of introducing an alkyl group into nucleophilic sites on DNA or RNA through covalent bond. Laromustine is an active member of a relatively new class of sulfonylhydrazine prodrugs under development as antineoplastic alkylating agents, and displays significant single-agent activity. 2. This is the first report of the population pharmacokinetic analysis of laromustine, 106 patients, 66 with hematologic malignancies and 40 with solid tumors, participated in five clinical trials worldwide. Of these, 104 patients were included in the final NONMEM analysis. 3. The population estimates for total clearance (CL) and volume of distribution of the central compartment (V1) were 96.3 L/h and 45.9 L, associated with high inter-patient variability of 52.9% and 79.8% and inter-occasion variability of 26.7% and 49.3%, respectively. The population estimates for Q and V2 were 73.2 L/h and 29.9 L, and inter-patient variability in V2 was 63.1%, respectively. 4. The estimate of Vss (75.8 L) exceeds total body water, indicating that laromustine is distributed to tissues. The half-life is short, less than 1 h, reflecting rapid clearance. Population PK analysis showed laromustine pharmacokinetics to be independent of dose and organ function with no effect on subsequent dosing cycles.

In murine models, laromustine demonstrated anti-tumor activity against leukemia and solid syngeneic and human xenograft tumors (Finch et al., 2001).
Laromustine as a single agent was initially studied in three phase I trials. The first of these trials (study CLI-011) included patients with advanced solid tumors treated by intravenous (IV) infusion over 15-30 min at dose levels ranging from 3 to 305 mg/m 2 every 4-6 weeks. The maximum tolerated dose (MTD) was 305 mg/m 2 and the dose-limiting toxicity was reversible myelosuppression. No drug-related dose-limiting non-hematologic toxicities were observed. The second phase I trial (study CLI-028) was also conducted in patients with advanced solid tumors. Patients were given three IV treatments weekly in four-week cycles at first cycle doses of 80, 100, 125 and 155 mg/m 2 . The third phase I study (study CLI-029) consisted of patients with relapsed or refractory leukemia given IV treatments at doses ranging from 220 to 708 mg/m 2 with treatment repeated monthly as indicated. A dose level of 600 mg/m 2 was considered well-tolerated, with no observable dose-limiting non-hematologic toxicities, and was selected for phase II evaluation.
A phase II trial of laromustine at a dose of 600 mg/m 2 was conducted in two strata of patients with hematologic malignancies (study CLI-033). Patients 60 years or older (median age 72, range 60-84) with poor-risk acute myelogenous leukemia (AML), including both de novo and secondary AML, or patients with high-risk myelodysplastic syndrome (MDS) were treated in Stratum A. Patients with AML in first relapse (median age 62, range 18-84 years) were treated in Stratum B. The overall response rate (ORR) including both CR and CR with incomplete platelet recovery (CRp) indicated that the drug was active with an early death rate consistent with that of other agents approved in this indication. Patients 60 years or older with de novo poor-risk acute myelogenous leukemia (AML) or high-risk MDS had a better ORR than patients with secondary AML or AML in first relapse.
Given the encouraging level of activity in de novo AML, a phase II trial of laromustine at a dose of 600 mg/m 2 was conducted in patients 60 years or older with de novo poor-risk AML (study CLI-043). A second induction cycle was administered at the same dose 4-5 weeks after the first cycle if the bone marrow was improved but contained residual disease. For patients achieving CR or CRp after the first or second induction cycle, or partial response (PR) after a second induction cycle, one or two consolidation cycles of AraC continuous infusion at a dose of 400 mg/m 2 /day for 5 days could be administered, starting 45-90 days after the last induction cycle. PK data were collected from the phase I dose escalation trials in patients with solid tumors (studies CLI-011 and CLI-028), and hematologic malignancies (study CLI-029). PK assessments were also performed in a cohort of patients with AML or high-risk MDS in the phase II trials CLI-033 and CLI-043. These data have been previously analyzed for each study separately (Abdelhameed, 2008;Jiang, 2008;Nassar, 2008a,b,c) and the PK parameters estimated are summarized in Table 1.
The geometric mean terminal half-life (t 1/2z ) was consistently less than 1 h in estimates from all studies. High inter-patient variability was observed in all other laromustine PK parameters estimated in the phase I studies. Body surface area normalization of mean systemic plasma clearance (CL) or mean volume of distribution at steady state (V ss ) for all patients at all doses of laromustine did not alter this variability. In the phase II studies (CLI-033 and CLI-043), conducted at a first cycle dose of 600 mg/ m 2 , high inter-patient variability was also observed in these laromustine PK parameters. Overall the CL and V ss estimated from these phase II studies appear somewhat larger than those reported from the phase I studies. However, more than 90% variability is associated with the CL and V ss estimates in the phase II studies. The mean CL value ranged from 95.0 to 352 L/h across the studies (48.0-181 L/h/m 2 when normalized for body surface area). Similarly, V ss ranged from 60.4 to 370 L (31.1-192 L/m 2 when normalized for body surface area). These estimates of systemic clearance are greater than the human liver blood flow rate and approximately equal to total cardiac output (Davies & Morris, 1993). The very high CL is consistent with extra-hepatic elimination. The rapid, non-enzymatic degradation characteristic of laromustine is also consistent with this high clearance rate. The estimate of V ss exceeds total body water for humans (Davies & Morris, 1993), indicating that laromustine is distributed extensively in tissues.
Population PK modeling aims to explain variability by identifying factors of demographic or pathophysiological origin that may influence the PK behavior of a drug and to provide quantitative estimation of the magnitude of the unexplained variability in the patient population. In mixedeffects modelling, this is achieved by estimating population mean parameter values (derived from fixed-effects parameters) and their variability within the population (derived from random-effects parameters) directly from the full set of individual data. The population PK approach offers the possibility of gaining integrated information on the PK of drugs from relatively sparse data or a combination of sparse and dense data, and allows pooled analysis of data from a variety of unbalanced study designs that is characteristic of most cancer patient studies.
Recently, we published the results of several in vitro and in vivo studies that were designed to examine the biotransformation and rearrangement of laromustine. High mass accuracy and ultrahigh resolution measurements, H-D, stable-isotope labeled analogue ( 13 C-labeled laromustine), NMR, and detailed analyses of the LC-MS n experiments were used to assist with the assignments of these fragments and possible mechanistic rearrangement. The results showed that laromustine undergoes rearrangement, dehalogenation and hydrolysis at physiological pH to form active moieties. Laromustine produces several reactive metabolites which were trapped by glutathione (GSH), N-acetylecysteine (NAC) and cysteine (CYS) in the in vitro systems (Nassar et al., 2009(Nassar et al., , 2010a(Nassar et al., ,b,c, 2011(Nassar et al., , 2015. Herein we report for the first time the details of the methodology and results of the population PK analysis of laromustine using mixed-effects modeling and the combined data obtained in the phase I studies CLI-011, CLI-028 and CLI-029 and phase II studies CLI-033 and CLI-043.

