ORIGINAL RESEARCH ARTICLE

Clin Pharmacokinet 2006; 45 (2): 177-197 0312-5963/06/0002-0177/$39.95/0 © 2006 Adis Data Information BV. All rights reserved.

Role of Mechanistically-Based Pharmacokinetic/Pharmacodynamic Models in Drug Development A Case Study of a Therapeutic Protein Scott Marshall,1 Fiona Macintyre,1 Ian James,1 Michael Krams2 and Niclas E. Jonsson3 1 2 3

Department of Clinical Pharmacology, Pfizer Global Research and Development, Sandwich, UK Department of Experimental Medicine, Pfizer Global Research and Development, Groton, Connecticut, USA Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden

Abstract

Background and objective: This case study describes the pharmacokinetic and pharmacodynamic modelling undertaken during the development programme for UK-279,276 (neutrophil inhibitory factor), focusing on the transition from early empirical-based models to a final mechanistic-based model. UK-279,276 binds to the CD11b/CD18 (MAC-1) on neutrophils and was under development for the treatment of ischaemic stroke. Methods: The aims, data, models, results and value-to-drug development processs across four stages of model development are described: (i) the validation of the pharmacokinetic assay; (ii) the development and application of an empirical patient pharmacokinetic/pharmacodynamic model; (iii) the development of a mechanistic-based model to bridge between patients and healthy volunteers; and (iv) propagation of the stage III model to a large efficacy study. The analyses utilised available concentration measurements (stages I–IV), CD11b receptor occupancy data (stages I–III) and neutrophil count data (stages III–IV) from three healthy volunteers (study 1, n = 51; study 2, n = 31; study 4, n = 15) and two patient studies (study 3, n = 169; study 5, n = 992). In studies 1–4, subjects received placebo or between three and six doses of UK-279,276 covering a range of 0.006 and 1.5 mg/kg as a single 15-minute intravenous infusion. In study 5, subjects received placebo or one of 15 possible doses of UK-279,276 (10–20mg) assigned through adaptive design and administered as a single 15-minute intravenous infusion. All model building was conducted using NONMEM version VI (beta). The empirical pharmacokinetic/pharmacodynamic model developed during stage I was used to demonstrate that the pharmacokinetic assay was measuring biologically active drug. Simulations from the stage II model, developed from study 3, were used in the design of study 5. The model supported the switch to a fixed-dose regimen and the selection of the maximum dose and dosage increments. The common mechanistic-based model developed during stage III was

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used to support the ‘comparability strategy’ for UK-279,276 and provided insight into the underlying clearance mechanisms. At stage 4, the prior functionality available with NONMEM was used to successfully propagate the model from stage III in order to analyse the pharmacokinetic data from study 5. The analysis indicated that the exposure in study 5 was consistent with prior data. The role of empirical-based models in providing the learning for future mechanistic model development was highlighted. Similarly, the qualitative and quantitative aspects to knowledge propagation and the ultimate benefits from the development of the mechanistic-based model were demonstrated. While the empirical-based models were used to guide some early drug development decisions for UK-279,276, the development of the mechanistic-based model was valuable in linking the complex pharmacokinetics/pharmacodynamics of UK-279,276 across the phases of drug development.

Introduction Pharmacokinetic/pharmacodynamic modelling, especially through the use of nonlinear mixedeffects models, is an important tool for the learningconfirming cycles of clinical drug development.[1,2] Pharmacokinetic/pharmacodynamic models are ideally developed during the learning phase and then utilised in the design of the confirming phase of each cycle. To fulfill this function they must allow both interpolation and extrapolation beyond the conditions on which the learning was made.[3] Logically, models formulated on a mechanistic basis, i.e. models that are derived from, or incorporate biological knowledge, are more likely to possess the required qualities compared with empirical models. A key component of model-based learning is the translation of the current state of knowledge into a mathematical form. This knowledge either reflects proven facts or scientifically plausible hypothesis; both can co-exist more easily in a model framework that is mechanistically based. However, mechanistic models take time to develop. With the increasing pressure of shorter drug development times, the use of mechanistic models, as opposed to less time-consuming empirical models, may appear to be an unnecessary luxury. The question of whether the long-term benefits of correct and informed decisions based on a mechanistic model outweigh the short-term time savings of using empirical models can only be addressed by studying © 2006 Adis Data Information BV. All rights reserved.

parts of, or complete drug development programmes in which modelling was an integral part. This commentary describes the development programme of the recombinant UK-279,276 (neutrophil inhibitory factor) in treatment of ischaemic stroke. The modelling spanned a period of approximately 3 years during which a mechanisticallybased model was updated several times. The aim of this commentary is to highlight the way information was propagated across studies to support the (mechanistic) modelling to respond to emerging drug development issues, and also to point out particular benefits the modelling brought to the development programme. Given the number of experiments described and the difference in aims at different stages of the drug development programme of UK-279,276, this paper has a nonstandard organisation. The first section provides some background information on stroke and the hypothesised mechanism of action of UK-279,276. This section also describes the data used and some general model specifications. The following four sections describe different modelling stages (stages I–IV), which correspond to the availability of data and the emergence of new key drug development questions. Each modelling stage, which essentially covers one analysis, has the following sections: Aim and Background, Data, Results and Value to the Drug Development Process. Stages I and II highlight the real time nature of this example and how empirical (‘fit for purpose’)Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

based modelling was used to facilitate early development decision making for UK-279,276. For the sake of brevity, detail around the associated interim models, in terms of structure and graphical and numerical results, is not provided. Instead, focus is given to the decisions made and how the knowledge from their application led to the development of the mechanistic model presented in stage III. The concluding Discussion section draws together some important issues and lessons learned from this case study. Background and Methods Proposed Mechanism of Action of UK-279,276 (Neutrophil Inhibitory Factor)

The processes of neuronal injury occurring in ischaemic stroke are complex. The initial event leading to cell necrosis is a reduction in oxygen and energy supply. Neutrophil infiltration into the area surrounding the infarct (the penumbra) and the release of neuroactive factors play a role in the final phases of neuronal injury and were therefore thought to be important in determining the extent of the injury following an ischaemic stroke. The interaction between neutrophils and endothelium is the critical factor that determines neutrophil migration into the site of the infarct.[4-6] Neutrophil-endothelium interactions are regulated by a specific adhesion cascade that consists of sequential steps of tethering, strong adhesion and transendothelial migration. An important component in this cascade is the strong adhesion that is mediated by integrins that bind to the counter receptors on the endothelium. The integrins, CD11a/ CD18 (lymphocyte function associated antigen [LFA]-1) and CD11b/CD18 (Mac-1) on neutrophils bind to intercellular adhesion molecule 1 expressed on endothelial cells and are involved in neutrophil aggregation and the actual process of trans-endothelial migration. CD11b/CD18 (abbreviated to CD11b) is expressed on the surface of resting neutrophils, (and other cell types such as monocytes, macrophages and small subpopulations of B cells, T cells and © 2006 Adis Data Information BV. All rights reserved.

