British Journal of Clinical Pharmacology. Chiara Zecchin 1, Ivelina Gueorguieva 1, Nathan H. Enas 2 and Lena E. Friberg 3

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1 British Journal of Clinical Pharmacology Br J Clin Pharmacol (2016) 1 PHARMACOKINETIC DYNAMIC RELATIONSHIPS Models for change in tumour size, appearance of new lesions and survival probability in patients with advanced epithelial ovarian cancer Correspondence Dr Ivelina Gueorguieva, PhD, Principal Research Scientist, Global PK/PD&Pharmacometrics, Eli Lilly and Company, Sunninghill Road, Windlesham GU20 6PH, UK. Tel.: ; Fax: ; gueorguieva_ivelina@lilly.com Received 8 December 2015; revised 31 March 2016; accepted 28 April 2016 Chiara Zecchin 1, Ivelina Gueorguieva 1, Nathan H. Enas 2 and Lena E. Friberg 3 1 Global PK/PD&Pharmacometrics, Eli Lilly and Company, Windlesham, UK, 2 Research Advisor Statistics-Oncology, Eli Lilly and Company, Indianapolis, USA and 3 Department of Pharmaceutical Biosciences, Uppsala University, Sweden Keywords carboplatin, gemcitabine, metastasis, Phase III AIMS The aims of this study were (i) to develop a modelling framework linking change in tumour size during treatment to survival probability in metastatic ovarian cancer; and (ii) to model the appearance of new lesions and investigate their relationship with survival and disease characteristics. METHODS Data from a randomized Phase III clinical trial comparing carboplatin monotherapy to gemcitabine plus carboplatin combotherapy in 336 patients with metastatic ovarian cancer were used. A population model describing change in tumour size based on drug treatment information was established and its relationship with time to appearance of new lesions and survival were investigated with time to event models. RESULTS Thetumoursizeprofiles were well characterized as evaluated by visual predictive checks. Metastasis in the liver at enrolment and change in tumour size up to week 12 were predictors of time to appearance of new lesions. Survival was predicted based on the patient tumour size and ECOG performance status at enrolment and on appearance of new lesions during treatment and change in tumour size up to week 12. Tumour size and survival data from a separate study were adequately predicted. CONCLUSIONS The proposed models simulate tumour dynamics following treatment and provide a link to the probability of developing new lesions as well as to survival. The models have potential to be used for optimizing the design of late phase clinical trials in metastatic ovarian cancer based on early phase clinical study results and simulation The British Pharmacological Society DOI: /bcp.12994

2 C. Zecchin et al. WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT Change in tumour size (CTS) following chemotherapy has been demonstrated to be predictive of overall survival (OS) in several tumour types and its relationship with drug exposure can be quantified using a drug-disease modelling approach. A corresponding analysis is not available for metastatic ovarian cancer. Such a modelling framework can be used to predict the outcome of a Phase III trial, based on CTS and OS observed in Phase II. The value of including the status of non-target lesions and presence or absence of new lesions during treatment as predictors of survival has recently been investigated for metastatic renal cell carcinoma. WHAT THIS STUDY ADDS The proposed modelling framework established a relationship between CTS, time to appearance of new lesions and OS in patients with metastatic ovarian cancer. The time to development of new lesions was predicted with a time-to-event model including covariates indicating the location of the metastases at enrolment and the tumour size change during treatment. OS probability was predicted using information on tumour size and ECOG status at enrolment and CTS and appearance of new lesions during treatment. Introduction Worldwide, ovarian cancer ranks fifth in cancer deaths among women and is the leading cause of death among all invasive cancers of the female gynaecological system [1 3]. While early diagnosis offers favourable outcome, with a 5-year survival rate of 92% for localized tumours confined to their primary site, the asymptomatic features of early-stage disease lead to frequent diagnosis at later stages. Indeed, 20% of ovarian cancers are diagnosed after spreading to regional lymph nodes and 60% are diagnosed when distant organs have already been metastasized. The 5-year survival rate drops to 73% in the first case and below 30% in the latter case [4]. Despite the demand for new treatments, clinical drug development in oncology has high attrition rates, especially during late phase clinical development, mainly due to the lack of efficacy superior to the standard of care [5, 6]. To be considered superior to the standard of care, a drug must demonstrate significant improvement in overall survival (OS). The use of surrogate endpoints may allow regulatory submission before the survival dataset matures. Commonly used endpoints include progression-free survival (PFS) and overall response rate (ORR), and there is growing interest in investigating how change in tumour size (CTS), which is a marker of cytotoxic drug effects, relates to these endpoints. This calls for the development of paradigms linking quantitative models describing tumour size progression or inhibition to models predicting clinical outcome, in particular OS [7]. Such models may help to predict clinical outcome, based on the observed dynamics of disease progression and, thus, could assist in the design and commitment of Phase III trials, based on CTS observed in Phase II studies [8]. The possibility of predicting the endpoint in Phase III on the basis of modelling and simulation and Phase II results was initially demonstrated for colorectal cancer [9, 10] and non-small-cell lung cancer [11, 12], and has subsequently been suggested for thyroid cancer [8] and for metastatic breast cancer [13]. Identification of the