Bridging Clinical Outcomes of Canakinumab Treatment in Patients With Rheumatoid Arthritis With a Population Model of IL-1β Kinetics

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1 Citation: CPT: Pharmaometris & Systems Pharmaology (202), e5; doi:.38/psp ASpt All rights reserved /2 ORIGINAL ARTICLE Bridging Clinial Outomes of Canakinumab Treatment in Patients With Rheumatoid Arthritis With a Population Model of IL-β Kinetis S Ait-Oudhia, PJ Lowe 2 and DE Mager Canakinumab, an anti-interleukin-β (IL-β) monolonal antibody, is approved for ryopyrin-assoiated periodi syndromes and is under investigation for the management of other inflammatory disorders. In this study, population-based pharmaokineti pharmaodynami models were developed to understand responses to anakinumab in patients with rheumatoid arthritis (RA). Total anakinumab and total IL-β onentrations were obtained from four linial trials (n = 472). In ontrast to traditional models, free IL-β onentrations were alulated and used to link anakinumab to hanges in C-reative protein (CRP) onentrations and Amerian College of Rheumatology (ACR) sores of 20, 50, and 70% improvement. Temporal patterns of total anakinumab, total IL-β, CRP, and ACR sores were all well desribed. Simulations onfirmed that 50 mg every 4 weeks improved ACR sores in patients with RA, but no additional benefit was provided by higher doses or more frequent administration. Integrating predited endogenous free ligand onentrations with biomarkers and linial outomes ould be extended to new therapies of anti-inflammatory diseases. CPT:Pharmaometris & Systems Pharmaology (202), e5; doi:.38/psp.202.6; advane online publiation 26 September 202 Rheumatoid arthritis (RA) is a hroni, systemi inflammatory disease affeting ~% of the world population.,2 Like many other autoimmune diseases, it disproportionately affets women. 3 Inflammation is the hallmark feature of RA whih usually starts within the small joints, but may also affet other organs suh as artilage and bone. 4 In inflammatory joints, the synovial membrane is hyperplasi, highly vasularized, and infiltrated with ativated immune ells. As the disease progresses, patients experiene pain, stiffness, and swelling of the joints leading to an impaired physial funtion and ultimately a redued life expetany. 5 Interleukin-β (IL-β) is a well-known proinflammatory ytokine released by various ells suh as marophages, keratinoytes, fibroblasts, mastoytes, endothelial, and neuronal ells. Initially, a full length preursor peptide (pro-il-β) is synthesized then leaved within the inflammasome omplex by the aspase- protein to form ative IL-β, whih is released into the extraellular spae. 6,7 IL-β exerts its effets upon binding to its reeptor (IL-βR). A dysregulation of IL-β ativity is harateristi of RA and ours from either an exess of IL-β prodution, resulting in inreased systemi onentrations of the ytokine, or from a qualitative or quantitative defiieny of IL-βR. 8 Current anti-ra therapies are symptomati and aim at reduing the unontrolled auto-inflammatory response. Four groups of anti-ra mediations are approved by the US Food and Drug Administration whih are ortiosteroids, disease modifying antirheumati drugs, nonsteroidal anti-inflammatory drugs, and biologi response modifiers. 9 In the latter group, therapies are either monolonal antibodies that inhibit the ativities of some proinflammatory ytokines suh as IL-6, tumor nerosis fator-α, 9 and IL-β or reombinant human proteins that are IL-βRI antagonists. 2 Although the effetiveness of biologis in RA treatment has been largely shown, disease progression and drug resistane are ommonplae. Canakinumab (Ilaris) 3 is a humanized monolonal antibody targeted against IL-β. Canakinumab was reently approved by the US Food and Drug Administration 4 for the treatment of the Mukle Wells syndrome and the familial old autoinflammatory syndrome. 5 The European Mediines Ageny approved anakinumab for all ryopyrin-assoiated periodi syndromes. 6 In addition to neutralizing IL-β, anakinumab exhibits intraellular effets with data suggesting that the drug an exert a negative feedbak on IL-β prodution and normalizes IL-β onentrations to those of healthy subjets. 