Data
Laromustine plasma concentration-time profiles were available from five clinical trials in cancer patients, conducted by Vion Pharmaceuticals, Inc. (Vion, New Haven, CT). Studies CLI-011 and CLI-028 were phase I dose escalation studies in patients with solid tumors. Study CLI-029 was a phase I dose escalation study conducted in patients with hematologic malignancies. PK assessments were also performed in a cohort of patients with AML or high-risk MDS treated with the MTD in the phase II study CLI-033. Additional PK samples were collected in AML patients treated in the confirmatory phase II study CLI-043.

Laromustine injection
It was supplied in 10 mL clear glass vials for all studies. The first lot manufactured, Lot 00-07-0027, contained 100 mg of laromustine formulated in a solution consisting of 30% (3 mL) anhydrous ethyl alcohol, USP and 70% (7 mL) polyethylene glycol 300, NF, and was diluted with 5% dextrose for injection, USP prior to infusion. This Lot was used to treat the first three patients in study CLI-011 only. For all subsequent lots, the formulation was slightly modified to include citric acid. The new formulation used in all studies contained 100 mg of laromustine formulated in a solution consisting of 30% (3 mL) anhydrous ethyl alcohol, USP, 70% (7 mL) polyethylene glycol 300, NF, with 0.6% (6 mg/mL) anhydrous citric acid, USP, and was diluted with 5% dextrose for injection USP prior to infusion.

Bioanalytical methods
Concentrations of laromustine in human plasma were determined by three different validated analytical methods using high performance liquid chromatography (HPLC) with tandem mass spectrometric (MS/MS) detection (18,19,20). The concentration ranges and the lower limit of quantitation (LLOQ) for each method used in each study are shown below. Concentrations below the respective LLOQ were excluded from the NONMEM dataset.
Bioanalytical methods used to measure plasma concentration of laromustine:

Vion study CLI-011
This was a dose escalating, open label, non-randomized phase I trial in patients with advanced or metastatic cancer (solid tumors). Patients received laromustine IV over 15-30 min at concentrations up to 4 mg/mL. Dose was escalated in successive cohorts of patients with cycles repeated every 4-6 weeks. Twenty-four patients receiving first cycle dosages ranging from 3 to 305 mg/m 2 were included in the PK portion of the study and 16 of the 24 patients had blood collected and PK calculated for more than one cycle. Blood samples for PK analysis were collected at the following time points on day 1 of each of the first two cycles and in any cycle with a change in dose: pre-infusion, at the end of the infusion, and at 5, 10, 20 and 40 min, 1, 2 and 4 h after the end of the infusion.

Vion study CLI-028
This was a dose escalating, open label, non-randomized phase I trial in patients with advanced or metastatic cancer (solid tumors). Patients received laromustine IV over 15 min at concentrations up to 2 mg/mL, with the dose escalated in successive cohorts of patients. Seventeen patients receiving first cycle dosages of 80, 100, 125 and 155 mg/m 2 weekly Â 3 in four-week cycles were included in the PK portion of the study. Ten of the 17 patients received more than one cycle and contributed blood samples for additional PK analyses. Blood samples for PK analysis were collected on day 1 of each of the first two cycles at the following time points: pre-infusion, at the end of the infusion, and at 5, 10, 20 and 40 min, 1, 2 and 4 h after the end of the infusion.

