Ethics statement

Murine studies in the UK were conducted in accordance with UK Home Office legislation, the Animal Scientific Procedures Act 1986, the AstraZeneca Global Bioethics policy or Institutional Animal Care and Use Committee guidelines. Experimental work is outlined in project license PP3292652.

Pharmacokinetic and tumour xenograft studies

Plasma concentration data obtained after single or multiple intravenous and oral dosage of AZD7648 and/or olaparib to SCID and Nude mice were obtained from a total of eight studies. Details on the design, execution and analysis of these PK study data have been reported before [3] (Fok et al.). Briefly, Immunocompromised SCID (C.B-17/IcrHan®Hsd-Prkdcscid) or Hsd:Athymic Nude-Foxn1nu female mice (Envigo) were used for PK studies of AZD7648 and Olaparib. Blood samples were taken via venipuncture of the tail vein. 20 ul whole blood was taken per time point and mixed 1:5 with PBS and centrifuged at 1500g for 3 min at 4 °C, and the plasma was extracted and frozen at − 80°C. In total a maximum of 100ul whole blood was taken over a 24 h period.

Each plasma sample was prepared using an appropriate dilution factor, and compared against an 11 point standard calibration curve (1–10,000 nM) prepared in DMSO and spiked into blank plasma. Protein precipitation was carried out by the addition of 4 volumes of ice cold acetonitrile containing the internal standard followed by shaking for 10 min and centrifugation at 3000 rpm for 10 min. Supernatant was then diluted in six volumes of water and analyzed via UPLC-MS/MS. Performance criteria used were % CV values of ± 25% and an LLOQ of 0.009nM for both olaparib and AZD7648. Data on xenograft growth, inhibition and regression were obtained from four in vivo studies. Xenograft studies using the FaDu ATM KO model was established by implantation of 100 μL of a cell suspension subcutaneously into the dorsal left flank of female severe combined immunodeficient (SCID) (C.B-17/IcrHan®Hsd-Prkdcscid) mice of at least 6 weeks of age. Tumours were measured (length x width) by bilateral Vernier calliper measurements and tumour volume calculated using Mousetrap software. Mice were randomized into treatment groups when mean tumour volume reached ~ 0.2 cm3. AZD7648 was formulated in 0.5% hydroxypropyl methylcellulose (HPMC)/0.1% Tween80 (HPMC/T) and orally dosed. Olaparib was formulated in 10% DMSO/30% Kleptose and orally dosed at 100 mg/kg once daily. Olaparib was dosed 1 h after the morning dose of AZD7648 or its vehicle HPMC/T in all combination studies. Tumour growth inhibition from start of treatment was assessed by comparison of the mean change in tumour volume for the control and treated groups, using the Mousetrap application and represented as tumour growth inhibition (TGI).

Computation and model development

The population PK and PK–PD analysis was performed by means of non-linear mixed-effects modelling as implemented in the NONMEM software package (version 7 level 4.3; Icon Development Solutions, Ellicott City, Maryland, USA) in combination with PsN (version 4.7.0). Gfortran (version 4.6.0) was used as compiler. Diagnostic graphics, exploratory analyses, and post-processing of NONMEM output were performed using R (version 3.4.4, The R foundation for Statistical Computing) and Rstudio (version 1.1.463, Rstudio Inc, Boston, USA) used in conjunction with a custom-built modelling interface. Calculations and computations were run on an Intel CITM i7-7700 CPU @ 3.60 GHz. Differential equations were solved numerically in NONMEM using ADVAN6 or 13. The first-order conditional estimation method with interaction (FOCEI) was used for parameters estimation [14, 15].

Population PK and PK–PD analyses are based on the assumption that treatment effects in living organisms are dependent on the drug concentration which changes over time after a dose is given. These changes can be captured as a function of time and exposure by a combination of fixed effect parameters (e.g. clearance and distribution volume) and two levels of random effect parameters: one for biological variability between individual subjects (intra-individual variability, IIV) and one level of variability within each subject, due to e.g. measurement errors, model misspecification and other sources of residual variability. Random effects for inter-individual variability were described using exponential terms reflecting log-normal distributions of model parameters. Residual variability was explored with a proportional error model on PK and PD observations [16, 17]. Goodness of model Fit to the data (GoF) was evaluated continuously during PK and PK model development by various diagnostic metrics [18, 19].