7 Pharmaologially, anakinumab binds to and aptures IL-β and thereby neutralizes its ativity, preventing interations with its reeptor (IL-βR). A single subutaneous injetion of 50 mg of anakinumab in patients with RA showed that peak serum onentrations our around 7 days; drug disposition appears to be linear and stationary, with half-life ranging from 22 to 33 days and a mean learane of the total drug of ~0.7 l/day in patients with an average weight of 70 kg. 8 The objetives of this analysis were to (i) develop a pharmaokineti (PK) model for total anakinumab and IL-β disposition in patients with ative RA, (ii) develop pharmaodynami (PD) models that link predited free IL-β exposure with the temporal profiles of a ontinuous biomarker and a ategorial linial outome, namely C-reative protein (CRP) and the Amerian College of Rheumatology (ACR x ) sores (x = 20, 50, or 70% improvement) and (iii) use final models to predit the signal from IL-β aross esalating doses of anakinumab and evaluate the impat on linial outome in patients with RA. ACR x sores are binary PD Department of Pharmaeutial Sienes, University at Buffalo, The State University of New York, Buffalo, New York, USA; 2 Department of Modelling & Simulation, Novartis Pharma AG, Basel, Switzerland. Correspondene: PJ Lowe (phil.lowe@novartis.om) Reeived 9 June 202; aepted 3 August 202;advane online publiation 26 September 202. doi:.38/psp.202.6

2 2 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis endpoints that reflet perent improvement levels in RA from baseline onditions. 9 These riteria were reommended in 995 by the ACR to standardize outome measures in RA trials and are now key riteria for regulatory deisions by the US Food and Drug Administration for antirheumatoid therapies. 20 In ontrast to traditional PK/PD models in whih drug onentrations are diretly linked to response variables, we used model predited plasma onentrations of free IL-β to regulate temporal hanges in plasma onentrations of CRP and the probabilities of ahieving ACR 20, ACR 50, and ACR 70 in patients with RA. Results Data were obtained from four linial trials inluding 472 patients with RA, 80% of whom were women, with a median age of 57 years (range 8 87 years) and a median weight of 74 kg (range 40 kg). A total of 349 patients reeived anakinumab (doses ranged 0. mg/kg to 900 mg) as a subutaneous injetion or 2-h intravenous infusion every 2 or 4 weeks, providing 6,98 total anakinumab and total IL-β plasma onentrations. The remaining 23 patients reeived plaebo. Biomarker measurements inluded 7,925 plasma onentrations of CRP;,394 ACR x sores were reorded. Strutural models The final PK/PD models are depited in Figure. The PK of total anakinumab was desribed using a standard two-ompartment model, with a first-order absorption rate onstant (k a ) and a linear learane (CL) from the entral ompartment. A quasi-equilibrium model was used to desribe the binding of anakinumab to the ligand (IL-β), 2 whih was assumed to be synthesized at a zero-order rate (k syn ) and eliminated with a learane CL L. Free anakinumab (A C ) binds free IL-β (A L ) to form a drug ligand omplex, governed by equilibrium A p V p Q A s K a F A V CL D iv + Plb max Plaebo /τ /τ ACRL E max, EC 50 k syn A L V CLL A DL V CL DL S max, SC 50 CRP CRP γ 2 CRP 3 k in k out kout k out Figure Pharmaokineti/pharmaodynami (PK/PD) model diagram for anakinumab. A s, A, and A p are the amounts of free anakinumab in the subutaneous site, entral, and peripheral ompartments, respetively. A L and drug ligand omplex are the amounts of free IL-β and the omplex of IL-β bound to anakinumab in the entral ompartment. CRP i are the transit ompartments for C-reative protein and ACRL is a latent variable. CRP, C-reative protein; V and V p the anakinumab entral and peripheral volumes of distribution. K d dissoiation onstant (K d ) and removed by a linear learane CL DL. Total anakinumab, T C, as assayed, is the sum of A C and drug ligand omplex; total IL-β, T L, is the sum of A L and drug ligand omplex. During the model building proess, estimates of CL DL and CL were found to be similar; therefore, CL DL and CL were assumed to be equal; therefore, CL represents the overall or total learane of anakinumab. The time delay in the dynamial response of CRP was aptured using a transit ompartment model. 22 As shown in Figure, three transit ompartments were inluded, with CRP prodution as a zero-order proess (k in ). The transfer from one ompartment to the next was through a first-order proess (k out ), assumed to be idential for eah ompartment. Normalized plasma onentrations of free IL-β served as a stimulatory driver for the prodution of CRP. An amplifiation proess, modeled as a γ-parameter on the input to the third differential in the CRP series, was inorporated empirially to ahieve a better fit to the CRP data. The final model for ACR x sores used a modified latent variable (ACRL) approah for multiple related binary outome variables. 