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natural killer cells). On activation of these cells, triggered by a trauma, such as an infection or stroke, the expression of CD11b is increased. UK-279,276 is a large recombinant glycoprotein (257 amino acids, 41 kDa) originally derived from the canine hookworm (Ancylostoma caninum) and produced for medicinal use by suspension culture. It is a selective antagonist of CD11b. The binding of UK-279,276 to CD11b blocks a number of neutrophil adhesion-dependent functions mediated by CD11b, for example the infiltration of activated neutrophils to the site of infarction.[7,8] Thus UK-279,276 displays in vivo efficacy in the transient rat middle cerebral artery occlusion model of stroke without having to cross the blood-brain barrier to exert a neuroprotective action. It was therefore hypothesised that UK-279,276 may be an effective therapy to reduce brain injury following ischaemic stroke. While UK-279,276 was ultimately not shown to be effective in the treatment of the general ischaemic stroke population,[9] it may still have a potential role as a therapeutic agent in the treatment of reperfusion injury following stroke.[10] Assay Validation and Implications for UK-279,276 Development

Therapeutic proteins, such as UK-279,276, have specific development challenges that can be usefully approached through modelling. A clear early goal is to correlate product-related material in the body with a mechanism-related biological effect. The initial assay developed to measure UK-279,276 concentration was an immunoassay (referred to as the dissociation enhanced lanthanide fluorescence immunoassay [DELFIA]). However, the epitopes against which the antibodies were directed were unknown, consequently the specificity for biologically active protein versus inactive breakdown products was unknown. A specific ‘bioassay’ was therefore sought. The minimum requirement of this assay was that it entailed specific binding to the target receptor (CD11b); however, ideally, a functional response would increase the confidence that quantification of active drug has been achieved. The CD11b occupancy assay was Clin Pharmacokinet 2006; 45 (2)

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therefore subsequently developed. The relationship between the DELFIA and CD11b occupancy assay was explored using modelling, to increase confidence in the specificity of the DELFIA. The Dissociation Enhanced Lanthanide Fluorescence Immunoassay

The DELFIA uses a polyclonal capture antibody and a labelled monoclonal detection antibody, to detect unbound UK-279,276. Concentration is derived through reference to a standard calibration curve. The assay was performed using two calibration ranges, 5–200 ng/mL and 100–10 000 ng/ mL. The imprecision and inaccuracy across the calibration range was <15%. However, the epitopes against which the antibodies are directed are uncharacterised and the potential to cross-react with inactive breakdown products of UK-279,276 is therefore unknown.

General Data Considerations The modelling was carried out over a period of 3 years, starting with healthy volunteer data and progressing to patient data when available. Different models were used to provide input to the drug development process during this period. In total, four studies were used over the course of the model development and were subsequently used to build a final model. The final model was then set as a ‘prior’ in the analysis of the sparse pharmacokinetic data from the fifth dose ranging study. More details of the five studies are displayed in table I. Dosing

Patients and healthy volunteers received only one dose of UK-279,276 as a result of a prolonged exposure (and the potential for an antibody response on multiple dosing). In all cases doses were administered by a 15 minute intravenous infusion. Observations

CD11b Occupancy Assay

The CD11b occupancy assay was developed using flow cytometry as an analytical platform. Anticoagulated blood samples were processed at each of the clinical sites and transported to the analytical laboratory for fluorescence-activated cells analysis. Samples were incubated with a cocktail of two antiCD11b antibodies conjugated to different fluorescent labels then fixed in paraformaldehyde. One antibody binds to CD11b irrespective of whether UK-279,276 is bound or not (giving total CD11b) and the second antibody binds to CD11b competitively with UK-279,276, thus determining the amount of unoccupied CD11b receptors (giving free CD11b). Neutrophils were initially selected using forward and sideways light scatter properties and the mean fluorescence of each of the bound antibodies determined in this cell population. The exact antibody to fluorophore ratio was previously determined for each antibody, enabling the percent occupancy of CD11b by UK-279,276 to be calculated. Intra-assay imprecision was <20%. © 2006 Adis Data Information BV. All rights reserved.

Pharmacokinetic observations were made in all studies. CD11b binding measurements were collected in studies 2, 3 and 4. The initial modelling stages (I and II) were based on the ratio of occupied CD11b receptors (average total number of receptors per neutrophil minus number of unoccupied receptors per neutrophil) to total number of receptors per neutrophil. Subsequently, the observed number of neutrophils (neutrophil count) was utilised and the absolute number of unoccupied and total number of receptors was calculated (product of the number of neutrophils and average number of receptors per neutrophil) and used directly in stage III. No receptor binding data were available for the stage IV model. The observed neutrophil counts were used in stages III and IV. The observed number of neutrophils in each subject was used in predicting the total and free CD11b receptors. In stage IV, given the lack of CD11b data, this prediction conditioned on the stage III model for predicting the number of free CD11b receptors. Clin Pharmacokinet 2006; 45 (2)

© 2006 Adis Data Information BV. All rights reserved.

NM

207

991

244

NM

155

757

184

NM

73 (40– 145)

71 (54– 100)

73 (38– 113)

71 (60– 91)

73 (60– 96)

Bodyweight (kg)b

546/446

8/7

102/67

29/3

51/0

Sex (M/F)

73 (36– 96)

68 (65– 74)

73 (39– 92)

30 (19– 70)

24 (18– 42)

Age (y)b

0, 10, 16, 22, 33, 38,

1 mg/kg

0, 0.06, 0.1, 0.5 and

1 and 1.5 mg/kg

0, 0.06, 0.1, 0.2, 0.5,

1.5 mg/kg

0, 0.2, 1.25 and

0.5 and 1 mg/kg

0.006, 0.02, 0.06, 0.2,

Doses

Values are expressed as median (range).

were used.

levels obtained without a corresponding measurement of the total number CD11b were ignored. In stage III, on the other hand, all measurements of free CD11b receptors

In stage I and II, binding ratios were computed from free and total number of CD11b observations obtained at the same time, meaning that observations of free CD11b

96, 108 and 120mg

2976

149

623

451

NM

No. of free No. of total CD11b CD11b observationsa observationsa

study

2881

143

1646

473

720

No. of neutrophil observations

45, 52, 59, 67, 76, 84,

992

15

169

32

472

No. of PK observations

proof of concept

Dose-ranging

in elderly HV

tolerability study

Safety and

stroke patients[9]

study in

tolerability

Safety and

study in HV

tolerability

Safety and

study in HV

51

No. of subjects

F = female; HV = healthy volunteers; M = male; NM = not measured; PK = pharmacokinetics.

b

a

5

4

3

2

Safety and

1

tolerability

Study description

Study

Table I. Description of the studies used

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Covariates

Sex, age (both categorical young/elderly and continuous), bodyweight and dose were included in the datasets for all studies.

functionality in NONMEM. This functionality is described in detail in the paper by Gisleskog et al.[11] The prior information was included according to the ‘Normal-Normal’ approach described in the same paper.