Vion study CLI-029
This was a dose escalating, open label, non-randomized phase I trial in patients with hematologic malignancies. Patients received laromustine IV ranging from 220 to 708 mg/m 2 over 15-30 min for a final dilution volume 250 mL, over 30-60 min for final dilution volume of 251-500 mL, and over 60-90 min for final dilution volume of 1000 mL. Dosing was administered every four weeks for up to six cycles. Thirty-five patients were included in the PK portion of the study. Among them, 10 patients had PK data collected in more than one cycle. Blood samples for PK analysis were collected at the following time points on day 1 for the first two cycles and in any cycle with a change in dose: pre-infusion, at the end of the infusion, and at 5, 10, 20 and 40 min, 1, 2 and 4 h after the end of the infusion.

Vion study CLI-033
This was an international, open label, phase II, multicenter trial in patients with AML or MDS. Patients received laromustine 600 mg/m 2 IV over 30 min in a total volume of 500 mL. A second cycle was administered at the same dose, 4-5 weeks after the first cycle if the bone marrow was improved but contained residual disease. A consolidation course of laromustine at a reduced dose of 400 mg/m 2 could be administered to patients achieving CR or CRp after the first or second induction cycle. Blood samples for PK analysis were collected for a subgroup of 17 patients at the following time points on day 1 of each cycle: pre-infusion, at the end of the infusion, and at 5, 10, 20 and 40 min, 1, 2 and 4 h after the end of the infusion.

Vion study CLI-043
This was an international, open label, phase II, multicenter trial in patients 60 years or older with de novo poor-risk AML. Patients received laromustine 600 mg/m 2 IV over 60 min in a total volume of 500 mL. A second induction cycle was administered at the same dose, 4-5 weeks after the first cycle if the bone marrow was improved but contained residual disease. For patients achieving CR or CRp after the first or second induction cycle, or PR after a second induction cycle, one or two consolidation cycles of AraC continuous infusion at a dose of 400 mg/m 2 /day for 5 days could be administered, starting 45-90 days after the last induction cycle. Blood samples for PK analysis were collected for a subgroup of 13 patients at the following time points on day 1 of each cycle: pre-infusion, 30 min after start of the infusion, 5-10 min before the end of the infusion, and at 5, 10, 20 and 40 min, 1, 2 and 4 h after the end of the infusion.

Software
Non-linear mixed-effects modeling was performed using the computer program NONMEM with double precision (version VI), installed on a PC. For data-file construction, data presentation, construction of plots and graphical exploration, WinNonlin TM , SAS Õ , SigmaPlot or the PDx-Pop 2.1 front for NONMEM were used, as appropriate.

Population PK analysis
The population PK (PopPK) data analyses and evaluations were performed according to appropriate guidelines (Guidance for Industry, 1999; Guideline on reporting, 2007) using the mixed-effects approach, as implemented in NONMEM. PopPK data analysis strategy was guided by modeling/statistical selection criteria and consisted of selection of appropriate PK structural models for laromustine, estimation of structural and error model parameters, identification of various covariate (COV) relationships and interoccasion variability (IOV) and derivation of final empirical Bayesian estimates of individual PK parameters.

Modeling/statistical selection criteria
In general, for a more complex model to be selected, the following criteria were considered collectively: Successful convergence of the minimization procedure; Termination of the covariance step without warning messages; A minimum of three significant digits in the estimated parameters, as a criterion for successful termination of the minimization procedure; A statistically significant decrease in the objective function value, as assessed by the log-likelihood ratio, which is approximately 2 distributed; Standard error of parameter estimates not larger than 50% the parameter value; Accuracy in the parameter estimates, as indicated by the 95% CI; A correlation coefficient between model parameters 50.95; Decrease in residual error estimate (a composite of intrapatient variability, assay variability, errors in clinical procedures, and model misspecification errors); A random distribution of the dependent variable (observed laromustine concentrations, OBS) versus population predictions (PRED) across the line of identity; A random distribution of OBS versus individual predictions (IPRED) across the line of identity; A random distribution in the WRES against PRED and against TIME.

Base model
During development of the base model, the appropriate structural PK model was selected based on visual inspection of exploratory plots, previous experience and model goodness of fit criteria. One, two and three compartment PK structural models were evaluated. Exponential error models were evaluated for inter-patient variability on the structural model parameters.
where P i is a PK parameter of the ith individual; i is the mean population estimate; ETA ( i ) is the shift of P i from i (inter-individual variability; a random variable assumed to be symmetrically distributed around zero with variance-covariance matrix denoted by diagonal elements (! 2 1 , . . . , ! 2 m , m being the number of parameters)).
The observations were expressed as follows: where OBS ij is the jth observation (laromustine plasma concentration) in the ith individual; i is the set of PK parameters for the ith individual; D i is the administered dose for the ith individual; t ij is the time of collection, after administration, of the jth observation in the ith individual and e ij is the residual shift of the observation from the model prediction (random variable assumed to be symmetrically distributed around 0 with variance 2 ). Different models for residual variability (additive, proportional and combined error model), representing a composite of deviations due to intra(within)-patient variability, assay variability, errors in clinical procedures, and model misspecification errors, as well as logarithmic transformation of observations and predictions were to be tested. The first-order conditional estimation (FOCE) or FOCE with interactions (INTER) were to be tested to identify the most appropriate mixed-effects model (Piotmovsky, 2000). If problems were encountered with the above estimation methods, the first-order (FO) method was to be used. To assess whether the difference in the objective function between hierarchical models statistically improved the fit of the model to the data, a decrease in the objective function (DOFV ! 3.84 (p50.05, 2 , 1 df)), when compared to the simpler model was considered significant. The base model consists of the structural PK parameters, inter-patient variability in each parameter and residual variability, without any COVs. Individual empirical Bayes PK parameter estimates were derived.