23 The disease ondition was modeled using a single transit ompartment with idential first-order prodution and loss rate onstants (/τ, reiproal of the mean transit time). The differene of free IL-β from its baseline was inorporated into a sigmoidal E max funtion to indiretly represent the inhibitory effet of the drug on disease proesses (desribed in Methods setion). The latent variable was related to the probability of ahieving 20, 50, or 70% improvement from baseline onditions using a logit transform. Pharmaokinetis of total anakinumab and total IL-β The timeourse of observed and predited total anakinumab and total IL-β onentrations for three representative patients are shown in the left and middle panels of Figure 2. Total anakinumab profiles suggested a long terminal halflife. Total IL-β onentrations inreased substantially, sometimes over 0-fold, to a new steady-state level. Estimated population PK parameters, along with variability between subjet (BSV) and residual terms for drug and IL-β, are reported in Table. All parameters were estimated with good preision. Bioavailability following subutaneous administration was inomplete at 67%. The interpatient variability for the absorption rate and bioavailability was estimated to be low at 5% and 4%. Espeially, the absorption rate may reflet the limited information available from relatively sparse sampling in the first half-week postdosing. As expeted, the volume of distribution of anakinumab was slightly greater than blood volume (about 7 liters), and the learane of IL-β was greater than that of the drug or drug ligand omplex (3.7 vs. 0.7 l/day). The effets of body weight, age, gender, and methotrexate omediation were tested for explaining BSV of model parameters ontrolling free drug and total IL-β. Only body weight was identified as a statistially signifiant ovariate on CL, CL L, CL D, V, and V p. Model diagnostis are provided in Supplementary Materials and Methods online (Supplementary Figures S S3 online) and normalized visual preditive heks are shown in Supplementary Figure S4 online. No systemati deviation from unity was observed for the ratio of the median to predited onentrations obtained after simulating 0 data sets. CPT: Pharmaometris & Systems Pharmaology

3 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis Canakinumab plasma onentrations (µg/ml) IL-β plasma onentrations, pg/ml CRP plasma onentrations, mg/l Time (days) Figure 2 The time-ourse of plasma onentrations of total anakinumab (left panels), total interleukin-β (IL-β) (enter panels), and C-reative protein (CRP) (right panels) for representative patients all administered subutaneously with anakinumab at 2 mg/kg. Symbols represent the observed onentrations. Solid and broken lines are the mean population and individual model predited onentrations. CRP pharmaodynamis The baseline plasma onentration of CRP was 8.4 mg/l, but exhibited a relatively high BSV of 67% (Table 2). Drug administration resulted in a gradual derease of CRP onentrations suggesting substantial inhibition of CRP in response to a derease in free IL-β (Figure 2, right panels). The model well aptured the overall trend of CRP onentration time profiles (Figure 2). Estimated model parameters for CRP are reported in Table 2; all terms showed good preision. The first-order transit rate onstant was slow (6/day) and a signal amplifiation fator signifiantly improved model fitting (γ =.92). Model diagnostis for CRP are also shown in the Supplementary Materials and Methods online (Supplementary Figures S S4 online) and suggest reasonable model performane. ACR x linial response The visual preditive heks for the probabilities of ACR x sores over time are shown in Figure 3. The model well desribed the data as demonstrated by the entrally loated 50th perentiles (dashed lines) and the 5th and 95th perentiles (shaded areas) enompassing the range of the observed ACR x frequenies. Estimated parameters and BSV terms are reported in Table 2. The apaity parameter for the maximal effet of the drug was greater than that of the plaebo treatment (E max 0.75 vs. 5). Model simulated responses To evaluate the role of anakinumab dose, model simulations of total drug, total and free IL-β, and the differene between baseline and predited IL-β onentrations were onduted for 50, 300, 600, and 900 mg given subutaneously every 2 weeks for five doses (Figure 4). With the exeption of anakinumab pharmaokinetis, temporal profiles of mean onentrations show little differenes aross dose levels. A drug effet was onfirmed in simulations omparing ACR x sores, and the latent variable (ACRL), in plaebo and anakinumab-treated patients with RA following a single subutaneous dose of 50 mg (Figure 5). However, the apparent lak of additional benefit from inreasing the dose beyond 50 mg was further