optimal prognostic factors linked to OS is challenging, given the low information in OS data, and it is unclear to what extent the predictors are drug- and/or indication-specific. The value of including the status of nontarget lesions and presence or absence of new lesions during treatment in the analysis has been demonstrated for metastatic renal cell carcinoma [14]. The connection between disease progression and clinical outcome is, potentially, specific for the disease, the therapy and the target treatment population. As a consequence, the relationships linking CTS and other biomarkers to OS probability should be explored for each tumour type of interest, line of treatment and drug therapy. Such an analysis has so far not been reported for metastatic ovarian cancer. Several predictors for OS have been investigated, based on patient baseline characteristics and/or metrics derived from a CTS model. Metrics indicating patient baseline characteristics include TS at baseline, number of lesions, number of organs with lesions, Eastern Cooperative Oncology Group (ECOG) performance status and drug exposure [15]. Metrics derived from CTS models include tumour size ratio (TSR) at a given time point, with respect to baseline, the estimated tumour growth rate constant, time to tumour net growth (TTG) and the full model-based tumour time course [15]. Table S1 summarizes significant predictors of OS for different cancer types published in the literature. It should be noted that when a model-predicted TSR at a fixed time-point has been related to OS in the literature, the TSR prediction has typically relied also on data from later time points. If only a single measurement of TS at week 6 8 (in addition to baseline) were available, the model predicted TSR would likely be a less precise predictor of OS than if determined from all available TS measurements [19]. This limitation will be explored in our analysis. The objectives of the present study were to quantitatively describe tumour size dynamics in patients with advanced epithelial ovarian carcinoma, to investigate the appearance of new lesions during treatment and to use the information extracted from these two models together with the characteristics of the patient at enrolment, to predict OS probability. Methods Data Data used to develop the models were from a randomized Phase III clinical trial comparing carboplatin (Cb) monotherapy to gemcitabine plus carboplatin (GCb) combotherapy in patients with platinum sensitive advanced epithelial ovarian 2 Br J Clin Pharmacol (2016)

3 Modelsfortumoursize,newlesionsandsurvival carcinoma who had failed a first-line platinum-based therapy, with appearance of new tumour lesions after at least 6 months of first-line treatment discontinuation [20, 21]. Data from 336 patients randomized (balancing for patient-level prognostic factors) into one of the two treatment arms were included in our analysis. The primary objective of the study was to compare time to progressive disease in the two treatment arms and the data cut-off point for the final analysis was planned to be after randomization of the last patient and when at least 300 patients had experienced disease progression. Tumour size was computed as the sum of longest diameter (SLD) of all target lesions. Lesions were assessed at baseline and then approximately every 6 weeks by radiological imaging (78%), or ultrasound (20%) or magnetic resonance imaging (2%). The original dataset included 356 subjects. In the current analysis, seven patients that did not receive study therapy (due to patient decision, ineligibility or thrombocytopenia) and 13 patients with all target lesions assessed by physical examination, judged to be less accurate than the other techniques, were excluded. The developed models were evaluated on external data from a randomized Phase II clinical trial [22] enrolling 40 patients with relapsed epithelial ovarian carcinoma who had failed a first-line platinum-based treatment, with appearance of new tumour lesions after at least 6 months of first-line treatment discontinuation. Characteristics of the patients and of the data are summarized in Table S2 and were comparable between the two datasets used to develop and evaluate the models. In the estimation dataset, a median of three measurements per patient, collected during drug treatment, plus the screening measurement were available. Tumour size was the SLD of all target lesions present at baseline. New lesions, detected during treatment, were considered as a separate time-varying dichotomous variable. The lower limit of quantification (LLOQ) for SLD was 5 mm. Measurements below this limit, representing 15% of the observed values, were treated as categorical data, adopting the M3 method [23] and simultaneously modelling of the continuous SLD and the below LLOQ categorical data. Patients in the Cb arm were administered carboplatin intravenouslyonday1every3weeks,inadosecorresponding to a target area under the curve (AUC) of 5.0 mg ml 1 min 1 [24]. Patients in the GCb arm were administered intravenously 1000 mg m 2 of gemcitabine once each week for 2 weeks (days 1 and 8), followed by a week of rest, and carboplatin was given on day 1 after gemcitabine, in a dose corresponding to a target AUC of 4.0 mg ml 1 min 1.Inthe data used for external model evaluation, all patients were assigned to the GCb arm and drugs were administered with the same dose and schedule described for the estimation data. In both treatment arms, patients received up to six cycles of treatment; however, at the discretion of the investigator, selected patients could receive additional cycles (maximum of ten). Patients could discontinue earlier if there was evidence of progressive disease, if unacceptable toxicity occurred, or if the attending physician or the patient requested discontinuation. The treatment of a patient could be postponedforupto2weeksifthepatienthadnotrecoveredfrom toxicity at the planned start of the next cycle. Drug administration restarted immediately