Covariate model
The base model that best described the data was used for the evaluation of potential COV relationships. Possible COV relationships were first assessed graphically by plotting individual Bayes PK parameter estimates versus COV and then evaluated through population modeling.
In accordance with regulatory guidelines and usual practice with this class of drugs, the effects of the following COVs, as well as IOV, were to be assessed for their significance and clinical relevance on the parameters of the PK structural model: Demographics: BSA, age, body weight, gender and ethnic origin; Tumor type (hematologic and solid tumors); Kidney function, as assessed by creatinine clearance; Liver function, as assessed by levels of alkaline phosphatase, ALT, AST, LDH, albumin, total proteins and bilirubin. Cycle baseline COV values (pre-dose assessments for each cycle) were used for COV testing. In general, the effect of a continuous COV was to be modeled using equations of the following form, centered on the median baseline of each COV: where i is the mean population estimate and p1 and p2 are parameters associated with changes in each COV. Reduced forms were also to be tested.
The following models were used to evaluate the effect of dose (DOSE, mg/m 2 ) on PK parameters: In general, the effect of a categorical covariate (CCOV) was to be modeled as follows: In the above equations i is the mean population estimate for the most common category (coded as 0), p1 and p2 are parameters associated with changes in categories 1 and 2 of the COV, respectively, and CC1 and CC2 are fixed to 0 if category equals 0, CC1 and CC2 are fixed to 1 and 0, respectively, if category equals 1, and vice versa if category equals 2.
During COV evaluation, missing COV values were assigned to a separate category. If the total number of patients with a missing COV was 15% or higher, this COV was not to be evaluated in the model, or a sub-population with only complete data was to be used for assessing the effect of the particular COV on a PK parameter.
If feasible, a three stage approach was to be followed: In a first step (univariate analysis), the COVs are introduced into the model one at a time. Only the COV model relationships that are deemed significant, as discussed below, are considered for further COV analysis.
In a second step (forward selection), the COV that has the highest significance in the model is included first (base 1 model), and the other significant COVs from the first step are then included one by one, in the rank order of their significance. Only COVs resulting in a significant improvement of the fit are retained and this comprises the most complex model (base 2 model).
In the third step (backward elimination), COVs are removed from the most complex model one at a time in the order of their significance until no further insignificant COVs remained in the model. A COV effect is deemed significant when the criteria are met and in addition: A statistical significant threshold defined as p50.05 ( 2 p=0.05, df=1 =3.84) for forward selection and as p50.01 ( 2 p=0.01, df=1 =6.63) for backward elimination is being met. Standard error of parameter estimates not larger than 50% of the parameter value and the 95% CI do not include zero. If applicable, following the above steps, IOV between cycles was modeled as described by Karlsson and Sheiner (1993).
where P i is a PK parameter of the ith individual; i is the mean population estimate; CYCL 1 , CYCL 2 , CYCL 3 and CYCL 4 are fixed to 1 for the respective cycle and to 0 otherwise; k 1i , k 2i , k 3i and k 4i are random variables, representing the shift of P i from one cycle to another (IOV) and ETA ( i ) represents the shift of P i from p (inter-patient variability). These random variables are assumed to be symmetrically distributed around 0 with identical variance for k 1i , k 2i , k 3i and k 4i , denoted by 2 and with variancecovariance matrix for ETA ( i ) denoted by diagonal elements (! 2 1 , . . . , ! 2 m , m being the number of parameters). Potential sources of IOV might include mechanistic reasons, data collection or study design issues.
The final model contains estimates for the PK parameters and their associated inter-patient variability, estimates of the residual variability as well as COV effects and IOV, if applicable. The possible criteria for accepting the NONMEM model estimation as the final run include the following: A ''successful minimization'' statement by the NONMEM program; The number of significant digits for the precision of the parameter estimate should preferably be !3 for all parameters (also a criterion for successful termination); Parameter estimates should preferably not be close to a boundary; There should preferably be no unacceptable trends in the basic goodness of fit plots; The included COVs should be physiologically and clinically relevant.

Sensitivity analysis
As a final step, any individual concentration records or complete patient profiles excluded from the analysis were to be re-introduced to evaluate the impact of these outliers on the final parameter estimates.