Modelling Technicalities All the modelling was performed in the software NONMEM version VI (beta) [GloboMax LLC, Hanover, MD, USA] using nonlinear mixed-effect modelling and the first-order estimation method (the preferable first-order conditional estimation method caused numerical problems and could therefore not be used). Interindividual variability, according to an exponential model, was modelled in various parameters as indicated by the data. These parameters are indicated by the subscript i in this article. In all models, residual variability was best accounted for by a log transformation both sides. Where multiple observations are presented for an individual this is denoted by the subscript j. In studies 1–4, the modelling was only based on data where observations were above the lower limit of quantification (LLQ) for the DELFIA concentration assay. In study 5, observations below the LLQ were made available. The first observation below the LLQ in each individual was included in the stage IV analysis by assigning it a value equal to half the LLQ. These values were assigned a fixed additive residual error with the standard deviation set to the LLQ (5 ng/mL). When information from previous studies was included in analyses, this was done either by pooling of data across studies or by the use of the prior

Stage I: Assay Validation/Confirmation of Biological Effect Aim and Background

The aim of the stage I modelling was to build a model based on the available healthy volunteer data: (i) to explain and characterise the nonlinearities in the pharmacokinetic and CD11b binding data; and (ii) for assay comparison/confirmation of biological activity to establish the relationship between the DELFIA data and the CD11b binding data to qualify the utility of the pharmacokinetic assay. Data For this modelling stage, the data from studies 1–2 were available (table II). The observed pharmacokinetic and binding ratios are shown in figure 1. Results One-, two- and three-compartment models with either linear, saturable or combinations of linear and saturable elimination were initially used to fit to the pharmacokinetics data. Models with saturable binding were also tried. However, the goodness-of-fit plots indicated that more than one saturable process would be required to describe the distinctive pharmacokinetic profile. Consequently, models with

Table II. Availability of data from the different studies over time Study

Stage I

Stage II

Stage III

1

PK

PK

PK, neutrophils

2

PK and ratio of bound to total number of CD11b receptors

PK and ratio of bound to total number of CD11b receptors

PK, neutrophils, free and total number of CD11b receptors

PK and ratio of bound to total number of CD11b receptors

PK, neutrophils, free and total number of CD11b receptors

3 4 5 PK = pharmacokinetics.

© 2006 Adis Data Information BV. All rights reserved.

Stage IV

PK, neutrophils, free and total number of CD11b receptors PK and neutrophils

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183

model. The bound state of the drug was modelled according to equation 1. dA4 = A1 · k · (B 1b max - A4) - A4 · kb1,i dT (Eq. 1) where Bmax is the maximum amount of drug that can be bound to the receptor, A1 and A4 are the amounts in the first and fourth compartments, respectively (figure 2) and T is the time. The rate constants k1b and kb1,i govern the rate of transfer of drug to, and from the bound state. kb1,i was modelled as the product of k1b and the dissociation rate constant kdiss,1. Predictions for the ratio of bound receptors (fb,ij) were derived using equation 2. Cu,ij fb,ij = Cu,ij + kdiss,2 (Eq. 2) where Cu,ij is the predicted ith unbound concentration from the jth individual and kdiss,2 is the dissociation rate constant. Models with separate kdiss values for the nonspecific pharmacokinetic binding and the specific neutrophil binding were initially tested (kdiss,1 and kdiss,2). However, the similarity in the kdiss,1 and kdiss,2 values meant that a single kdiss value could be applied to both the nonspecific pharmacokinetic binding (equation 1) and specific neutrophilic CD11b binding (equation 2). The effect of the covariates (dose, bodyweight, study and young/elderly) were explored and in the final model both Michaelis-Menten constant (Km) and maximum rate of metabolism by the enzymemediated reaction (Vmax) were expressed as functions of bodyweight such that clearance increases with increasing bodyweight. Value to the Drug Development Process

both saturable elimination and saturable binding were considered. Finally, both sets of observations (pharmacokinetics and degree of CD11b binding) could be adequately described by a three-compartment model with both saturable binding and saturable elimination. Figure 2 shows a picture of this © 2006 Adis Data Information BV. All rights reserved.

Nonlinear Pharmacokinetics

The incorporation of both saturable elimination and binding into the model allowed the nonlinearity in the pharmacokinetic profile to be well described. In describing both the pharmacokinetics and the CD11b binding data the model allowed interpolaClin Pharmacokinet 2006; 45 (2)

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4

Bound drug (Cb)

k1b(Bmax − A4)

kb1 2

1

Q1/V2 Q1/V1

3

Q2/V1

Central (Cu)

Peripheral 1

Peripheral 2 Q2/V3

* Fig. 2. The stage I model. Compartments are numbered 1–4 in the order: central, peripheral 1, peripheral 2 and bound drug. The arrow marked with an asterisk indicates a Michaelis-Menten process. A4 = the amount in the fourth compartment; Bmax = maximum amount of drug that can be bound to the receptor; Cb = concentration of bound drug; Cu = concentration of unbound drug; k1b, kb1 = rate of transfer of drug to, and from the bound state; Qi = intercompartmental clearance from central to the ith peripheral compartment; V1 = volume of distribution of the central compartment; V2, V3 = volume of distribution of the peripheral compartments.

plore the effect on variability in exposure of moving from bodyweight-adjusted dosing to a fixed-dose regimen; and (ii) to aid in the selection of the maximum dose and the individual dose increments for the dose-ranging study (study 5). The planned approach in this stage was to update the stage I model using both the stage I data and data from patients (study 3) simultaneously; however, it was not possible to find a common model that could describe the data from the healthy volunteers (studies 1 and 2) and the patient study 3 simultaneously. Two- and three-compartment models with various combinations of saturable binding and elimination were tried. Given the time constraints with respect to design of the dose-ranging study, the pragmatic solution was to develop a separate model for the patient data alone and to use this model in the simulations for the dose-ranging study. Data

tion to doses where CD11b binding data were not currently available. Assay Comparison and Confirmation of Biological Activity

An early goal of the development programme was to correlate the concentration measurements from the DELFIA with the mechanism-related biological effect (CD11b binding). The estimation of a single kdiss supports the hypothesis that the pharmacokinetic binding and specific neutrophilic CD11b receptor binding are in fact describing the same process and allowed the CD11b binding to be predicted from pharmacokinetic data. This suggests that the pharmacokinetics and CD11b binding assays are measuring active UK-279,276. This confirmed the utility of the DELFIA in measuring biologically active drug. Stage II: Patient Pharmacokinetics/ Pharmacodynamics

The data used at this stage were initially that from studies 1–3 but were later restricted to study 3 (table II). The observed pharmacokinetics and binding ratios for study 3 are shown in figure 3. Results

The final stage II model was a two-compartment model with saturable binding and two elimination pathways – one linear and one saturable (figure 4). The bound drug and the predictions of the fraction of occupied receptors was obtained in the same way as in the stage I model (equations 1 and 2). Covariate relationships were explored and in the final model Vmax and volume of distribution in the central compartment (V1) were expressed as a function of bodyweight (increasing with increasing bodyweight), and Vmax was a function of age (decreasing with increasing age). Value to the Drug Development Process

Aim and Background

The aim of the modelling in this stage was to derive a model to be used for dose selection for the dose-response study. Specific goals were: (i) to ex© 2006 Adis Data Information BV. All rights reserved.