PK model

A 2-compartment model with 1st order absorption and a mixed linear/non-linear clearance was used to describe AZD7648 pharmacokinetics

$$\begin \frac} & = K_ \cdot A_ - Q \cdot \frac }} + Q \cdot \frac }} \\ & \quad - \left( }} + \left( }} + Km}}} \right)} \right) \\ \end$$

(1)

$$\frac} = Q \cdot \frac }} - Q \cdot \frac }}$$

(2)

where Ka is the absorption rate, Ag is the amount of drug in gut (µmol), Q is the intercompartmental clearance, A1 is the quantity of AZD7648 in the central compartment (µmol), A2 is the quantity of AZD7648 in the peripheral compartment (µmol), Cp,AZ is the concentration of AZD7648 in plasma, Vc and Vp are the volumes of distribution in the central and peripheral compartments, Cl is the linear clearance, Vmax is the maximal elimination rate and Km is the concentration at half maximal elimination.

Similarly, olaparib was described by a 2 compartment model with 1st order oral absorption and linear clearance. An additional interaction term was included to account for the observed drop in clearance when in combination with AZD7648:

$$\frac} = K_ \cdot A_ - Q \cdot \frac }} + Q \cdot \frac }} - \left( }} \right) \cdot CmS$$

(4)

$$\frac} = Q \cdot \frac }} - Q \cdot \frac }}$$

(5)

$$Cms = 1\quad if\;\,Dose_ = 0$$

(7)

$$Cms = 1 - \frac }} + CmD50}}\quad if\;\, Dose_ > 0$$

(8)

where A3 is the amount of olaparib in the central compartment (µmol), A4 is the amount of olaparib in the peripheral compartment (µmol), Cp,olap is the concentration of olaparib in plasma, Cms is the combination interaction term, DoseAZ is the dose of AZD7648 (mg/kg/day) and CmD50 is the daily dose of AZD7648 that reduces clearance by 50%. All parameter values are listed in Tables 1 and 2 and the model code is provided in the supplementary materials.

Table 1 Parameters of the population PK model for AZD7648 in SCID and nude miceTable 2 Parameters of the population PK model for olaparib in SCID and Nude miceTumor PK–PD model

Tumor volume was described by a proliferating cell compartment (Prol), quiescent cell compartment (Quiesc), and two dying cell compartments (ApopI/II). Untreated tumor cells undergo logistic growth described by the growth rate (GC) and carrying capacity (KC). Treatment with olaparib causes proliferating cells to enter a reversible DNA-damage induced quiescent state, where cells can irreversibly transition to damaged states before dying. Quiescent cells undergo DNA repair through NHEJ, which can be inhibited by AZD7648:

$$_=Prol+Quiesc+ApopI+ApopII$$

(9)

$$\begin \frac} & = Prol \cdot GC \cdot \left[ }}} \right) \cdot \frac }}} \right] \\ & \quad \cdot AlleeEff - OlEff \cdot K_ \cdot Prol \\ & \quad + AzEff \cdot K_ \cdot Quiesc \\ }\left( 0 \right) & = } \\ \end$$

(10)

$$\begin \frac} & = - K_ \cdot Quiesc + OlEff \cdot K_ \\ & \quad \cdot Prol - AzEff \cdot K_ \cdot Quiesc \\ }\left( 0 \right) & = 0 \\ \end$$