Model evaluation
Goodness of fit, as assessed from scatter plots of individual (IPRED) and population (PRED) predicted against observed laromsutine concentrations (OBS), as well as scatter plots of weighted residuals (WRES) against PRED and against TIME, was used at each step of the analysis for model qualification.
The predictive performance of the PK model was evaluated by applying a visual predictive check (Gelman et al., 1996;Yano et al., 2001). For the predictive check, the population parameters and their associated variability obtained from the final model were used to simulate predicted individual profiles. The same population as that on which the analysis was performed was sampled one thousand times for the range of doses and observed sampling times. The obtained 90% prediction interval was superimposed on the observations to evaluate their distribution with respect to the 90% PI for each dose or COV subpopulation. The percentage of observations falling outside the 90% PI interval overall and for selected doses was calculated and any outliers were identified and discussed.

Analysis of data sets
Serial PK plasma samples (up to nine time points per patient pre-dose and over a 4 h period following single dose laromustine infusion) were obtained from 106 patients at 154 dosing occasions: 105 profiles from first dose exposure (cycle 1), 42 from second dose exposure (cycle 2), four from third dose exposure (cycle 3) and three from fourth dose exposure (cycle 4). There was one quantifiable pre-dose concentration (50.6 mg/L, ID 51, cycle 1, study CLI-029, patient no. 3107-010), which was set to missing. All other pre-dose concentrations were BLQ. The complete dataset included 1151 PK assessments at times ranging from 0.083 to 5.917 h post start of the infusion and 154 dosing records. No demographic COVs were missing. Clinical chemistry baseline COV values were missing for the following parameters (% missing): albumin (4%), protein (6%), bilirubin (2%), alkaline phosphatase (4%), ALT (7%), AST (40%) and LDH (8%). From the 106 patients included in the complete dataset, 65 patients had PK assessments following one cycle only (ID 64: cycle 1; ID 69: cycle 2), 36 patients following two cycles (cycles 1 and 2), three patients following three cycles (ID 3 and 43: cycles 1, 2 and 3; ID 22: cycles 1, 2 and 4) and two patients following four cycles (ID 7 and 23). During preliminary analyses treating each dosing occasion as independent, five individual concentration records during the first cycle of treatment, arising from three AML patients (IDs 84, 89, 90) taking part in study CLI-033, were identified as pharmacokinetically inconsistent (high outliers).
In addition, profiles from AML patient IDs 55 and 65 (study CLI-029) in cycle 1 and patient ID 62 (study CLI-029) DOI: 10.1080DOI: 10. /00498254.2016 in cycle 2 had very high concentrations at serial samples. During preliminary runs it was noted that these profiles interfered with the successful convergence of the minimization procedure and the implementation of the covariance estimation step. The above individual concentration records and all data from patients ID 55 and 65 (cycle 1) were excluded from the analysis. Patient ID 62 cycle 2 profile was also excluded but cycle 1 profile was retained. Thus, the reduced NONMEM analysis dataset included 104 patients, 1122 PK assessments at times ranging from 0.083 to 5.417 h post start of the infusion, and 151 dosing occasions (103 from first dose exposure [cycle 1], 41 from second dose exposure [cycle 2], four from third dose exposure [cycle 3] and three from fourth dose exposure [cycle 4]). Of the 104 patients in the reduced dataset, 64 had PK assessments following one cycle only (ID 63: cycle 1; ID 69: cycle 2), 35 patients following 2 cycles (Cycles 1 and 2), three patients following 3 cycles (IDs 3 and 43: Cycles 1, 2 and 3; ID 22: Cycles 1, 2 and 4) and two patients following 4 cycles (IDs 7 and 23).

Base model development
One, two and three compartment PK models with zero order input, parameterized in clearance and volume terms (ADVAN1 TRANS2, ADVAN3 TRANS4 and ADVAN11 TRANS4, respectively) were tested and a two compartment model was found to best describe the data. Alternative parameterization in terms of V ss (TRANS3) was also tested but failed to converge successfully. Models utilizing untransformed and log-transformed observations and predictions (laromustine concentration) were tested and using untransformed data resulted in a more even random distribution of the weighted residuals, therefore untransformed concentrations were used thereafter.
The FOCE and INTER estimation methods were tested first. However, problems were encountered with the COV step. Convergence of the minimization procedure was highly dependent on initial estimates and in all subsequent analysis the FO estimation method was applied. The distribution of the parameters, when the FO estimation method was used, resembled the log normal distribution. FO method was used as estimation method.
Initially, the complete dataset was used. Exponential error terms for inter-patient variability on all PK parameters and proportional, additive and combined residual variability models were tested. Since bioanalytical assay variability is confounded in the residual variability estimated by the model, the inclusion of separate residual error terms for each method was also tested. During these steps, PK outliers were identified, the presence of which did not permit estimation of the variability terms with adequate precision. These were excluded from the analysis and the above steps were repeated with the reduced dataset. All subsequent analyses were performed using the reduced dataset.
It was not possible to estimate inter-patient variability on inter-compartmental clearance with adequate precision. Further, despite the lower objective function reached when using a model with a separate residual error term for bioanalytical assay VNPHPP and a common residual error term for assays MET010 and QC-T035, no improvement in terms of inter-patient or residual variability was observed versus the simpler model, and a common residual error term for all assays was considered adequate.
The Base model was a two-compartment PK model estimating total clearance (CL), volume of distribution of the central compartment (V 1 ), inter-compartmental clearance (Q) and volume of distribution of the peripheral compartment (V 2 ) (ADVAN3 TRANS4), with exponential error models for inter-patient variability on CL, V 1 and V 2 and a proportional error model for residual variability. The model was fitted to untransformed concentrations using the FO estimation method in NONMEM. The distribution of the parameters when the FO estimation method was used resembled the log normal distribution.
The estimation and COV routines converged successfully and precision in both structural and variance parameter estimates was good. Goodness of fit (GoF) plots of observed (DV) versus predicted laromustine concentrations (population [PRED] and individual [IPRED]) and weighted residuals (WRES) versus TIME and versus PRED plots are plotted. No bias was observed in the DV versus PRED and IPRED plots and there was good agreement between predictions and observations. No trends were observed in the WRES versus TIME plots and randomness was observed in the WRES versus PRED plots. The Base model provided individual empirical Bayesian PK parameter estimates common for all dosing occasions of a given subject by evoking the POSTHOC option in NONMEM, and was used for COV evaluation in conjunction with cycle baseline COV values.