Fixed Versus Weight-Adjusted Dosing

Consistent with standard practice of intravenous therapy, a weight corrected mg/kg dosing regimen was used in the early development of UK-279,276. Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

While the model demonstrated that recorded bodyweight was correlated with volume of distribution and the nonlinear component of clearance, the combined consequence of this in terms of drug

185

exposure variability is not easily predicted. Therefore, simulations were conducted to investigate whether switching to a fixed-dose regimen would significantly increase the variability in the area under the concentration-time curve (AUC) or the degree of CD11b binding measured as the area under the binding curve (AUB). The simulations showed that the difference in variability was relatively small and that the variability in AUC and AUB decreases with increasing doses as a result of the nonlinear elimination and CD11b binding. Based on the simulations and the good tolerability profile of UK-279,276 in acute stroke patients,[9] it was decided to switch to a fixed-dose regimen for the dose-ranging study. The potential advantages of this switch included simpler dosing instructions (with the potential for reduced dose calculation errors), reduced drug waste (and therefore cost) and facilitation of rapid treatment initiation. Aiding the Selection of Maximum Dose and Individual Dose Increments

Fig. 3. The observed study 2 data used in the stage II analysis. (a) The observed UK-279,276 (neutrophil inhibitory factor) concentrations vs time; and (b) the observed fraction of occupied CD11b receptors vs time. Each individual’s observations are connected with a line. The graph displays a random selection of about 50% of the total number of individuals. The negative fractions observed in (b) are the result of the number of free and total CD11b receptors being measured with separate assays.

© 2006 Adis Data Information BV. All rights reserved.

Binding to neutrophilic CD11b is at the centre of the therapeutic effect of UK-279,276; however, the target degree of CD11b binding and duration of binding required for a therapeutic effect is unknown. Exploration of a wide range of exposures was therefore required in study 5.[12] A Bayesian adaptive design, with sequential dose allocation was conceived to identify the optimal exposure.[13] This approach required a safe maximum dose and a number of doses across the dose range of interest. Various reports have indicated that the processes of neuronal injury following the initial stroke continue for up to 5 days (120 hours). Predictions from the model indicated that the typical individual, when receiving a fixed dose of UK-279,276 approximately 45mg, would achieve >90% binding to CD11b for at least 5 days. It was therefore considered unnecessary to study higher exposures than previously observed and prudent to keep the maximum exposures close to the maximum achieved in the patient safety and tolerability study (i.e. approximately 120mg). Simulations showed that with a fixed dose of 120mg only about 5% of subjects receiving this maximum dose would exceed the maximum previous exposure

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3

Bound drug (Cb)

kb1 2

k1b* (Bmax – A3) 1

Q1/V2

Central (Cu)

Peripheral Q1/V1

k21

*

Fig. 4. The stage II model. Compartments are numbered 1–3 in the order: central, peripheral and bound drug. An arrow marked with an asterisk indicates a Michaelis-Menten process. A3 = the amount in the third compartment; Bmax = maximum amount of drug that can be bound to the receptor; Cb = concentration of bound drug; Cu = concentration of unbound drug; k1b, kb1 = rate of transfer of drug to, and from the bound state; k21 = transfer rate constant (first-order) from the peripheral (2) to central (1) compartment; Q1 = intercompartmental clearance from central to the ith peripheral compartment; V1 = volume of distribution of the central compartment; V2 = volume of distribution of the peripheral compartment.

and the maximum dose of 120mg was set on this basis. Also, the vast majority of patients would achieve >90% binding to CD11b for at least 5 days with a dose of 120mg. This approach received regulatory and ethics approval. A total of 15 dose increments between placebo and 120mg were set to ensure equally spaced increases in the duration above 90% saturation of neutrophilic CD11b. This resulted in an allocation that was linear with respect to CD11b binding and nonlinear with respect to dose. Stage III: Bridge between Patients and Healthy Volunteers Aim and Background

An important aspect of a development programme is that any future clinical pharmacology findings in healthy volunteers (drug interactions, comparability between different batches, special population studies) can be extrapolated to the patient population. Therefore, while the stage I and II models could separately describe the healthy volunteer and patient data respectively, the goal was to have one model describing both populations. © 2006 Adis Data Information BV. All rights reserved.

The stage I and II modelling indicated that CD11b binding was a determinant of the pharmacokinetics of UK-279,276. Indeed binding to the CD11b, and similar integrins (e.g. LFA-1) has been implicated in the elimination of compounds similar to UK-279,276 through endocytosis.[14-16] In addition, trauma such as acute infection has been reported to increase the number of circulating neutrophils, thus increasing the absolute number of CD11b receptors. Although such increases have not been reported following stroke in humans, data presented in this paper suggest that acute stroke causes similar neutrophil dynamics (see The Neutrophil Model section). It was therefore hypothesised that a difference in CD11b expression between patients and healthy volunteers may be implicated in the pharmacokinetic differences between the two populations. If correct, a model to describe both populations would encompass a mechanistic model of neutrophil proliferation. Differentiations of stem cells into neutrophils occurs through a number of stages; the mitotic stage, the postmitotic stage and circulating mature neutrophils.[17] Neutrophils in the circulation are either demarginated (circulating) or marginated (neutrophils that adhere to the vessel walls and are not measurable by venous blood sampling). The ratio between the two pools is about unity in the absence of trauma.[18] Following trauma, the levels of measurable neutrophils in plasma increases acutely through a number of mechanisms: increased ratio of de-marginated to marginated neutrophils, increased proliferation rate of stem cells, prolonged residence time of neutrophils in plasma and release of neutrophils from the postmitotic reservoir.[17] The latter comprises mature and less mature neutrophils that the body holds as a reserve. To implement the mechanistic hypothesis it was necessary to use the actual measurements of the total number of CD11b receptors rather than simply the binding ratios that had been used in stage I and II. It was therefore necessary to describe the dynamic changes in the number of neutrophils after stroke. To complicate matters further, CD11b is also present on other blood cell types, for example monoClin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

cytes,[19] thus non-neutrophilic CD11b may be involved in UK-279,276 elimination. Finally, data from the rat and the dog indicated that UK-279,276 may also be metabolised via an additional pathway, desialylation in the liver.[20] The specific goals of this modelling stage were: (i) to create a common model to explain the differences between healthy volunteer and patient; and (ii) to develop a mechanistic model framework to improve the understanding of the pharmacokinetics and pharmacodynamics of UK-279,276. Data

Data from the same studies (studies 1–4, table II) used in stages I and II were used to derive the stage

187

III model. The important difference was that the free and total numbers of CD11b receptors per neutrophil was used, as opposed to the binding ratios. The receptor measurements, together with the routine neutrophil counts (per nL), allowed the derivation of the molar concentration of CD11b receptors to compare with the molar concentrations of UK-279,276. The data used in this stage are shown in figure 5. Results

The results of the stage III analysis have been presented elsewhere[10] and will therefore only be presented very briefly in this paper. Three submodels were created: one for the neutrophil dynamics after stroke; one for the total numb

a

c

d

Fig. 5. The observed data for the stage III analysis. (a) the observed neutrophil counts vs time; (b) the observed UK-279,276 (neutrophil inhibitory factor) concentrations vs time; (c) the total number of CD11b receptors per neutrophil vs time; and (d) the number of free CD11b receptors per neutrophil. Each individual’s observations are connected with a line. The graph displays a random selection of about 40% of the total number of individuals.