after recovery. In case of grade 3 non-hematologic toxicity, successive doses were reduced by 50%. In case of hematologic toxicity, doses were reduced as follows: in the Cb arm carboplatin was reduced to a dose corresponding to a target AUC of 4 mg ml 1 min 1 ;inthegcb arm carboplatin was unchanged while gemcitabine was reduced to 800 mg m 2 ondays1and8forthefirst hematologic toxicity event and it was reduced to 800 mg m 2 on day 1 only after any following hematologic toxicity event. Patients in the GCb arm received 75.6% of the planned mean dose of gemcitabine (92.8% on day 1 and 63.4% on day 8) and 96.2% of the planned dose of carboplatin. Of the planned gemcitabine doses, 10.4% were reduced and 13.7% were omitted; 1.8% of carboplatin planned doses were reduced and 0.2% were omitted. Patients inthecarboplatinarmreceived 98.2% of the planned mean dose with 3.8% of the planned doses reduced. Dose reduction and delays were taken into account to compute exposure to the drug, i.e. dose and AUC were time-varying predictors in the analysis. In the dataset information relating to drug administration dates and doses was recorded, but no pharmacokinetic measurements were available. After discontinuation from treatment, patients continued to be followed for OS. In the estimation dataset, a total of 173 deaths (51% of patients) were reported, while the remaining 163 patients were censored, either because they were lost-to-follow-up (15% of the censored patients), or mainly because of study cut-off (85% of the censored patients) after the study termination criteria was met (300 patients had experienced progression of the disease). In the dataset used for external evaluation, 24 patients died (60%) and 16 (40%) were censored for OS at the end of the study. Individual SLD profiles were heterogeneous in both treatment arms, as illustrated in Figure S1. The majority of patients responded to treatment and a decrease in TS was observed (e.g. ID 1061 and ID 4458). For a few subjects an initial decrease of TS was followed by progression of the disease (e.g. ID 1063 and ID 7323), or no response to treatment was observed and TS remained stable (e.g. ID 4152 and ID 7425) or even increased (e.g. ID 1255 and ID 4487). Model for change in tumour size The starting point for describing change in tumour size during treatment was the model by Claret et al. [9].TheTS dynamics were modelled by an exponential tumour growth, a drug-mediated tumour decrease and a time-dependent resistance to treatment (equations (1) and (2)) dtsðþ t dt ¼ k g TSðÞ k t d ExposureðÞTS t ðþe t λt (1) TSð0Þ ¼ TS BASE (2) where TS(t) is tumour size at time t, TS BASE is the estimated TS at time 0, k g and k d are the tumour growth and death rate constants, respectively, λ is the rate constant related to the half-life of time to drug resistance and Exposure(t)isameasure related to the drug effect at time t. Several measures of drug exposure were investigated: dose, drug concentration and AUC relative to the treatment cycle. Drug exposure was a time-varying covariate for the CTS model and its value was calculated considering delays in treatment and dose reduction. Drug concentration and Br J Clin Pharmacol (2016) 3

4 C. Zecchin et al. AUC were predicted using literature pharmacokinetic models for carboplatin [25] and gemcitabine [26]. A kineticpharmacodynamic (K-PD) approach was evaluated as well, both with separate compartments for each treatment drug and with a common compartment gathering the effect of the two drugs. The presence of a delay in drug effect was tested as well using an effect compartment model. Drugmediated tumour cell death-rate parameters (k d )wereconsidered drug-specific, while the resistance term was evaluated to be either drug-specific or common for the two drugs. An additive and a synergistic model for drug interaction were explored. We did not test an antagonist model for drug interaction, because we did not have any data relating to gemcitabine monotherapy. The individual parameters were assumed to be log-normally distributed. Parameters were removed if estimated to be non-statistically significant. Additive, proportional and combined additive and proportional errors were tested to model the unexplained residual variability for TS. The magnitude of the residual error was assumed to bethesameforthethreemethodsusedtoassesstumourlesions (i.e. radiologic imaging, ultrasound and magnetic resonance imaging). Dropout from SLD assessment was modelled using a parametric time-to-event (TTE) approach. Exponential and Weibull models were investigated and the base parametric model was selected based on visual inspection and objective function value (OFV). Patient-specific covariates tested as predictors for dropout included the tumour growth rate constant (k g ), the tumour size at baseline and a categorical timevarying covariate indicating progression of disease, computed according to the RECIST v1.0 criteria [27]. Models for appearance of new lesions and for overall survival A parametric TTE approach was used to describe both the time-to-observation of appearance of new lesions and for OS. For observation of appearance of new lesions, the time to event was set to be the time of the visit at which a new lesion was detected for the first time. For OS the time after start of treatment until death was set as the time to event. Different parametric TTE models were explored for both types of data, namely exponential, Weibull, Gompertz and loglogistic models. The base parametric model was selected based on visual inspection and the log-likelihood value. Patient-specific covariates as predictors of appearance of new lesions were evaluated using the forward inclusion (P < 0.01, likelihood ratio test) backward elimination (P < 0.005) algorithm [28]. Covariates considered in the analysis are summarized in Table 1. Since one of the aims was linking CTS during treatment to OS, we performed a thorough analysis to determine which covariaterelatedtotswasmostpredictiveofos.theoptimum