acture probability of no fr - metrum research group · institute...

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INSTITUTE Linking a Mechanistic Model of Bone Mineral Density to a Time-To-Event Model of Fracture Rena J. Eudy 1 , William R. Gillespie 3 , Matthew M. Riggs 3 , Marc R. Gastonguay 1,2,3 (1) Department of Biomedical Engineering, University of Connecticut, (2) Metrum Institute, (3) Metrum Research Group, LLC Objectives 1. To predict regional changes in bone mineral density (BMD) in patients with osteoporo- sis on three classes of osteoporosis drugs, using a multiscale systems model (MSM) 1 of bone metabolism. 2. To implement a time-to-event (TTE) model of fracture in order to examine the effect of mono- or combination therapy on the probability of fracture during long-term (10-yr) treatment. Methods To develop the MSM, data were assembled from 27 documented clinical trials with teriparatide, denosumab and/or combination therapy. Parameters were optimized using the R package minqa and changes in BMD were simulated using R package mrgsolve. The final model was evaluated by sensitivity analysis. Miller et al. 660mg Miller et al. 1460mg_1 Miller et al. 3060mg Miller et al. 1460mg_2 Miller et al. 60mg Miller et al. 10060mg Miller et al. 210mg Bone et al. 60mg Roux et al. 60mg Leder et al. 60mg Brown et al. 60mg Kendler et al. 60mg Bolognese et al. 60mg 100.0 102.5 105.0 107.5 110.0 100 105 110 100.0 102.5 105.0 107.5 110.0 100.0 102.5 105.0 107.5 110.0 112.5 100 104 108 112 100 105 110 100.0 102.5 105.0 107.5 100 102 104 106 100 102 104 100.0 102.5 105.0 107.5 110.0 100 102 104 100 101 102 103 104 100.0 102.5 105.0 107.5 110.0 036 12 24 48 time (months) % of baseline lumbar spine BMD +/95% CI Bone et al. 60mg Roux et al. 60mg Leder et al. 60mg Brown et al. 60mg Kendler et al. 60mg Bolognese et al. 60mg 100 101 102 103 100 101 102 100 102 104 100 101 102 100 101 102 100 101 102 103 104 036 12 48 036 12 48 036 12 48 time (months) % of baseline femoral neck BMD +/95% CI Miller et al. 660mg Miller et al. 1460mg_1 Miller et al. 3060mg Miller et al. 1460mg_2 Miller et al. 60mg Miller et al. 10060mg Bone et al. 60mg Roux et al. 60mg Leder et al. 60mg Brown et al. 60mg Kendler et al. 60mg Bolognese et al. 60mg 100 102 104 106 100 102 104 106 97.5 100.0 102.5 105.0 100 102 104 106 100 102 104 106 100 102 104 106 100 101 102 103 104 100 101 102 103 100 101 102 103 104 105 100 101 102 103 100 101 102 103 100 101 102 103 104 105 036 12 036 12 036 12 036 12 time (months) % of baseline total hip BMD +/95% CI Figure 1: Trials with denosumab. Graphs show simulated (blue) overlaying data (red) and 95%CIs ●● PhRMA Web Synop et al. Orwoll et al. Miyauchi et al. Miyauchi_2 et al. Cosman et al. Cosman_2 et al. Deal et al. Deal_2 et al. Hwang et al. Saag et al. LY IND et al. Panico et al. Leder et al. Muschitz et al. Yamamoto et al. Walker et al. 97.5 100.0 102.5 105.0 107.5 110.0 97.5 100.0 102.5 105.0 107.5 95 100 105 110 115 100 104 108 100.0 102.5 105.0 107.5 100.0 102.5 105.0 107.5 100 102 104 106 100 102 104 106 100 102 104 106 95 100 105 110 96 100 104 108 100 110 95 100 105 110 100 105 95 100 105 110 115 100 105 110 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 Time (months) % baseline lumbar spine BMD +/95% CI 20ug/day ●● PhRMA Web Synop et al. Orwoll et al. Miyauchi et al. Miyauchi_2 et al. Cosman et al. Cosman_2 et al. Deal et al. Deal_2 et al. Hwang et al. Saag et al. LY IND et al. Panico et al. Leder et al. Muschitz et al. Walker et al. 100 101 102 103 100 101 102 103 100 101 102 103 104 105 99 100 101 102 103 100 101 102 103 104 100 101 102 103 104 100.0 100.5 101.0 101.5 102.0 100 101 102 103 98 99 100 101 100 102 104 106 100 101 102 103 104 100.0 102.5 105.0 107.5 110.0 99 100 101 102 103 104 105 100 102 104 106 108 100 102 104 106 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 Time (months) % baseline femoral neck BMD +/95% CI 20ug/day ●● PhRMA Web Synop et al. Orwoll et al. Miyauchi et al. Miyauchi_2 et al. Cosman et al. Cosman_2 et