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a

5

Reservoir De-margination

1

2

Stem cells

3

Mitotic

4

Postmitotic

Blood

Increased release

Longer MRT

Production feedback

b 7

Central (unbound drug)

4

(←Fig. 6a)

Neutrophils in blood

8

Peripheral

1* 2 3*

Neutrophil model

PK model

Total number of CD11b

6

Free CD11b

CD11b per neutrophil Receptor model

Fig. 6. The full stage III model. (a) The final neutrophil model with the four processes accounting for the dynamic changes in neutrophil levels after stroke; and (b) the combined PK and receptor level models with the dashed diagonal and vertical lines defining the boundaries between the models. The dashed arrows indicated dependencies and arrows marked with an asterisk indicate a nonlinear process. The shaded boxes specify where observations were available. The unshaded boxes indicate where observations were not available. The boxes with solid lines correspond to differential equations in the model and the number in the top right corner of these boxes indicates the integrated variable in the equations in the body of the text. MRT = mean residence time; PK = pharmacokinetics.

ber of receptors per neutrophil; and one for the pharmacokinetics of UK-279,276, including the saturable binding to the receptor. The latter model, together with the molar concentration of receptors, could then be used to predict the number of free receptors per neutrophil. From a practical point of view, the neutrophil model was developed first and then fixed in the simultaneous analysis of the pharmacokinetics, total number of receptors and free number of receptors per neutrophil. The full © 2006 Adis Data Information BV. All rights reserved.

model is presented graphically in figure 6a and figure 6b. The Neutrophil Model

The model for the neutrophils was inspired by the general model for white blood cell proliferation and maturation suggested by Friberg et al.[21] but reformulated according to Walker and Willemze.[17] It consists of a stem cell compartment with autogeneration of new stem cells. This compartment is linked Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

to a mitotic compartment, which in turn is linked to a postmitotic compartment. Neutrophils are released from the postmitotic compartment into a blood compartment. A reservoir compartment is linked to the postmitotic compartment. Because not all parameters of this model are identifiable, some of the parameters were fixed to literature values. Thus, the mean transit times through the mitotic and postmitotic compartments were fixed to 120 and 168 hours, respectively,[17] the initial ratio between the levels in the postmitotic state and the reservoir were set to unity, and the mean residence time of the neutrophils in blood for healthy volunteer were set to 7 hours.[17] Four processes were used to account for the dynamic changes in the neutrophil counts after stroke and were only applied to the data from the patients. The first process was an instantaneous increase in the neutrophil levels in plasma, which can be viewed as a change in the ratio of de-marginated to marginated neutrophils.[17] The second process was an increased release from the postmitotic compartment to blood. This also leads to a shift in the ratio of precursor neutrophils from the reservoir to the postmitotic compartment. This increased release was assumed to decrease with time in an exponential fashion. The third process was an increased residence time of neutrophils in plasma.[17] This increase is expected to return to the baseline residence time, with time; however, this return to baseline occurred very slowly and could not be characterised in the model. The fourth process was a feedback from the postmitotic compartment to the autogeneration rate of stem cells.[21] Note that this is different from the model presented by Friberg et al.[21] where the feedback signal is driven by the circulating neutrophils rather than the levels in the postmitotic compartment. However, according to goodness-of-fit graphics and statistical criteria, the feedback signal in the present data was better described in this way. © 2006 Adis Data Information BV. All rights reserved.

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The Model for the Total Number CD11b Receptors Per Neutrophil

The total number of CD11b integrins per neutrophil in healthy volunteers showed no distinctive patterns and was set to be constant. In patients, on the other hand, the counts appeared to be higher at early timepoints with a gradual decline over time. This was modelled as an exponentially decreasing initial increase in the ‘production’ rate of receptors in patients. Predicting the Number of Free CD11b Receptors

Using the predicted number of neutrophils and number of receptors it was then possible to compute the total molar concentration of CD11b receptors. The predicted number of free CD11b receptors at each timepoint could then be obtained by equation 3.

æ

CD11bfree,ij = CD11bN,ij ç1−

ç è

ö ÷ γ + kdiss,γ ÷ø CuN,ij γ CuN,ij

(Eq. 3) where γ is a modulator that, since it was estimated to be <1, accounts for steric hindrance by already γ bound UK-279,276 molecules, CuN,ij is the ith individual’s jth predicted molar concentration of un-

bound UK-279,276 and CD11bN,ij is the total number of CD11b receptors. The Model for the Pharmacokinetics of UK-279,276 and the Saturable Binding to the Neutrophilic CD11b Receptors

The UK-279,276 disposition was found to be adequately described by a two-compartment model with three elimination pathways. The first of these three was a linear (first-order) pathway, the second was nonlinear according to a Michaelis-Menten process and the third was limited by the total number of free CD11b receptors ( CD11bfree ). In terms of differential equations, this model was specified as (equation 4): Clin Pharmacokinet 2006; 45 (2)

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dA7 dT

= R0 +

Q1 • A8 – A7 • V2

⎞ ⎟ ⎠

k10,ij – k102 • CD11bfree,ij –

dA8 dT

=

Q1 ⎞ Vmax,i • A7/V1,i ⎟– V1,i ⎠ Km,i + A7/V1,i

Q1 Q1 • A7 – • A8 V1,i V2

(Eq. 4) where k10 and k102 are the rate constants for the linear and CD11b limited pathways, respectively, Q is the intercompartmental clearance, A7 and A8 are the compartment amounts according to figure 6, T is the time, R0 is the infusion rate and V1,i is the ith individual’s value of the volume of distribution of the central pharmacokinetic compartment. If the mechanistic assumptions that non-neutrophilic CD11b elimination and hepatic desialylation are involved holds, then the linear pathway in this model would relate to the desialylation and the Michaelis-Menten pathway would relate to the nonneutrophilic CD11b elimination. The pharmacokinetics structural model parameter estimates are shown in table III. Covariate Analysis

Given the mechanistic nature of the present state of the model, it was decided to take a mechanistic approach to the identification of candidate covariate relationships (in contrast to, for example, a forward selection type of search strategy[22]). The method used is describe elsewhere[10] but the candidate relationships tested were bodyweight on the linear elimination pathway, and bodyweight and healthy volunteer/patient on the non-neutrophilic, saturable elimination pathway. The final model expressed Vmax as function of both bodyweight (increasing with increasing bodyweight) and healthy volunteer/patient status (higher for patients). Value to the Drug Development Process Common Model to Explain the Differences Between Healthy Volunteer and Patient