TSR(week n) time point was evaluated from individual model-predicted TS values ranging from week 6 to week 15. The individual model predicted TS at baseline was used in the calculation of TSR, according to equation (3) Table 1 Predictors assessed in the TTE models for appearance of new lesions and OS Predictor Time to new lesion appearance Overall survival Univariate analysis Multivariate analysis Univariate analysis Multivariate analysis TSR (week n) n [3, 14] P < (best n =12) P < (best n =12) TSR(t) scenario 1 P < 0.01 P > 0.2 TSR(t) scenario 2 P < 0.01 P < 0.01 TSR(t) scenario 3 P < P < P < P < k g P < P < TSbase AverageTSbase P > 0.1 P < P < ECOG P > 0.1 P < P < ARM P > 0.1 P > 0.2 N lesions P > 0.2 P > 0.01 N organs with lesions P > 0.1 P > 0.2 Lesions in the liver (categorical) P < P < P < Platinum free interval P > 0.2 P < Previous treatment with paclitaxel P > 0.03 P > 0.2 Age P > 0.05 P > 0.2 New lesion(t) (categorical) P < P < TSR: tumour size ratio. TS: tumour size. TSR(week n) corresponds to the time constant covariate computed as in equation (3). TSR(t) scenario 1: TSR (t) was computed until the time of the event (appearance of new lesion or death); TSR(t) scenario 2: TSR(t) was computed until the time the patient dropped out from treatment and afterwards the last predicted value on treatment was used; TSR(t) scenario 3: TSR(t) was computed until week 12 and afterwards TSR(week 12) was used. Note that in the time to new lesion analysis, scenarios 1 and 2 coincide. In the univariate analysis (forward inclusion step) predictors were included in the model if dofv was at least 6.6 points (P 0.01). In the multivariate analysis (backward elimination step) a predictor was retained in the model if the OFV increased at least +7.9 points (P 0.005) when it was excluded. Bold p-values indicate a significant predictor. Given the small number of patients with ECOG above 1 at enrolment, values higher than 1 were coded as 1 during the analysis. 4 Br J Clin Pharmacol (2016)

5 Modelsfortumoursize,newlesionsandsurvival TS TSRðweek nþ ¼ c ðweek nþ TS BASE (3) TS BASE where TS(week n) is the model-predicted TS at week n and TS BASE estimated TS at time zero. The predictive power of the timevarying individual model-predicted covariate TSR(t) was also investigated. Three scenarios were compared: (1) TSR(t) was computed until the time of the event (observation of appearance of new lesion or death); (2) TSR(t) was computed until the time the patient dropped out of treatment and afterwards the last predicted value on treatment was used; (3) TSR(t) was computed until week n and afterwards TSR(week n) was used (with n ranging from week 6 to week 15). As mentioned in the introduction, if only a few measurements of TS until week n were available, the model-predicted TSR(week n) would likely be a less precise predictor of OS than when determined from all available TS measurements collected during the clinical trial [19]. To assess the true predictive value of TSR(week n), we estimated the individual parameters (empirical Bayes estimates) of the TS model based on the final model, using fixed population estimates and SLD data until week n only. Afterwards, we evaluated the predictive value of the individual model-predicted TSR(week n) for the OS model. In this analysis we evaluated n = week 6 and week 12 that corresponded, for the majority of the subjects, to completion of two and four treatment cycles, respectively, and to one and two SLD assessment after baseline, respectively. Nonlinear mixed effects model Model development was performed using nonlinear mixed effects modelling. The software NONMEM (version 7.3 by ICON Development Solutions, Ellicott City, MD) with the ADVAN6 subroutine was used [29]. Estimations were made by maximizing the likelihood of the data, using the Laplacian method, with eta-epsilon interaction when appropriate. The simultaneous modelling of continuous and categorical data in NONMEM was accomplished by using the indication variable F_FLAG [29]. Data pre- and post-processing and graphical representations were done in R [30], using the PsN suiteandthexposepackage[31]. Model parameters were estimated sequentially. First, the parameters of the CTS model were determined. Thereafter, the parameters of the models for appearance of new lesions were estimated while fixing the individual PK parameter values (empirical Bayes estimates) estimated in the previous step and assuming no error in parameters (IPP approach). Finally, the parameters of the OS model were similarly estimated using the IPP approach. Simultaneous estimation of the parameters of the models for CTS and TTE for appearance of new lesions and OS was tested using the IPPSE [32] and PPP&D [33] estimation approaches, but did not converge successfully; the estimation was unstable and the covariate selection step could not be performed due to convergence issues. A simultaneous fit might be preferable to minimize bias [34, 35], but we believe the choice of structural model and prediction performance would not be affected. When assessing the predictive performance of the models, all variables were simulated simultaneously. Thus, based on the information on drug treatment and ECOG performance status in the observed dataset, TS time course was predicted and related covariates were used to predict the time to appearance of new lesions. Covariates derived from the models predicting TS and time-to-appearance of new lesion were used to simulate data on OS. Model selection and validation Selection and evaluation of the final model were based on the likelihood value (as customary for nested models), relative standard errors (RSEs), goodness-of-fit plots and simulationbased visual predictive checks (VPCs). The agreement between measured and predicted TS was assessed by evaluating the individual predicted profiles and VPCs were generated to determine the ability of the model to predict the typical trend and variability in the population. The observed values were compared with the 