4 4 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis Table Fixed and random effet parameters of anakinumab and IL-β kinetis Parameter (unit) Definition Estimate (%RSE) Variability a (%RSE) θ ka (day ) First-order absorption 66 (3) 5 (4.47) rate onstant θ V (l) Central volume of 3.7 (4) 37 (8) distribution θ Vp (l) Peripheral volume of 2.24 (4) 39.9 (9) distribution θ CL and θ CLDL (l/day) Drug (and drug ligand) (5).8 (9.4) learane θ CLL (l/day) Free IL-β learane 3.7 (7) 32.4 () θ Q (l/day) Interompartment 0.65 (5) 3.2 (5.4) learane θ Kd (nmol/l) Equilibrium dissoiation 0.38 (8) 34 (2) onstant θ F ( ) Bioavailability 67 (3) 3.68 (5.88) Residual variability a (%) Total drug proportional. (6) error b (nmol/l) Total drug additive error 7 () a 2 (%) Total IL-β proportional 6.6 (7.8) error b 2 (nmol/l) Total IL-β additive error 0.37 (2) IL, interleukin; RSE, relative standard error. a Estimates are apparent oeffiients of variation for the between-subjet variability. θ ksyn = 7.4 ng/day, is the zero-order prodution rate onstant of IL-β and is alulated as θ = ksyn C T,L (0) CL DL Table 2 Fixed and random effets of the population pharmaodynami model for CRP and ACR x Parameter (unit) Definition Estimate (%RSE) Variability a (%RSE) CRP θ CRP0 (mg/l) Baseline CRP 8.44 (6) 66.9 (4) θ kout (day ) First-order transit rate onstant 6 () 32.4 (7.4) θ β ( ) θ γ ( ) Power oeffiient for the stimulatory funtion Power oeffiient for the transit ompartment ACR x θ Emax ( ) Maximum effet of free IL-β 0.74 () θ EC50-IL-β-free (pg/ml) θ τ (day) θ kplb (day ) Free IL-β onentration 04 (2) induing 50% of E max Transit time for the latent variable First-order rate onstant for plaebo onset 5 (2) 75.3 (7.2).92 (2) 63.6 (.7) 55.9 (9) (.24) θ plbmax ( ) Maximum plaebo effet 59 (NA) θ η ( ) Between subjet variability 54.3 (2.) Residual variability a (%) Exponential error term for CRP. (6) ACR x, Amernian College of Rheumatology with x% amelioration; CRP, C-reative protein; NA, not available; RSE, relative standard error. a Estimates are apparent oeffiients of variation for the between subjet variability. supported with simulations omparing the probability of ACR x responses following single subutaneous injetions of inreasing doses (Supplementary Figure S5 online). Disussion In this analysis, population-based models were developed to provide insights into the potential use of anakinumab for treating RA. A wide range of dose levels were evaluated following intravenous and subutaneous administration on one every 2- or 4-week shedules. Although anakinumab appeared to improve linial sores, based on our simulations, inreasing dose levels beyond 50 mg (up to 900 mg) failed to further improve outomes. The final PK/PD models effetively linked a ontinuous endogenous biomarker (i.e., IL-β) to a binary linial response variable (i.e., ACR x ) and provided insights into the apparent lak of a dose response relationship. The pharmaokinetis of total anakinumab appear to be linear and stationary over the range of dose levels tested. A standard two-ompartment model was suffiient for haraterizing total anakinumab disposition, with dose linearity onfirmed by a nonompartmental analysis. 24,25 The integrated anakinumab-il-β PK PD model resembles a quasi-equilibrium approximation of target-mediated drug disposition 2 where temporal hanges in both antibody and ligand are available and influene one another. As total anakinumab disposition is linear, the individual parameters of the two-ompartment model were fixed and the binding model was applied to total IL-β onentrations. The half-life of IL-β was less than that of anakinumab (4.5 h vs. 25 days). The learane of the drug ligand omplex was assumed to be the same as that of the free antibody. As expeted for monolonal antibodies, the absorption half-life for anakinumab was extended (.9 days) and its bioavailability inomplete (67%, Table ). These findings are aligned with previously published results following a subutaneous administration of anakinumab The estimated equilibrium dissoiation onstant was 6.4-times lower than the in vitro measurement, but similar to the estimated value reported in patients experiening ryopyrin-assoiated periodi syndromes. 5,7 The well-estimated PK parameters were also in good agreement with values submitted to the US Food and Drug Administration. 