Establishing a common model for patients and healthy volunteers was important to the develop© 2006 Adis Data Information BV. All rights reserved.

ment of UK-279,276, in allowing extrapolation of clinical pharmacology findings to patients. The most important consequence was the enabling of the clinical component of the comparability strategy. The term ‘comparability’ is related to the in vitro and in vivo methods used to determine that a new batch of protein is equivalent to previous batches. The role of the stage III model in underpinning the clinical component of the strategy for UK-279,276 is described in more detail elsewhere.[10] Mechanistic Model Framework to Improve the Understanding of the Pharmacokinetics and Pharmacodynamics of UK-279,276

Since the mechanistic modelling approach is guided by prior knowledge, the results cannot be considered as independent evidence of the existence of the underlying mechanisms. Nevertheless, since the model is consistent with the data, it supports the theory that CD11b binding contributes to the clearance of UK-279,276 (equation 4 and figure 6b). Importantly, the proposed disposition of UK-279,276 agrees with literature reports of other proteins that bind to the Mac-1 or LFA-1 (CD11a/ CD18) integrins and contribute to the clearance of the proteins.[14-16] Following preclinical investigations with UK-279,276 two clearance mechanisms were postulated. In addition to the saturable CD11b receptor mediated pathway, a high-capacity, low-affinity clearance pathway via the asialoglycoprotein receptor has been identified in rats.[20] While the rat has only the asialoglycoprotein pathway (and demonstrates linear pharmacokinetics), both pathways appear to be present in the dog and man.[20] The mechanistic model supports the presence of both pathways in humans. However, simulations shown in figure 7 indicate that, the linear pathway is less important than the neutrophilic CD11b pathway or the currently unidentified saturable pathway that we hypothesis to be a non-neutrophilic CD11b clearance. Clin Pharmacokinet 2006; 45 (2)

© 2006 Adis Data Information BV. All rights reserved.

141

0.00862

Vmax,pt (μg/h)

Effect of BWT on Vmax,pte

18

4.9

35

0.00908

132

0.017

0.409

7.5

2.1

7.0

7.3

3.3

1.1

0.94

1.0

1.1

1.0

1.0

0.42

0.42

0.20

0.41

0.77

0.71

0.35

0.000436

58

2.9

NAc

0.0163b

138

10

3.8

19

6.4

2.5

0.363

375

222

5.65

2.99

4.4

0.05

0.98

NAc

0.94

1.0

1.0

1.5

1.1

0.66

0.93

3.26

0.59

NAc

0.57

0.89

0.95

0.34

0.51

0.55

0.50

0.52

γ = binding modulator; BWT = bodyweight; k10 = rate constant for the linear pathway; k102 = rate constant for CD11b limited pathways; kdiss = dissociation rate constant; Km = Michaelis-Menten constant for the nonspecific, nonlinear pathway; NA = not available; Q1 = intercompartmental clearance from the central to first peripheral compartment; RSE = relative standard error; V1 = volume of distribution of the central compartment; V2 = volume of distribution of the peripheral compartment; Vmax,HV = maximum nonlinear pathway elimination rate for healthy volunteers; Vmax,pt = maximum nonlinear pathway elimination rate for patients.

Change in Vmax,pt per kg different from 70kg.

0.0163

Effect of BWT on Vmax,HVd

18

386

15

1.1

0.45

63.7

1.3

1.3

e

0.385

k102 (h pM)–1

4.3

222

6.7

1.0

0.43

3.96

7.1

NAc

ratio of RSE

Change in Vmax,HV per kg different from 70kg.

373

γ

20

4.08

2.2

0.94

0.79

62.6

NAc

d

221

kdiss (pM)

19

2.76

3.4

0.99

0.44

NAc

121b

Not obtained since study 5 did not include any healthy volunteers.

3.77

k10 (h–1)

4.8

90.9

2.0

1.0

0.30

c

2.73

V2 (L)

8.0

4.23

6.0

0.98

Fixed to the estimate obtained in the stage III analysis since no healthy volunteer data were collected in study 5.

96.2

Q1 (L/h)

2.6

48.2

1.6

Stage IV/stage III ratio

b

4.26

V1 (L)

14

119

RSE (%)

Stage IV estimate

Estimates obtained from the analysis of the stage III data minus the number of free and total CD11b measurements using a prior from the analysis of all stage III data.

48.4

Km (μg/L)

5.4

ratio of RSE

Truncated stage III/stage III ratio

a

121

estimate

RSE (%)

Truncated stage IIIa

estimate

RSE (%)

Stage III

Vmax,HV (μg/h)

Parameter

Table III. Selected pharmacokinetic parameter estimates from the stage III, truncated stage III, and stage IV pharmacokinetics models. Also tabulated are the ratios of the truncated and stage IV estimates to the stage III estimates

Mechanistic PK/PD Models in Drug Development 191

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Linear pathway Neutrophil Non-neutrophilic Subject: Patient BWT: 50kg

Subject: Patient BWT: 70kg

Subject: Patient BWT: 90kg

Subject: Healthy BWT: 50kg

Subject: Healthy BWT: 70kg

Subject: Healthy BWT: 90kg

1.0 0.8

Fraction of UK-279,276 eliminated

0.6 0.4 0.2 0.0

1.0 0.8 0.6 0.4 0.2 0 0

0.5

1.0

1.5

0.0

0.5

1.0

1.5

0.0

0.5

1.0

1.5

Dose (mg/kg) Fig. 7. Fraction of UK-279,276 (neutrophil inhibitory factor) eliminated via the linear, neutrophilic and nonspecific pathways according to the stage III model plotted vs dose. The display is stratified by bodyweight (BWT) and subject type.

Stage IV: Establishing Efficacy in Acute Ischaemic Stroke Patients

Aim and Background

The focus of study 5 was to establish the efficacy of UK-279,276 in acute ischaemic stroke.[9] The collection of CD11b data in this large and complex trial was considered impractical and not necessary given that the relationship between UK-279,276 pharmacokinetics and the CD11b binding had been established in patients and healthy volunteers. Instead of collecting more data, the stage III model was reformulated to provide a prior in support of the analysis of the observed pharmacokinetic data and subsequent prediction of the CD11b binding. In an initial step to assess robustness of this approach, the © 2006 Adis Data Information BV. All rights reserved.

analysis of the data from stage III without CD11b binding based on this prior were compared with the results of the original stage III analysis. The subsequent demonstration that UK-279,276 did not improve recovery in acute stroke patients, refocused the aim of this stage to confirm that the lack of efficacy was not a result of a reduction in expected drug exposure that was not apparent by visual examination of the observed plasma or free CD11b levels.[9] Data

The stage IV data came from the dose-ranging study (study 5, table II) and did not contain any receptor binding data. The observed data from study 5 are shown in figure 8. Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