95% confidence interval (CI) around the fifth, median and 95th percentiles of the simulated data. For the appearance of new lesions and OS models Kaplan-Meier VPCs, obtained from 100 simulated replicates of the data, were applied. Therein the 95% CI of the simulated probability of having an event at a given time was compared to the Kaplan-Meier curve derived from the observed data. The ability of the model to predict CTS during treatment and OS probability was also tested on the dataset for external evaluation using VPCs (for further details, see section External model evaluation below). Results Drug effect As no drug concentration data were available, literature PK models were used to predict the drug concentration profile and exposure relative to each dose. The measure of exposure giving the best fit tothetsdatawasthe per-cycle AUC, i.e. the AUC relating to the administered dose, divided by the time interval between the given and the next planned dose, which was applied for the duration of a treatment within a cycle. This exposure measure resulted in lower OFV and better VPCs than when dose or the predicted time profile of drug concentration were assumed to be driving the drug effect. The K-PD approach and the model with the effect compartment accounting for delay in drug effect did not result in an improvement in model fit comparedtousingauc. Model for change in tumour size The final model was defined by the following equation dtsðþ t ¼ k g TSðÞ t ðk dcb AUC Cb ðþþk t dg AUC G ðþ t ÞTSðÞ t (4) dt where AUC Cb and AUC G are carboplatin and gemcitabine percycle AUC, respectively, and k dcb (1/week/AUC Cb )andk dg (1/ week/auc G ) are, respectively, the carboplatin and gemcitabine mediated tumour death rates. The rate constant related to the half-life time to drug resistance, represented by λ in equation (1), was not significantly different from zero and thus omitted from the model. The two drugs were estimated to independently and additively contribute to tumour reduction during treatment. Br J Clin Pharmacol (2016) 5

6 C. Zecchin et al. The between subject variability (BSV) of k dcb and k dg could not be estimated independently, thus the two drugmediated tumour death parameters were assumed to share the same BSV. Correlations between parameters did not improve the OFV and were therefore not included in the final model. The unexplained residual variability for TS(t)wasbest described using an additive error model. Parameter estimates, reported in Table 2, show that the two drug treatments contribute to tumour reduction with comparable effects. k dcb AUC Cb and k dg AUC G were predictedtobeofthesameorderofmagnitudeforatypical patient, with a TS decrease from baseline by 45% in the monotherapyarmandby60%inthecombotherapyarm after the planned six cycles of treatment. The RSEs of typical population parameters and BSV parameters, representative of estimation precision, were all satisfactory and <40% (Table 2). BSV was large, with shrinkages lower than 30%, except for k g (56%). The model predicts sufficiently accurately individual TS profiles (Figure S1), and classical goodness-of-fit plotsdonot show any bias in the model-predicted population TS values (Figure S2). The VPC illustrated in Figure 1 shows a good agreement between the observed and simulated TS values. Dropout from SLD measurement was included in the simulation. Hazard of dropout from SLD assessment was best described by a Weibull function. Significant predictor of dropout was the categorical time-varying covariate indicating progression of disease, computed as per RECIST v1.0 criteria [32]. The model describing the time to dropout was characterized by the hazard function in equation (5) αdrop 1 h Drop ðþ¼λ t Drop α Drop λ Drop t exp ð δpd PDðÞ t Þ (5) where h Drop (t) is the hazard of dropout at time t, λ Drop is the scale parameter, α Drop is the shape parameter and δ PD is the parameter associated with the categorical time-varying covariate indicating progression of disease. Model for appearance of new lesions A Weibull model best described the hazard of appearance of new lesions. Significant predictors of new lesions in the multivariate model were the presence of liver metastasis at enrolment and TSR(t)fort < week 12 and TSR(week 12)fort week 12 (scenario 3 described in the section Models for appearance of new lesions and for overall survival ), indicated as TSR(t) inequation(6)and in Table 2 for simplicity of notation (Table 1). The final model describing the time to observation of appearance of new lesions was thereby characterized by the hazard function reported in equation (6) h NewLes ðþ¼λ t NewLes α NewLes ðλ NewLes t exp β TSRðÞ t TSRðÞþβ t LIVER Liver 0 Þ αnewles 1 where h NewLes (t) is the hazard of having a new lesion at time t, λ NewLes is the scale parameter, α NewLes is the shape parameter, β TSR(t) is the parameter associated with the model predicted TSR (t) andβ LIVER is the parameter associated with the dichotomous covariate indicating the presence of liver metastasis at enrolment (Liver 0 ). Parameter values (Table 2) indicate that patients with a (6) Table 2 Parameter estimates Parameter (unit) Estimate RSE (%) BSV (CV%) RSE BSV (%) Model for CTS k g (1/week) k dcb (1/week /AUC Cb ) k dg (1/week /AUC G ) TS BASE (mm) TS res err (mm) Model for dropout from SLD assessment λ Drop α Drop δ PD Model for new lesion appearance λ NewLes α NewLes β TSR(t) β LIVER Shrinkage (%) Model for OS λ OS α OS γ NewLes(t) γ TSR(t) γ SLD γ ECOG BSV, between-subjects variability; CV, coefficient of variation; RSE, relative standard error; k g, tumour growth rate; k dcb, carboplatinmediated tumour death rate; k dg, gemcitabine mediated tumour death rate; TS BASE, tumour size at baseline; λ Drop,scaleparameterfor Weibull function describing the hazard of drop-out from SLD assessment (timescale of weeks); α Drop, shape parameter for Weibull function describing the hazard of dropout from SLD assessment; δ PD, parameter associated with the categorical time-varying covariate