(11)

$$\frac} = K_ \cdot Quiesc - Apop I \cdot K_ \quad }\left( 0 \right) = 0$$

(12)

$$\frac} = K_ \cdot Apop I - Apop II \cdot K_ \quad }\left( 0 \right) = 0$$

(13)

where TXeno is the total tumor volume, BL is the initial tumor volume, Kto is the turnover rate constant for various transitions, GC is the tumor growth rate, and KC is the carrying capacity. The effects of olaparib (OlEff) and AZD7648 (AZEff) on tumor cells were described using biophase concentrations Ce,Olap and CeAZ to account for the delay between pharmacokinetics and pharmacological effect. The olaparib effect was best described by a linear function, while AZD7648 was best described by a sigmoidal function:

$$\frac_}=_\cdot \left(_-_\right)$$

(14)

$$\frac_}=_\cdot \left(_-_\right)$$

(15)

$$AzEff=1 - \frac_}_+_}$$

(17)

where Ce,Olap and Ce,AZ are the effective concentrations of olaparib and AZD7648 in the biophase compartment, Cp,Olap and Cp,AZ are the plasma concentrations of olaparib and AZD7648, Ktr is the transit rate constant for biophase distribution, EColap is the linear effect coefficient for olaparib, and EC50AZ is the concentration to illicit 50% inhibition of transition from Quiesc to Prol.

Additionally, an Allee effect term was added to the proliferating compartment to account for non-linear growth and regressions, which was described by sigmoidal function

$$AlleeEff=\frac^}^+AE^}$$

(18)

where AEc is the proliferative cell mass that corresponds to 50% effect and G is the slope.

PK analysis for AZD7648 and/or olaparib in mice

Plasma concentration data after single or multiple oral dosage of AZD7648 and olaparib as mono- or combination therapy in SCID and nude mice were pooled in a single comprehensive dataset to allow for population PK analysis according to NONMEM required data formatting. In the PK analysis, the data were subjected to compartmental PK analyses, with two-compartment distribution, first order absorption from a dose compartment with linear and/or Michaelis–Menten elimination from the central compartment.

PK–PD analysis for tumour growth inhibition (TGI)

Xenograft growth data over time were collected from two studies in (SCID) mice that were combined in a single PK–PD dataset and assigned to model-calibration and validation subsets (Table S1). Unperturbed xenograft growth was analysed by fitting the logistic Verhulst model to xenograft data from vehicle-treated control animals.

The calibration dataset for PK–PD model development consisted of xenograft data from one study in which eight animal groups received either active treatment QID with 50–100 mg/kg AZD7648 and/or 50–100 mg/kg olaparib for a period of 4 weeks, followed by a wash-out phase of up to eight weeks (Fig. S3). Control groups were treated with vehicle continuously for 4 weeks.

The validation subset consisted of a mouse study, in which eight groups of animals were treated during six weeks according to various dose schedules, partially following subsequent active treatment/recovery phases, summarized in Table S1 with raw results visualized in Fig. S6.

Xenograft growth and turn-over was postulated based on the family of indirect response models [20], according to various papers from the literature on pre-clinical oncology models [10, 21] and a priori knowledge on the mechanism of action for both compounds.

The primary xenograft cell state was described by two compartments represent either proliferative or apoptotic cell states. Transit compartments were applied for delay between apoptosis and cell death resulting in loss of xenograft volume. Olaparib stimulates cell transition from a proliferative to an apoptotic state and AZD7648 acts by inhibiting transition of cells from an apoptotic to a proliferative state. System- and drug-specific model parameters were iteratively optimised by simultaneous fitting of model parameters to all eight treatment groups in S1822. The model structure was expanded and refined by learning from the data through population-based model development, based on forward addition/backward deletion of fixed and random effects with diagnostic analyses of the residuals between observations and model-predictions [18].

During the entire model development process, various assumptions on rate constants for xenograft cell dynamics were tested to identify rate-limiting steps and reduce parameter space when necessary and if possible.

For optimal system and drug-specific parameter identification, PK–PD model development was performed by sequential and simultaneous fitting to data from control, single and combination treatment groups reported in study S1822, which served as the main model calibration dataset.

Model evaluation

Goodness-of-fit was determined using the minimum value of the objective function (MVOF) defined as minus twice the log-likelihood. For nested models, a decrease of 10.8 points in the MVOF (corresponding to p < 0.001 in a chi-squared distribution) after adding an additional parameter was considered significant. The goodness-of-fit was also investigated by visual inspection of the plots of individual predictions and the diagnostic plots of (weighted) residuals. In addition, visual predictive checks (VPC) were performed in which the median and the 95% prediction interval of data simulated with the developed model (N = 200) were plotted together with the observations [18].