Results

A multivariate normal distribution corresponding to the fixed effects and the interindividual variability parameter estimates and variance/covariance matrix obtained from the stage III analysis was propagated using the prior functionality available with NONMEM.[11] A selection of the posterior parameter estimates from the analysis of the data from stage III without CD11b binding using this prior were compared with the results of the original stage III analysis (table III). This indicated that the prior would be appropriate in the analysis of the stage IV data. A selection of the parameter estimates from the analysis of stage IV data using the prior are also shown in table III as well as the parameter estimates from stage III and IV (stage IV/stage III). When the ratio for the parameter estimates is close to unity, the information provided by the stage IV data sets either lacks information on this aspect of the model or provides very similar information to the prior. With the former, the ratio of the corresponding standard errors (SEs) would also be relatively unchanged. With the latter, the ratio of the corresponding SEs would be less than unity since more information on the parameters is added. In the case where the stage IV data are inconsistent with the prior, the ratio of the parameters would change and the corresponding ratio of SE would increase. The ratios of most parameter estimates were close to unity and in most cases the ratio of the SEs was reduced, indicating that the stage IV data contained information on most of the model parameters that was consistent with the prior information. However, the small ratio for the parameter estimates of the bodyweight effect on Vmax (0.050) and the large ratio for the corresponding SEs indicate that this parameter is not supported by the stage IV data.

193

ics in study 5 were essentially unchanged from that observed in the previous patient study (study 3) and therefore that underexposure was not a factor in the failure of UK-279,276 to demonstrate improved recovery in acute stroke patients.

Value to the Drug Development Process

The stage IV parameter estimates were similar to the prior stage III estimates and the key parameters describing the pharmacokinetics of UK-279,276 (Vmax, Km V1, V2, Q1, Q2, and k10) were similar across the stages. This indicates the pharmacokinet© 2006 Adis Data Information BV. All rights reserved.

Fig. 8. The observed data used in the stage IV analysis. (a) The pharmacokinetic data vs time; and (b) the neutrophil counts vs time. The pharmacokinetic observations below 101 in (a) are observations coded as below the lower limit of quantification. The graph displays a random selection of about 35% of the total number of individuals.

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The approach used here demonstrates the utility of using priors to propagate information across drug development phases. This technique was particularly beneficial in this setting, since not all aspects of the mechanistic model could have been estimated from the stage IV data alone. Discussion The Role of Qualitative Learning in Mechanistic Model Development

The sequential nature of drug development demands that knowledge be propagated across studies to guide decision-making and aid future experimental design. While the discrete nature of individual studies can lead to an entirely informal qualitative approach to knowledge propagation, quantitative integration of prior data is necessary when testing hypotheses that transcend individual studies. During the course of this work, we aimed to be as quantitative as possible, utilising model-based methods to combine data and propagate the associated learning. However, in establishing the mechanistic framework of the stage III model, most aspects were, out of necessity, based on existing qualitative knowledge. It should also be recognised that even if the aim is to develop a mechanistic model, there is no reason to include more features in the model than necessary to simulate and predict new data. For example, the data on neutrophil proliferation were neither sufficient nor specific enough to provide informative priors on the temporal aspects of circulating neutrophil levels in patients following an acute stroke. Instead the available information in the literature after acute infection was used to build a structure within which stroke specific parameters were estimated. Based on our data, we considered the neutrophil dynamics after stroke to be qualitatively similar, such that the same basic model construct could be applied. As system complexity increases, the inadequacy of qualitative, quantitative or even empirical modelbased approaches becomes more apparent. The inability of our stage I (healthy volunteer) model to © 2006 Adis Data Information BV. All rights reserved.

provide an adequate framework for the interpretation of the stage II (patient) data exemplifies this point. Nevertheless, the learning from the attempted extrapolation provided the indication that a better understanding of the underlying biology was required. This failure, combined with an improved understanding of preclinical clearance mechanisms of UK-279,276 and the identification of a framework to describe the neutrophil dynamics, provided the qualitative information required to build the mechanistic model established in stage IIII. How Do You Propagate Knowledge?

While the application of qualitative learning is valuable to drug development and model development in general, it is necessary to use quantitative information when attempting to characterise and apply a large complex mechanistic model. Various approaches, with varying degrees of sophistication, are available to facilitate the information propagation between model stages in a drug development programme.[11] The simplest method is to fix parameter values to previous point estimates. In our case, we fixed several of the initial conditions for the neutrophil model to mean literature values. When the raw data are available, and as long as the overall quantity of data is manageable, data pooling is probably the best approach, since it conserves the entire information content. We used this method in the analysis of data from studies 1–4 in the stage II and III analyses. As the quantity of data and number of model iterations increases it becomes more desirable to propagate the information content of the model in the absence of the actual prior data. The prior functionality in NONMEM VI (beta) provides such an approach (it is of course also possible to use a full Bayesian approach[23]). In the stage IV analysis, the use of formal priors for the parameters of the stage III model provided the ideal framework for analysis of the sparse pharmacokinetic data and the most facile way in which individual estimates of CD11b binding could be provided based on the available data. Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

The Value of the Empirical-Based Modelling and Simulation in the Development of UK-279,276

The joint objective of this work was to develop a mechanistic pharmacokinetic/pharmacodynamic model to describe a complex system across healthy volunteers and patients, while providing ongoing support to drug development decisionmaking. These two aspects are naturally concomitant, with the early empirically-based models providing the platform for both decision-making and learning about the complexities of the underlying system. For example, a key finding from the stage I empirical model was that the pharmacokinetic binding and specific neutrophilic CD11b receptor binding were in fact describing the same process. This meant that both assays were measuring active UK-279,276, which increased the confidence in the utility of the more facile pharmacokinetic assay. In addition, it supported the future incorporation of the CD11b receptor mediated clearance mechanism in the final model. The nature of drug development means that decisions are often made in the absence of complete understanding. We believe that model-based decision-making is no different. In both instances, there is a need to assess the potential impact of what is not fully known, and determine how the associated risk may be mitigated. The following three decisions made on the basis of the empirical stage II model exemplify this point. 1. The risk to development in proceeding to dose ranging, without the link between the pharmacokinetics/pharmacodynamics in healthy volunteers and patients being established, was considered minimal when compared against the wider uncertainty of the likely clinical effect of UK-279,276. 2. The risk of accepting the dosing predictions for the stage IV study design was minimal because the predictions were based on interpolation within the range of data used to build the model. The risk associated with the choice of doses on the basis of CD11b binding was also minimised by the decision to run an adaptive design, with a large dose range. © 2006 Adis Data Information BV. All rights reserved.

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3. The risk of overexposing smaller subjects on moving to a fixed dose on the basis of the simulations was set against the good tolerability profile of the compound and the appointment of an independent safety data monitoring committee for this study. Therefore, provided the underlying model assumptions are not critical to the validity of the simulation, we see no reason why empirical models established on the path to development of the best mechanistic model cannot be utilised in decisionmaking. Nevertheless, it was establishing the link between healthy volunteers and patients through the mechanistic model that ultimately provided the greatest value to the future development of UK279,276. Why Did Getting Mechanistic Help?