indicating progression of disease, computed as per RECIST v1.0 criteria [29]; λ NewLes, scale parameter for Weibull function describing the hazard of appearance of new lesions (timescale of weeks); α NewLes, shape parameter for Weibull function describing the hazard of appearance of new lesions; β TSR(t), parameter associated with TSR(t); β LIVER, parameter associated with presence of metastasis in the liver at baseline; λ OS,scale parameter for Weibull function describing the hazard of death (timescale of months); α OS, shape parameter for Weibull function describing the hazard of death; γ NewLes(t), parameter associated with appearance of new lesions; γ TSR(t), parameter associated with TSR(t); γ SLD0,parameter associated with SLD at baseline; γ ECOG, parameter associated with ECOG status at enrolment. more pronounced reduction of TS have a lower hazard to acquire new lesions, while patients whose baseline lesions don t respond to treatment have a higher probability of developing new lesions. Furthermore, the presence of liver metastasis at baseline was associated with a 70% higher hazard to acquire new lesions. The model for appearance of new lesions adequately described the observed Kaplan-Meier curves as shown in VPC (Figure 2). 6 Br J Clin Pharmacol (2016)

7 Modelsfortumoursize,newlesionsandsurvival Figure 2 Visual predictive check (VPC) for the Kaplan-Meier new lesion-free survival curve (based on 100 simulations). The observed Kaplan- Meier curve (solid line) is compared to the 95% confidence interval (green area) derived from model simulations of the parametric model predicting the time-to-new lesion appearance Figure 1 Visual predictive check (VPC) of the model capacity of predicting change in tumour size (CTS) during treatment (based on 500 simulations). Top panel: TS values are plotted vs. time. The red area represents the 95% confidence interval (CI) of the 50th percentile of simulated data. The blue areas represent the 95% CI of the 5th and 95th percentiles of simulated data. Red lines represent the median (solid line) and the 95th percentiles (dashed lines) of the observations. The 5th percentile of the observations is not plotted because it lies below the lower limit of quantification (LLOQ). Blue dots represent the observations. The grey horizontal line represents the LLOQ. Bottom panel: the proportion of TS data below the LLOQ vs. time. The blue area represents the 95% CI of the proportion of simulated TS below the LLOQ. The blue line represents the proportion of observed data below the LLOQ. In the simulation a dropout model was included. Dropout from SLD assessment was modelled using a TTE approach, with baseline hazard of dropping out described by a Weibull function and a categorical time varying covariate indicating progression of disease, computed according to the RECIST v1.0 criteria, as predictor [27] Since new lesions could be detected only during planned visits for SLD assessment, the simulation dataset was created to reproduce the visit schedule observed in the data and predicted new lesion events were allowed to be observed only during preplanned visits, i.e. approximately every 6 weeks. Model for overall survival A Weibull model best described the hazard of death. In the multivariate model, significant predictors of OS were TSR(t) for t < week 12 and TSR(week12)fort week 12 (scenario 3 described in the section Models for appearance of new lesions and for overall survival ), indicated as TSR(t) inequation(7) and in Table 2 for simplicity of notation, appearance of new lesions during treatment, TS at baseline and ECOG status at enrolment (Table 1). In the final model, the death hazard was described by equation (7) h death ðþ¼λ t OS α OS ðλ OS tþ αos 1 expðγ NewLesðÞ t NewLesðÞ t þγ TSRðÞ t TSRðÞþγ t SLD0 SLD 0 þ γ ECOG ECOGÞ where h death (t) is the hazard of death at time t, λ OS is the scale parameter, α OS is the shape parameter and γ NewLes(t) is the parameter associated with the appearance of new lesions (NewLes(t)), γ TSR(t) is the parameter associated with the model-predicted TSR(t), γ SLD0 is the parameter associated with SLD at baseline and γ ECOG is the parameter relating to ECOG status at beginning of treatment. Parameter estimates (Table 2) predict that the hazard of death of the individual more than tripled from the time instant a new lesion appears. An ECOG performance status above 0 was also a strong predictor of poor survival probability. The TSR during treatment and the baseline SLD were less strong predictors of OS, although statistically significant. A higher relative reduction of TS was associated with lower hazard of death and thereby a higher survival probability. Low SLD at the start of treatment was also related to a higher survival probability. TSR(t) computed as in scenario 1 was not a significant predictor of OS. This scenario relies on the model s capability to extrapolate the tumour size time course after the end of treatment, i.e. exponential growth in this case (a more complex tumour growth model was not supported by theavailabledata).tsr(t) computedasinscenario2wasa significant predictor of OS; however, TSR(t) computedasin scenario (3) was the most significant predictor in terms of OFV ( 5.8 points with respect to scenario 2 and 24.7 points with respect to scenario 1). Scenarios 2 and 3 assume that only the initial response is important for OS, but on the other hand they do not rely on post-treatment extrapolations. (7) Br J Clin Pharmacol (2016) 7