Covariate analysis
Scatterplots of individual empirical Bayes estimates of ETA CL, ETA V 1 and ETA V 2 from the Base model against Dose, BSA, age, body weight, creatinine clearance, and actual levels of serum creatinine, albumin, total proteins, bilirubin, alkaline phosphatase, ALT, AST and LDH were constructed. In addition, box plots of individual empirical Bayes estimates of ETA CL, ETA V 1 and ETA V 2 from the Base model were constructed by phase, cycle, gender, ethnic origin, tumor type and categories (within, above and below normal limits and missing values) for serum creatinine, albumin, total proteins, bilirubin, alkaline phosphatase, ALT, AST, and LDH.
Despite the fact that no obvious relationships were observed from close examination of the plots, the COV evaluation steps were performed in NONMEM for completeness. AST was not evaluated as a COV, since information in this parameter was missing in more than 30% of the subjects. The remaining clinical chemistry parameters were evaluated as CCOVs.
During the single COV analysis, when COVs were introduced into the model one at a time, COV effects were selected for inclusion in the forward selection step if they resulted in a statistically significant reduction of the OFV and model parameters were estimated with adequate precision (95% CI did not include zero). Due to the high correlation between BSA and body weight, when both COVs were identified as significant only BSA was selected, since this class of drugs are commonly dosed based on BSA.
The COV effect that resulted in the greater reduction of the OFV from the single COV analysis was considered the Base1 model for the forward selection step. In this step, the rest of the selected COV effects were introduced into the model in the order of their significance and were only retained if they resulted in a statistically significant reduction of the OFV and model parameters were estimated with adequate precision (95% CI did not include zero).
The model with the effect of tumor type on CL, LDH and serum creatinine on V 2 and age on V 1 comprised the most complex model and was considered the Base2 model for the backward elimination step. During that step, when COV effects were removed one at a time, in the reverse order of their significance, all the above effects caused a significant increase in the OFV; therefore, they were retained in the model.

Inter-occasion variability and model refinement
When examining individual observed and predicted concentrations versus time plots from the Base2 model, despite the inclusion of COVs, some lack of fit was still observed in profiles from patients that had received more than one cycle, indicating that inclusion of IOV should be considered. In addition, when inter-patient and residual variability estimates from Base2 model are compared to those of the Base model, no improvement is observed, indicating that no portion of the variability was explained by the inclusion of the selected COV effects. This was consistent with the lack of trends observed in the ETAs versus COV plots from the Base model.
In the next step, IOV was introduced in the Base2 model, to account for deviations in PK parameters between cycles and to further evaluate the significance of the identified COV effects. Various combinations of IOV variability terms were assigned to CL, V 1 and V 2 , and models were tested allowing IOV either to differ for each parameter or to be the same. Despite the fact that including IOV in the Base2 model resulted in a marked drop in the NONMEM OFV, parameters and inter-patient error terms were not reliably estimated.
Given obvious differences between cycles in the observed profiles from patients that had received more than one cycle and since none of the identified COVs appear to explain part of the inter-patient variability, Base2 model was considered over-parameterized and it was deemed appropriate to revert to the Base model with no COV effects. Inclusion of various combinations of IOV terms was tested and all resulted in marked reductions in the OFV. The model with IOV terms on CL and V 1 resulted in reliable parameter estimates, as well as a reduction in inter-patient and residual variability. Seeking further improvement in variability estimates, the FOCE and INTER estimation methods were employed, however errors were issued from the estimation step and the COV step was either not implemented or aborted.