We argue that aiming to formalise learning by implementing knowledge within a mechanisticallybased model is the ideal paradigm. Such models continue to have important advantages over empirical models. Firstly, there can only be one true mechanistic model for which the blueprint is given by biology. This means that the model must be able to describe all the available data. If a model cannot accomplish this, it is an indication that the model is not correct. In fact, it can be argued that where the biology is complex and particularly where the acute disease process influences drug pharmacokinetics, empirical models will become redundant as data emerge. Secondly, since the model is formulated in terms of biology and has components that can be directly related to biological observations, it allows subject matter specialists to join modellers in discussions on model improvement and interpretation. Indeed, the model may inform the subject matter specialist by questioning currently accepted theories. In this regard, we were able to postulate clearance pathways for UK-279,276 based on prior preclinical knowledge and then test their relevance in the model. The resulting feedback with respect to the potential importance of the non-neutrophilic CD11b clearance supported the need to explore the CD11b Clin Pharmacokinet 2006; 45 (2)

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expression on other blood cell types. Thirdly, as is true for many types of mathematical models, it is possible to turn the model into a predictive tool. The advantage of mechanistically-based models compared with empirical models is the credibility of any potential extrapolations. This advantage has been pointed out by others and ties well into the proposal that predictive simulation is an important tool towards more efficient drug development.[2,24-26] Short-Term Gains of Empirical Modelling Versus Long-Term Learning for Mechanistic Modelling

As we have discussed, interpolative predictions from empirical models can provide sufficient confidence to facilitate rational decision-making. However, the major drawback of empirical models is that they become redundant when new data emerge. The focus tends to shift to the emerging data and the prior learning may ultimately be lost when the model is updated. So while empirical approaches can be adequate for decision-making, this gain may be at the expense of long-term learning. In contrast, the development of a mechanistic model offers a clear benefit in terms of developing long-term understanding. However, as a tool for making quick decisions, it may be considered an unnecessary luxury if the decision could have been adequately informed through simple empirical methods. Nevertheless, the application of an existing mechanistic model to new data can be a very efficient process. We found that creating formal priors based on the current parameter values essentially allowed the stage IV analysis to be completed in one NONMEM run. The same would not be true for an empirically-based model since the inherent need to retest aspects of the underlying model would still remain. It is also worth pointing out that a mechanistic model can be re-used across compounds acting in the same biological environment. This means that it is not necessary to go through the process of developing a mechanistic model for any follow-up candidates since the mechanistic model framework is valid regardless of the drug studied. © 2006 Adis Data Information BV. All rights reserved.

With this long-term perspective, the development of a mechanistic model can be regarded as a sound investment in time. It should also be noted that our modelling only started once the compound passed into clinical development. If the modelling and simulation resource and assays had been available earlier much of the learning could well have been done in preclinical setting using animal models of stroke. Therapeutic proteins present specific drug development challenges, for example support to the comparability strategy,[10] that in our case have at least been best addressed by investing in the development of mechanistic models. Central to this development was the need to correlate product-related material in the body to a mechanism-related biological effect. The early understanding of assay specificity (stage 1 model ), underpinned the development of the mechanistic model linking healthy volunteers and patients (stage III), which in turn allowed clinical pharmacology findings in healthy volunteers to be extrapolated to patients and thereby minimised the need to use patients to conduct standard clinical pharmacology studies. Conclusion Modelling and simulation played an important role in the early development of UK-279,276, by providing important insights into the mechanistic nature of the pharmacokinetic/pharmacodynamic relationship and underwriting elements of the future study designs. One of our key tenets in the development and subsequent application of the various models used throughout the development of UK-279,276 was the importance of knowledge propagation in facilitating the learning aspect of the learning and confirming cycles. In this respect, despite showing that empirical models can facilitate some drug development decisions, we believe there is a greater need to develop mechanistic models, particularly when attempting to characterise and propagate the complex pharmacokinetics/pharmacodynamics of therapeutic proteins. Clin Pharmacokinet 2006; 45 (2)

Mechanistic PK/PD Models in Drug Development

Acknowledgements This work was sponsored by Pfizer Global Research and Development, Sandwich, UK, and the Swedish Foundation for Strategic Research, Stockholm, Sweden. Drs Marshall, Macintyre, James and Krams are employees of Pfizer, Inc., and Dr Jonsson was an employee at the University of Uppsala when this work was performed but is presently working at Roche Pharmaceuticals.

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al., editors. Studies in Bayesian statistics. Vol 5. New York: Springer-Verlag, 2002: 99-181 14. Bauer RJ, Dedrick RL, White ML, et al. Population pharmacokinetics and pharmacodynamics of the anti-CD11a antibody hu1124 in human subjects with psoriasis. J Pharmacokinet Biopharm 1999; 27 (4): 397-420 15. Bowen JD, Petersdorf SH, Richards TL, et al. Phase I study of a humanized anti-CD11/CD18 monoclonal antibody in multiple sclerosis. Clin Pharmacol Ther 1998; 64 (3): 339-46 16. Simon DI, Ezratty AM, Francis SA, et al. Fibrin (ogen) is internalized and degraded by activated human monocytoid cells via Mac-1 (CD11b/CD18): a nonplasmin fibrinolytic pathway. Blood 1993; 82 (8): 2414-22 17. Walker RI, Willemze R. Neutrophil kinetics and the regulation of granulopoiesis. Rev Infect Dis 1980; 2 (2): 282-92 18. Jagels MA, Hugli TE. Mechanisms and mediators of neutrophilic leukocytosis. Immunopharmacology 1994; 28 (1): 1-18 19. Kato H, Kogure K, Liu XH, et al. Progressive expression of immunomolecules on activated microglia and invading leukocytes following focal cerebral ischemia in the rat. Brain Res 1996; 734 (1-2): 203-12 20. Webster R, Phipps J, Hyland R, et al. Evaluation of the role of the asialoglycoprotein receptor in the clearance of UK-279,276 (recombinant neutrophil inhibitory factor). Xenobiotica 2003; 33 (9): 945-56 21. Friberg LE, Henningsson A, Maas H, et al. Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 2002; 20 (24): 4713-21 22. Jonsson EN, Karlsson MO. Automated covariate model building within NONMEM. Pharm Res 1998; 15 (9): 1463-8 23. Lunn DJ, Best N, Thomas A, et al. Bayesian analysis of population PK/PD models: general concepts and software. J Pharmacokinet Pharmacodyn 2002; 29 (3): 271-307 24. Arlington S. Pharma 2005: an industrial revolution in R&D: Somers (NY): PriceWaterhouseCoopers, 1998 25. Arlington S. Pharma 2005 silicon rally: the race to e-R&D: Somers (NY): PriceWarterhouseCoopers, 1999 26. Arlington S. Pharma 2010: the threshold of innovation: Somers (NY): IBM Business Consulting Services, 2003

Correspondence and offprints: Dr Niclas E. Jonsson, Department of Pharmaceutical Biosciences, Uppsala University, Box 591, Uppsala, SE-75124, Sweden. E-mail: [email protected]

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