8 C. Zecchin et al. Figure 3 Visual predictive check (VPC) for the Kaplan-Meier overall survival (OS) curve (based on 100 simulations). The observed Kaplan-Meier curve (solid line) is compared to the 95% confidence interval (green area) derived from model simulations of the parametric model predicting OS probability The OS model adequately described the observed Kaplan- MeiercurvesasshowninVPC(Figure3).Theeffectsofcovariates on OS were adequately captured by the model as shown in VPCs stratified by covariates (Figure S3). Table S3 reports median OS and the 95% CIs of OS in the estimation dataset and median model-predicted OS and the 95% CIs of modelpredicted OS, stratified by covariate values. When the individual parameters (empirical Bayes estimates) of the CTS model were determined based on the final model, using fixed population estimates and SLD data until week n only, the individual model-predicted TSR at week 12 remained a significant (though less strong) predictor of OS. These results indicate that given the developed CTS model and its population parameter, the model-predicted individual TSR at week 12 would remain asignificant predictor of OS even if SLD were assessed only at baseline and at weeks 6 and 12 and no SLD data after week 12 were available. External model evaluation TheCTSmodeladequatelypredictedtheTStimecourseobserved in the study used for external evaluation, as indicated by the VPC (Figure 4). The predicted OS probability was also consistent with the Kaplan-Meier curve derived from the observed data (Figure 5). OS was slightly underestimated in the time interval (7 11) months. Notably, in the data used for external evaluation, the first death occurred at month 8 (day 241), while in the dataset used to develop the model, 14% of the patients had died or were censored for OS before that time. Only five patients in the study used for external evaluation had new lesions during treatment and this number was considered not sufficient to robustly assess the performance of the developed model describing the time to appearance of new lesions on the external dataset. Figure 4 External model evaluation. Visual predictive check (VPC) of the ability of the model to predict change in tumour size (CTS) when applied to a different study (based on 500 simulations). Top panel: TS values are plotted vs. time. The red area represents the 95% confidence interval (CI) of the 50th percentile of simulated data. The blue areas represent the 95% CI of the 10th and 90th percentiles of simulated data. Red lines represent the median (solid line) and the 10th and 90th percentiles (dashed lines) of the observations. Blue dots represent the observations. The grey horizontal line represents the lower limit of quantification (LLOQ). Bottom panel: the proportion of TS data below the LLOQ is plotted vs. time.thebluearearepresents the 80% CI of the proportion of simulated TS below the LLOQ. The blue line represents the proportion of observed data below the LLOQ Discussion In this analysis, models describing CTS during treatment and TTE models for appearance of new lesions and survival probability were developed for metastatic ovarian cancer. Relating potential biomarkers, such as change in tumour size and appearance of new lesions during drug treatment, to probability of survival of patients is of great value. Such models could support the design of Phase III trials, based on data observed in Phase II clinical studies [9] and on earlier derived models specific for the disease area. Optimizing Phase III trials could be performed via selection of important prognostic factors for patient stratification, using modelling to increase statistical power for detecting important treatment effects without increasing sample size, and using early OS-predictive endpoints to enable more timely registration of novel therapies by regulatory agencies. In the proposed model describing CTS during chemotherapy, tumour growth was best described as exponential where 8 Br J Clin Pharmacol (2016)

9 Modelsfortumoursize,newlesionsandsurvival Figure 5 External model validation. Visual predictive check for the OS model, applied to a new study (based on 100 simulations). The observed Kaplan-Meier curve (solid line) is compared to the 80% confidence interval (green area) derived from simulation from the model the estimated k g ( week -1 )wasofthesameorderof magnitude as the tumour growth rate reported for thyroid cancer ( week -1 [36]) and metastatic breast cancer ( week -1 [13]) but resulted in a slower growth compared to what has been estimated for gastrointestinal stromal tumour ( week -1 [17]; week -1 [18]), metastaticrenalcellcarcinoma(0.0255week -1 [18]) and colorectal cancer treated with capecitabine (0.021 week -1 ) or fluoruracil and leucovorin (0.015 week -1 ) [9]. This could reflect the less aggressive nature of platinum sensitive ovarian cancer compared to the latter cancer types or could be due to the high uncertainty with which k g is often estimated, because of the general lack of data relating to TS net growth and the rare occurrence of a pure placebo arm in oncology trials. Carboplatin and gemcitabine were estimated to contribute to tumour reduction at the administered doses with comparable independent additive effects. The BSV of the estimated parameter values was high. This reflects in part theheterogeneityofthedataandinpartisduetotheuseof model predicted values of AUC as a measure of drug exposure, instead of the actual individual PK of the drugs that was not available in the dataset. The development of resistance to drug treatment over time was not supported by the data. This is likely due to the limited amount of data that shows an initial response followed by progression. The model provided realistic prediction of individual tumour size profiles, and simulation-based diagnostics (Figure 1) illustrated that the CTS model, combined with a dropout model, can adequately reproduce the distribution of observed data. The CTS model could adequately reproduce the distribution of data from patients with same tumour type, line of treatment and drug therapy in the external dataset (Figure 4), further supporting the use of the model for future trial design. Survival was best described by a parametric TTE model incorporating information on TSR during treatment, SLD at baseline, appearance of new lesions during treatment and ECOG performance status at enrolment. The model captured the pronounced reduction in life expectancy once new lesions appeared (Figure S3) with median OS of 21 