28 This model was used to predit free IL-β onentrations to drive downstream pharmaologial effets of IL-β on inflammatory proesses. The model mean estimated baseline CRP onentration was similar to the average value reported for healthy volunteers. 29 The number of transit ompartments for desribing the CRP profiles was varied and three ompartments were determined to be optimal (data not shown). Despite identifying the optimal number of ompartments, simulations suggested that the stimulatory signal from normalized free IL-β onentrations on CRP prodution was relatively low (data not shown). Therefore, an amplifiation fator was applied on the input to the third transit ompartment to enhane CPT: Pharmaometris & Systems Pharmaology

5 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis 5 Plaebo 50 mg 300 mg 600 mg 900 mg Prob (ACR70 = ) Prob (ACR50 = ) Prob (ACR20 = ) Prob (non resp = ) Time (months) Figure 3 Visual preditive heks for Amerian College of Rheumatology with x% amelioration probabilities. Symbols represent observed frequenies, and broken lines are the median (i.e., 50th perentile) of 0 simulated data sets. Shaded areas represent the bounds of the 5th and 95th perentiles of the predited onfidene interval. the signal. This addition signifiantly improved model fitting and, although the mehanisti explanation remains to be determined, temporal CRP profiles in plasma were then well aptured for all patients. The half-life of the CRP response system, 5.7 h, alulated from the value of k out, of 6/d, was similar to the half-life of CRP itself (about 9 h). 30 A logisti regression model was used to link endogenous IL-β onentrations and a latent variable to apture the timeourse of the probability of ACR x response with high fidelity (Figure 4). We modified the ACRL approah of Hu et al. 23 to inlude regulation of the latent variable by an endogenous fator. The model of Hu et al. 23 is an extension of the mixed effet logisti regression approah with a ontinuous latent variable desribed by Hutmaher et al. 3 Another approah inludes a Markov transition model; 32 however, the multiple outomes methodology allows for the simultaneous fitting of the model to all ACR x sores. At the beginning of the study (time = 0), the logit term approahes, resulting in a probability response prob (ACR x = ) of 0, whih is representative of the initial linial ondition for these patients. In addition, the standard logisti regression approah requires an interept to be estimated for eah ACR x probability response, whereas the ACRL tehnique uses a modified logit term that is flexible and allows interepts to differ aording to the ACR x sore without adding more parameters to the model. The final ACR x model differed from the original 23 in that ACRL was modeled using a transit ompartment driven by predited free endogenous ligand exposure rather than drug onentrations. Despite the relatively large BSV (54% oeffiient of variation), the model well aptured the trend of the observed data (Figure 3). The mean transit time for the amelioration of RA was 56 days and was onsistent with literature results. 23 Model preditions showed that the drop in free IL-β onentrations after binding to free anakinumab has a greater potential for the amelioration of patient symptoms as ompared with the plaebo effet (E max 0.75 vs. 5). The ellular signaling of IL-β is omplex and involves multiple ompeting ligands interating with different forms

6 6 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis a Total anakinumab onentrations (µg/ml) b, Total IL-β onentrations (pg/ml) Free IL-β onentrations (pg/ml) EC d (IL-β baseline-free IL-β) onentrations (pg/ml) Time (days) Figure 4 Simulated temporal profiles for (a) total anakinumab, (b) total IL-β, () free IL-β, and (d) differene between baseline and predited free IL-β onentrations. The simulated regimen was anakinumab administered subutaneously at 2 (solid line), 4 (dashed line), 8 (dotted line), and 2 mg/kg (dashed and dotted line) Q2W. of IL-β membrane-bound or soluble reeptors. 8 The IL-RI reeptor and its assoiated aessory protein, IL-RAP, initiate IL-β signaling ativity, whih is tightly ontrolled by physiologial proesses inluding negative feedbak regulation loops, neutralization and endoytosis of IL-β and binding to deoy and soluble reeptors. 33 Canakinumab seletively attenuates systemi high onentrations of IL-β to the pmol/l range, but allows high onentrations of IL-β in loal inflammatory spaes, suh as joint synovial fluid. Although IL-β is thought to at loally, rather than systemially, it is a potent ytokine, requiring <5% reeptor oupany to indue maximum response. 