Final model
The final population PK model for laromustine was a twocompartment PK model with zero order input, parameterized in terms of total clearance (CL), volume of distribution of the central compartment (V 1 ), inter-compartmental clearance (Q) and volume of distribution of the peripheral compartment (V 2 ), with exponential error models for inter-patient variability on CL, V 1 and V 2 , IOV on CL and V 1 and a proportional error model for residual variability. The model was fitted to the untransformed data using the FO estimation method, the estimation and COV routines converged successfully with structural, inter-patient and residual variability parameters estimated with good precision.
Goodness of fit (GoF) plots of observed (OBS) versus predicted laromustine concentrations (population [PRED], and individual [IPRED]) and weighted residuals (WRES) versus TIME and versus PRED for the final model are presented in Figure 2. No bias was observed in the OBS versus PRED and IPRED plots and there was very good agreement between predictions and observations. No trends were observed in the WRES versus TIME plots and there was randomness in the WRES versus PRED plots. Histograms of empirical Bayesian estimates of the parameters for the final model were presented. No significant trends were observed in box-plots and scatter-plots of empirical Bayesian estimates of laromustine PK parameters from the final model against COVs. Specifically, box-plots of estimated and derived PK parameters by Cycle show no differences in laromustine PK parameters between the first and subsequent cycles (n = 103, 41, 4 and 3 for Cycles 1,2, 3 and 4, respectively), suggesting time-linearity in laromustine pharmacokinetics. The lack of trends in scatterplots of estimated and derived PK parameters against dose, suggests dose-linearity in laromustine pharmacokinetics across a broad dose range (3-708 mg/m 2 ).
The population parameter estimates from the final model are presented in Table 2. Laromustine total clearance and volume of distribution of the central compartment were 96.3 L/h and 45.9 L, with inter-patient variability of 52.9% and 79.8%, respectively. This variability could not be explained by any of the tested COVs, while IOV was 26.7% and 49.3% for CL and V 1 , respectively. The population estimates for Q and V 2 were 73.2 L/h and 29.9 L, respectively, and inter-patient variability in V 2 was 63.1%. Structural parameter estimates were similar to those for the Base model while inter-patient variability in CL and V 1, although slightly reduced, still remained high. Residual variability dropped from 36.3% for the Base model to 29.7% for the Final model. Summaries of empirical Bayesian and derived PK parameters for the final model, overall and for Cycles 1 and 2 show no differences in PK parameters between cycles.

Sensitivity analysis
The final model was applied to the complete NONMEM dataset, and while estimation and covariance steps converged successfully, inter-patient variability parameters were not estimated with good precision (%RSE 47-110%). Laromustine population PK parameters were estimated from the final model run including outliers. Differences from the run with the reduced dataset in structural parameter estimates were observed, mainly in Q and V 2 , which 80 and 40% reduced, respectively. Inter-patient variability estimates were inflated by 65-90%, IOV estimates by 130-160% and residual variability by 44% relatively to the run with the reduced dataset.
The results of this analysis supported the decision to exclude a small percent (3%) of the observations that would have had such a large effect on structural and variability parameter estimates. The reason for the three outlying profiles belonging to patient IDs 55, 65 (cycle 1) and 62 (cycle 2) could not be attributed to any of the available COV information as these patients did not share any abnormalities in terms of demographics or organ function.

Model evaluation
Examination of the goodness of fit plots show no bias and very good agreement between predictions and observations, as well as lack of trends and randomness in the residual plots (Figure 2), thus confirming the validity of the model. Visual predictive checks were performed using the Final model for each dose level. Predicted and observed concentrations were grouped by nominal time after the end of the infusion and the % observations outside the respective 90% CI were calculated for each dose level and overall.
The 90% PIs simulated by dose, with observations superimposed, for all dose levels are determined. Overall  The %CV for both inter-patient and residual variability is taken as the square root of the variance Â 100. and for each dose level, the majority of the observations was included in the 90% PI. The 90% PIs simulated by cycle, with observations superimposed for doses 100 mg/m 2 (representing 8.6% of the total observations included in the analysis) and 600 mg/m 2 (28.2% of the total observations included in the analysis) for Cycles 1, 2 and overall are presented in Figures 3  and 4, respectively. These plots confirm the validity of the Final model that assumes the pharmacokinetics of laromustine are independent of dose for the range studied and that any differences in patient profiles between cycles are accounted for by IOV.