vs. 12 months, for patients not developing any new lesion vs.developing new lesions. ECOG performance status also had a strong influence on survival (Figure S3), as reported by others for other indications [8, 11, 16, 37, 38]. Additional significant covariates for OS were the SLD at enrolment and the predicted TSR(t) (Figures S3), in line with what has been reported previously [8, 11 13]. The presence of liver metastasis at enrolment highly increased the probability of developing new lesions early during treatment (70% higher hazard of new lesions). Another factor associated with a shorter time to development of new lesions was a reduced decrease of the tumour burden during the first months of drug treatment. To evaluate the potential of the model to predict survival based on SLD measurements up to week 12 only, we fixed the population parameters of the CTS model to their optimal value and we determined the individual parameters (empirical Bayes estimates) using SLD data until week 12 only. The individual model-predicted TSR at week 12 was then used to predict OS. Results were satisfactory. The aim of our analysis was not to suggest stopping the assessment of SLD at week 12; indeed, if SLD measurements over a longer time span are available, a more precise TSR can be predicted using the SLD model and survival can be predicted more accurately. However, results suggest a few early assessments of SLD could be used to robustly predict a patient s OS probability in clinical practice and the treatment could be modified based on this information in case of short predicted survival. The developed models undoubtedly simplify the reality of the actual biological processes. The model we proposed for describing CTS, for example, assumes there is no delay in the drug-related reduction in tumour size. While we are aware that a delayed response is physiologically more plausible, the sparseness of measured tumour size data did not allow us to robustly estimate delays and dynamics in the effect of the therapy and a simplified model structure had to be adopted. A limitation of the study is that we retrospectively studied the optimal time point (12 weeks), until which change in tumour size is predictive of appearance of new lesions and survival. Results are influenced by trial protocol and we cannot know if different time points would have been optimal for measuring change in tumour size if the study protocol were different. Another limitation is that tumour size is the sumoflongestdiametersofmetastasesindifferentorgans. As a consequence, the analysis could not detect the dynamics of individual lesions in different organs and we could not investigate potential relationships between the dynamics of individual lesions and survival. In conclusion, the modelling framework described here captures SLD evolution during drug treatment and links its time course to the probability of developing new lesions as well as to survival expectancy in patients with platinum sensitive metastatic ovarian cancer. To our knowledge, this analysis is the first to investigate the relationship between SLD time course and OS in ovarian cancer. In addition, this is the first contribution on a pharmacometric model for the time to appearance of new lesions, which included exploration of patient characteristics at enrolment and TS time Br J Clin Pharmacol (2016) 9

10 C. Zecchin et al. course as predictors. The strong correlation characterized between the appearance of new lesions and OS highlighted the importance of monitoring not only the evolution of the target lesions detected at enrolment, but also the development of new lesions and, possibly, the status of non-target lesions during drug treatment. Finally, the ability of modelbased simulations to adequately reproduce TS profiles and survival probability observed in an external study suggest the models could effectively help to simulate and optimize future clinical trials in ovarian cancer. The NONMEM code of the models described in this manuscript and simulated realistic datasets are available in the DDMoRe model repository (repository.ddmore.eu/models). Competing Interest All authors have completed the Unified Competing Interest form at (available on request from the corresponding author) and declare: no support from any organization for the submitted work; CZ, IG and NHE were employees of Eli Lilly and Company in the previous 3 years; no other relationships or activities that could appear to have influenced the submitted work. The research leading to these results has received support from the Innovative Medicine Initiative Joint Undertaking under grant agreement no , resources of which are composed of financial contributions from the European Union s Seventh Framework Programme (FP7/ ) and EFPIA companies in kind contribution. The DDMoRe project is also supported by financial contribution from Academic and SME partners. This work does not necessarily represent the view of all DDMoRe partners. LEF also received support from the Swedish Cancer Society. Contributors All authors contributed extensively to the work presented in this paper. CZ analysed the data, implemented the simulation models and analysed the results. NHE assembled input data and pre-analysed the data. IG and LEF supervised the project. LEF gave technical support and IGandLEFgaveconceptual advice. All authors discussed the results and implications, wrote and commented on the manuscript at all stages. References 1 Chen YB. MedlinePlus [Internet]. Leukemia/Bone Marrow Transplant Program, Massachusetts General Hospital, Boston, MA, Available at: ency/article/ htm (updated 2015 November 19; last accessed 26 November 2015). 2 American Cancer Society. Cancer Facts and Figures 2014, American Cancer Society, Atlanta, Available at: cancer.org/acs/groups/content/@research/documents/ webcontent/acspc pdf (last accessed 24 May 2016). 3 Jemal A, Bray F, Center MM, Ferlay J, Ward E, Forman D. Global cancer statistics. 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