34,35 In addition, experimental measurements of IL-β onentrations in peripheral tissues are often unavailable. Hene, the final model was implemented using IL-β systemi onentrations to avoid parameter identifiability onerns. A ell-based ativity assay for IL-β signaling ativity following exposure to XOMA-052, a reombinant monolonal antibody with high affinity and speifiity for IL-β, onfirms ativity at low IL-β onentrations around 2 pmol/l. 36,37 The final model predited a -fold lower EC 50 for IL-β than this in vitro measurement (Table 2); this may result from ompetitive binding proesses to IL-RI that our in vivo but not in vitro. Of note, simulations of free IL-β systemi onentrations following esalating doses given at the same shedule reveal that onentrations remain below the EC 50 for all regimens, whih may explain the lak of a dosedependent benefit in ACR x responses for patients reeiving anakinumab (Supplementary Figure S5 online). Indeed, it is the insight into potential mehanisms whih are advantageous over more traditional methods of linking plasma drug onentrations to linial responses. Although it may have been possible, and perhaps quiker, to reate a model where anakinumab indiretly influened CRP and the probability of an ACR response, it would have been neessary to invoke virtual or latent intermediaries to ahieve a model fit. As data were available diretly quantitating the apture of IL-β by anakinumab, it was sensible to inorporate this to generate CPT: Pharmaometris & Systems Pharmaology

7 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis 7 a ACR 20 b ACR mg Plaebo 50 mg Probability of ACR response = ACR 50 d Plaebo ACRL mg Plaebo Plaebo 50 mg Time (months) Figure 5 Simulations of the probability of (a) ACR 20, (b) ACR 50, () ACRr70, and (d) the latent variable (ACRL) after single s injetion of anakinumab. Comparisons are shown for the temporal hanges of the probability of ACR x responses and ACRL between plaebo (solid line) and treated patients with rheumatoid arthritis (dotted line) following administration of anakinumab at a single s dose of 2 mg/kg. ACR, Amerian College of Rheumatology. further understanding on the role of ytokine binding on the dose-time-responses. In summary, this analysis onfirmed that anakinumab does have a linially small but statistially signifiant effiay in RA. It also demonstrated that inreasing anakinumab doses to >50 mg are unlikely to provide further benefit in RA linial outomes. The final PK/PD models aptured the temporal hanges in total anakinumab and IL-β exposure as well as CRP onentrations and linial ACR x sores. On the basis of IL-β signal transdution that an result from low reeptor oupany, the linial endpoint model used exposure of a free endogenous ligand as the pharmaologial driver for subsequent effets. The model also provided a hypothesis for the lak of a lear dose response for anakinumab in RA, in that the extent of the involvement of IL-β in the RA disease proess, though definitely existent, is not as marked as other ytokines suh as tumor nerosis fator-α and IL-6, making the early development detetion and haraterization of a dose response more diffiult. Furthermore, following this analysis is the realization that lower doses would have had to have been tested. Nevertheless, the final model improves understanding of this system and ould be further adapted to pre-existing or new therapies of inflammatory diseases with ontinuous and binary linial endpoints. Methods Clinial trials. Data were obtained from four randomized, plaebo-ontrolled linial studies lasting from 2 weeks to 2 years and 4 months. 27,38 A total of 472 patients with ative RA were reruited, and 349 patients reeived anakinumab at doses ranging from 0. mg/kg to 900 mg (23 patients reeived plaebo). Canakinumab was administered following a short intravenous infusion (2 h) or subutaneously every 2 or 4 weeks (Q2W or Q4W) alone or in assoiation with methotrexate. Individual study designs and linial trial referenes are listed in Supplementary Materials and Methods online (Supplementary Table S online). Study protools were approved by medial ethis ommittees and institutional review boards of the partiipating enters and all subjets provided written informed onsent before enrollment. Analytial assays Total anakinumab and total IL-β serum onentrations. A ompetitive enzyme-linked immunosorbent assay was used to determine total anakinumab onentrations in human plasma as desribed elsewhere. 7 The limit of quantifiation was 42.6 ng/ml. IL-β serum onentrations were measured using the Quantikine HS Human IL-β immunoassay (R&D