Discussion
Considerable variability was associated with the laromustine concentration-time profiles, mainly between patients but also between cycles for the same patient, for all doses. This had been observed during NCA PK analysis of the individual studies. In general, laromustine concentrations appear to decline bi-exponentially following termination of the IV infusion; although, for individual cases associated with the lower doses only, a mono-exponential phase could only be observed. When tested, a two-compartment model was clearly superior to a one-compartment model. A three compartment model was also tested but did not converge successfully. Firstorder conditional and first-order conditional with interactions estimation methods were tested but there were problems with the minimization routine and implementation of the covariance step, therefore the FO method was used throughout. The models were fitted to both untransformed and log-transformed data, however trends were observed in the residual lots when log transformation was used, thus it was decided to proceed with untransformed data. The population PK model for laromustine was thus a twocompartment PK model parameterized in terms of total clearance (CL), volume of distribution of the central compartment (V 1 ), inter-compartmental clearance (Q), and volume of distribution of the peripheral compartment (V 2 ). Exponential error terms were evaluated for inter-patient variability on all structural parameters; however, the term for inter-compartmental clearance (Q) had to be set to zero. Since bioanalytical assay variability is confounded in the residual variability estimated by the model, the inclusion of separate residual error terms for each of the three methods used was also tested but a proportional error model common for all assay methods was found to adequately describe residual variability (representing a composite of model misspecification, assay variability and intra-patient variability).
Demographics (BSA, age, weight, gender and ethnic origin), as well as study Phase, tumor type, dose, and cycle were tested as COVs. Kidney function, as assessed by creatinine clearance, and liver function, as assessed by albumin, total proteins, bilirubin, alkaline phosphatase, ALT and LDH, were also tested. Overall, COV values were quite similar between the first and subsequent cycles, apart from LDH, due to a couple of very high values observed in the first cycle. When plots of individual Bayes empirical estimates of the PK and inter-patient variance parameters from the Base model were examined, no obvious relationships were observed, nevertheless, the full COV evaluation was performed in NONMEM for completion.
Although during the formal COV evaluation a number of effects (Tumor type on CL, LDH and serum creatinine on V 2 and age on V 1 ) were identified as statistically significant, their inclusion did not appear to explain any portion of the interpatient variability in PK parameters, or reduce residual variability. In addition, when IOV was introduced in the model that included COVs, in order to account for differences observed between cycles in individual profiles arising from the same patients, PK parameters and their variability could not be reliably estimated.
Based on the above evaluation it was deemed appropriate to revert to the Base model without COVs, to which IOV was included as an additive term on the variance of CL and V 1 and resulted in a reduction of the residual variability. This was then considered the final population PK model. The population estimates for laromustine total clearance and volume of distribution of the central compartment were 96.3 L/h and 45.9 L, associated with high inter-patient variability of 52.9% and 79.8%, respectively, and IOV 26.7% and 49.3%, respectively. The population estimates for Q and V 2 were 73.2 L/h and 29.9 L, respectively, and inter-patient variability in V 2 was 63.1%. Residual variability was 29.7%.
Following preliminary evaluations, a limited number of individual concentrations and three complete patient profiles were excluded from the analysis since it was thought that they might obscure any potential COV relationships. When these were re-introduced and the Final model was applied to the complete dataset, differences in structural parameters Q and V 2 were observed. The estimates of variability parameters appeared to be inflated and were also not reliably estimated. These results supported the decision to exclude a small percent (3%) of the observations that would have had such a large effect on structural and variability parameter estimates. The reason for the three outlying profiles belonging to patient IDs 55, 65 (cycle 1) and 62 (cycle 2) could not be attributed to any of the available COV information as these patients did not share any abnormalities in terms of demographics or organ function.
The final model was further evaluated using visual predictive checks by dose and 93% of the total observations were included within the 90% PI. For the 100 and 600 mg/m 2 dose, which represent 8.6 and 28.3% of the observations, respectively, at least 89.5% of the observations for each cycle were included within the 90% PI. This confirmed the validity of the Final model that assumes the pharmacokinetics of laromustine are independent of dose for the range studied and that any differences in patient profiles between cycles are accounted for IOV.
Mean NCA analysis estimates of CL and V ss from studies CLI-011 and CL-029, were 95.0 L/h and 60.4 L and 103.1 L/h and 89.6 L, respectively, with coefficient of variation, %CV, ranging from 39 to 74%. Mean NCA analysis estimates of CL and V ss from studies CLI-028, CLI-033 and CLI-043 ranged from 261 to 352 L/h and 206 to 370 L, respectively, with %CV ranging from 70 to 203%. Mean NCA terminal half-life estimates for all five studies ranged from 0.673 to 0.841 h, with a % CV of 18 to 34%.
The population estimate for laromsutine clearance, derived V ss and t 1/2 (96.3 L/h, 75.8 L and 0.684 h respectively) are  similar to those from studies CLI-011 and CL-029, which account for about 60% of the profiles (55% of the patients) included in the analysis. This estimate of systemic clearance is equal to or greater than the human liver blood flow rate (87 L/h) and V ss is double that of total body water (42 L), indicating that laromustine is distributed to tissues. The very high systemic clearance is consistent with extra-hepatic elimination, with rapid, non-enzymatic degradation, also a plausible mechanism.

Conclusions
A two-compartment PK model parameterized in terms of total clearance (CL), volume of distribution of the central compartment (V 1 ), inter-compartmental clearance (Q) and volume of distribution of the peripheral compartment (V 2 ), with exponential error models for inter-patient variability, a proportional error model residual variability and IOV on CL and V 1 adequately described the concentration-time profiles following laromustine infusion. The population estimates for laromustine CL and V 1 were 96.3 L/h and 45.9 L and were associated with high inter-patient variability of 52.9% and 79.8% and IOV of 26.7% and 49.3% for CL and V 1 , respectively. The population estimates for laromustine Q and V 2 were 73.2 L/h and 29.9 L, respectively, and interpatient variability in V 2 was 63.1%. COVs including demographics, dose, cycle, type of tumor, renal function and liver function did not explain any of the variability in laromustine PK parameters. Visual predictive checks using the final model showed that the majority (93.3%) of the observed laromsutine concentrations were within the 90% prediction intervals. The population estimate of systemic clearance is equal to or greater than the human liver blood flow rate, consistent with extra-hepatic elimination or degradation. The estimated V ss (75.8 L) exceeds total body water, indicating that laromsutine is distributed to tissues. The half-life is short, less than 1 h, reflecting the rapid clearance. Population PK analysis showed laromustine pharmacokinetics to be independent of dose and organ function with no effect of subsequent dosing cycles, although considerable inter-patient and IOV was observed.