8 8 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis Systems, Minneapolis, MN), whih was validated at Novartis (data not shown). Total IL-β (i.e., sum of free IL-β and anakinumab-il-β omplex) was deteted with a limit of detetion of 0. pg/ml in human serum. CRP plasma onentrations. CRP onentrations were measured with a high-sensitivity automated miropartile-enhaned latex turbidimetri immunoassay (CO-BAS MIRA; Rohe, Rotkreuz, Switzerland). The limit of quantifiation was mg/l with an interassay oeffiient of variation of 6.3% at mg/l. Mathematial models Total anakinumab and total IL-β PK. Total anakinumab PK was desribed with the following set of differential equations with T s, T, and T p as the total amounts of anakinumab at the subutaneous injetion site, the entral, and peripheral ompartments, respetively, V and V p the anakinumab entral and peripheral volumes of distribution, and Q the interompartmental drug learane. Initial onditions were defined as T s (0) = F Dose, T (0) = 0, and T p (0) = 0. The bioavailability parameter was modeled in the logit domain: F = (/ + θ F e ηf. Total anakinumab onentrations in the sampled entral ompartment were alulated as T /V and onverted from molar onentrations to (µg/ml) by aounting for moleular weight (50 kda).,3 The binding and dissoiation of anakinumab to IL-β was haraterized using an equilibrium target-mediated disposition model. 2 Endogenous total IL-β turnover was desribed by the following equation dt whih desribes the zero order prodution of IL-β, k syn, followed by a loss of the drug ligand omplexes (TC AC), (e.g., by internalization, CL DL /V C ), then elimination of free IL-β (TL- (TC-AC)) by CL L /V C. The learane of the drug ligand (DL) omplex, CL DL, was assumed to be the same as free drug. The onentration of total IL-β (pg/ml) was alulated as C T,L = T L /V, onverted from molar onentrations by aounting for its moleular weight (7 kda), 33 and the initial ondition was fixed to observed baseline values. Free amounts of anakinumab, A C in Figure, were defined as the solution to the quadrati 2 AC= 0.5 ( T TL KD V) + ( T TL KD V ) +4 KD V T (5) Predited free IL-β onentrations were alulated as C f,l = C T,L C DL, with C DL as the drug ligand omplex: C L DL A = CT,L V C dt K s D = k T dt dt K T CL Q Q = T V V V T a s + + dt p A + V C a s Q V T Q = V T CL CL DL L CLL = k T A V V V T syn C C ( ) p p p p L () (2) (3) (4) CRP dynamis. Predited free IL-β onentrations were used as a driver for stimulating the prodution of CRP. The series of differential equations for the transdution model was dcrp = kin S() t kout CRP dcrp2 = k out ( CRP CRP2) dcrp3 γ = k out ( CRP2 CRP3) The stimulation funtion was defined as S(t) = (C f,l /C f,l (0)) β. An E max or Hill type funtion was evaluated; however, the EC 50 parameter was not identifiable. Thus, a more simplisti equation with a redued number of parameters to be estimated was used to stabilize the model. The initial onditions, CRP(0), were CRP (0) = CRP 2 (0) =k in /k out and CRP 3 (0) = [CRP 2 (0)] γ = [k in /k out ] γ. The zero-order prodution rate onstant (k in ) was omputed as a seondary parameter: k in = [CRP 0 k outγ ] /γ. An empirial amplifiation parameter, γ, was added to the input of the final differential equation, dcrp 3, in order to better fit the model to plasma CRP data. The output from the transdution series, CRP 3, was fitted to the plasma CRP data. ACR x probability responses. The rate of hange of a ontinuous latent variable was desribed as a transit ompartment model 23 dacrl = ( PROD ACRL) τ The initial ondition to Eq. 9 was set to, with τ the mean transit time. The input signal (PROD) was defined as PROD = E f,l E plb, whih is driven by a stimulatory Hill funtion inluding the differene between baseline and free predited IL-β onentrations. E f,l ( ) ( f,l 50 ) ( f,l ( ) f,l ) Emax Cf,L ( 0) Cf,L = C ( 0) EC + C 0 C (6) (7) (8) (9) () The ontribution of the plaebo effet (E plb ) on the latent variable was added to the prodution proess as: E e k plb =plb t plb max ( ) () where plb max is the maximum plaebo effet; t is the time after the first dose; and k plb is a first-order rate onstant. The probability of ahieving 20, 50, or 70% improvement from baseline was desribed using a logit transform logit prob ACR = x ( [ logit x ]) = 0 (2) + logit ( ACRL) +η where the logit funtion is defined as logit(n = ln(n/ n). Simultaneous modeling of ACR x was ahieved by transforming the binary outomes to ategorial variables ahieving ACR 20 = prob(acr 20 = ) ahieving ACR 50 = prob(acr 50 = ) prob(acr 20 = ) ahieving ACR 70 = prob(acr 70 = ) prob(acr 50 = ) not ahieving ACR 20 = prob(acr 20 = ) with probabilities given by Eq. 2. CPT: Pharmaometris & Systems Pharmaology

9 Canakinumab Treatment Outomes in Patients With Rheumatoid Arthritis 9 Data analysis. Population parameters were estimated with the Stohasti Approximation Expetation Maximization algorithm in Monolix (version 3. R2; 39 The BSV on population parameters were estimated and all interindividual terms were assumed to follow a log-normal distribution: P i =θ Pi ηpi e (3) where P i was the PK parameter for the ith individual, θ Pi the population typial value for P i, and η Pi the BSV random effet, whih was normally distributed with a mean of 0 and variane ω 2 Pi. Additive and proportional residual variability models were applied for total anakinumab and total IL-β onentrations C = Cˆ + ε+ε Cˆ (4) ( 2 ) whereas an exponential residual variability error model was used for CRP plasma onentrations: C = Cˆ e ε (5) with C as the observed plasma onentrations, Ĉ the model predited value, ε, ε 2, and ε the additive, proportional, and exponential residual error terms of the observed onentrations for D, L, and CRP, respetively, whih were assumed to be random Gaussian variables with mean zero and variane (σ 2 ). The final model inluded body weight as a signifiant ovariate on D and L learanes as well as the entral and peripheral volumes of distributions suh as: CL = θ CL e ηcl (BWT/70) ¾ and V = θ v e ηv (BWT/70). Goodness of fit for anakinumab, total IL-β, and CRP variables were evaluated by visual inspetion of diagnosti plots. Binning was required to overome the differenes in sampling times over the four studies and visual preditive heks were performed through simulations of 0 data sets using the final PK and PD parameters. For drug, ligand, and CRP measurements, the ratios from the median of the predited data over the median of the observed data were alulated and plotted against time. For ACR x sores, 5th, 95th, and 50th perentiles of the predited ACR x probability responses were superimposed with the observed ACR x response frequenies. Confidene intervals around the frequenies were obtained aording to CI = Pˆ ±.96 Pˆ ( Pˆ )/ N, where ˆP is the observed ACRx frequeny and N the total number of patients at time, t. Aknowledgments. We wish to thank all the patients, liniians, and staff that were responsible for generating the data used in this study. We thank Staey Tannenbaum for her helpful review and disussion of the modeling results. This analysis was supported by the Laboratory of Protein Therapeutis, University at Buffalo, SUNY, and NIH GM57980 (D.E.M.). Author Contributions. P.J.L., S.a-O., and D.E.M. wrote the manusript. P.J.L. and D.E.M. designed the researh. S.a-O. and D.E.M. performed the researh. S.a-O. analyzed the data. Conflit of Interest. P.J.L. is employed by and owns shares in Novartis Pharma AG, Switzerland, the manufaturer of anakinumab. S.A.O. and D.E.M. delare no onflits of interest. As an Assoiate Editor for CPT:PSP, Don Mager was not involved in the review or deision proess for this paper. Study Highlights WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC? Currently, population pharmaokineti pharmaodynami models tend to desribe links between drug onentrations and downstream pharmaodynami responses via diret or indiret response systems whereby drug onentrations are set to ontrol a response or turnover thereof. WHAT QUESTION DID THIS STUDY ADDRESS? This study addressed the inlusion of more mehanismbased detail, desribing, at the molar level, anakinumab binding to and apture of IL-β in patients with RA. WHAT THIS STUDY ADDS TO OUR KNOWLEDGE The alulated suppression of an unmeasurable variable, free (unbound) IL-β was linked to downstream biomarker and linial responses, C-reative protein and ACR sores for 20, 50, and 70% improvement in disease status. HOW THIS MIGHT CHANGE CLINICAL PHARMACOLOGY AND THERAPEUTICS Given that the model fitted the data well, simulations were used to extrat the dose time response relationships. These onfirmed that 50 mg every 4 weeks aptured the majority of IL-β, lowering it below an EC 50 for improving ACR sores in patients with RA; no additional benefits were provided from higher doses or more frequent administration.. Tabrizi, M.A., Tseng, C.M. & Roskos, L.K. Elimination mehanisms of therapeuti monolonal antibodies. Drug Disov. Today, 8 88 (2006). 2. Harris, E.D. Jr. Rheumatoid arthritis. 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