al. Deal et al. Deal_2 et al. Hwang et al. Saag et al. LY IND et al. Leder et al. Muschitz et al. Walker et al. 100 101 102 103 100 101 102 103 99 100 101 102 103 104 99 100 101 102 103 100 101 102 103 100 101 102 103 99.5 100.0 100.5 101.0 101.5 100 101 102 103 98 99 100 101 100 102 104 106 99 100 101 102 103 104 99 100 101 102 103 104 100 102 104 106 98 100 102 104 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 0 612 24 36 Time (months) % baseline total hip BMD +/95% CI 20ug/day Figure 2: Trials with teriparatide. Graphs show simulated (blue) overlaying data (red) and 95%CIs The data used to develop the hazard model for fracture was comprised of: A subset of individual-level data from the NHANES (2005-2008) database Summary-level BMD and fracture data from publications identified by specific search criteria (39 trials in total involving various treatments). The BMD timecourse used by the fracture model was simulated by the MSM. Candidate models were evaluated by DIC and PPC. 1 2 3 4 5 6 7 9 10 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0.85 0.86 0.87 0.88 0.89 0.90 0.780 0.785 0.790 0.795 0.72 0.75 0.78 0.81 0.61 0.63 0.65 0.76 0.78 0.80 0.801 0.804 0.807 0.810 0.68 0.70 0.72 0.74 0.81 0.82 0.83 0.84 0.72 0.74 0.76 0.78 0.820 0.825 0.830 0.75 0.76 0.77 0.78 0.78 0.80 0.82 0.84 0.86 0.77 0.78 0.79 0.74 0.75 0.76 0.77 0.78 1.05 1.06 1.07 1.08 1.09 1.10 0.84 0.86 0.88 0.90 0.90 0.93 0.96 0.99 0.78 0.80 0.82 0.84 0.76 0.78 0.80 0.82 0.86 0.90 0.94 0.72 0.74 0.76 0.77 0.79 0.81 0.910 0.915 0.920 0.925 0.930 0.72 0.74 0.76 0.78 0.78 0.79 0.80 0.81 0.82 0.83 0.76 0.78 0.80 0.82 0.84 0.85 0.90 0.80 0.81 0.82 0.825 0.850 0.875 0.900 0.77 0.78 0.79 0.80 0.78 0.79 0.80 0.81 0.82 0.83 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.83 0.84 0.85 0.785 0.790 0.795 0.800 0.805 0.75 0.78 0.81 0.78 0.80 0.82 0.825 0.850 0.875 0.900 0.79 0.80 0.81 0.82 0.83 0.84 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 0.0 2.5 5.0 7.5 10.0 0 1 2 3 0.0 0.5 1.0 1.5 0.00 0.25 0.50 0.75 1.00 0 1 2 3 4 0 1 2 3 0 1 2 3 0.00 0.25 0.50 0.75 0 1 2 3 0 1 2 3 0 1 2 3 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 0.0 2.5 5.0 7.5 0 1 2 3 0 1 2 3 4 5 0.0 0.5 1.0 1.5 0 1 2 3 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.3 0.6 0.9 0.0 0.5 1.0 1.5 2.0 0 1 2 3 0.0 0.5 1.0 1.5 0.00 0.25 0.50 0.75 1.00 0.0 0.5 1.0 1.5 0.00 0.25 0.50 0.75 1.00 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.0 2.5 5.0 7.5 10.0 0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 0 1 2 3 Time (years) g/cm^2 Lumbar Spine Bone Mineral Density study 1 0 2 years study 2 0 0.5 years study 2 0 1 years study 2 0 1.5 years study 3 0 5 years study 3 5 10 years study 4 0 2.89 years study 4 0 3.12 years study 5 0 0.5 years study 5 0.5 1 years study 5 0 1.5 years study 6 0 1 years study 7 0 4 years study 8 0 1 years study 8 0 2 years study 8 0 3 years study 9 0 3 years study 10 0 0.85 years study 11 0 0.5 years study 11 0.5 1 years study 11 1 1.5 years study 11 2 3 years study 11 0 2 years study 12 0 1 years study 12 0 2 years study 12 0 3 years study 13 0 1 years study 13 0 1.5 years study 13 0 2 years study 13 0 3 years study 14 0 2 years study 15 0 2 years study 16 0 4 years study 17 6 9 years study 17 0 3 years study 18 0 3 years study 19 0 5 years study 20 0 1.5 years study 21 0 3 years study 22 0 2 years study 23 0 2 years study 24 0 1.08 years study 25 0 1 years study 26 0 3 years study 27 0 1.58 years study 27 0 1.5 years study 28 0 1 years study 29 0 1.5 years study 30 0 1 years study 31 0 2 years study 32 0 1 years study 33 0 2 years study 34 0 1 years study 35 0 1 years study 36 0 3 years study 36 5 10 years study 37 0 2 years study 38 0 4 years study 39 0 3 years 0 10 20 30 40 % of Patients Experiencing Fracture Fracture Rate by Trial Arm A B Figure 3: Metadata summary by trial of longitudinal changes in BMD (A) and fracture rate (B). Colors identify corresponding treatment arms in plots A & B .) R. Eudy, M. Gastonguay, K. Baron, and M. Riggs. Connecting the Dots: Linking Osteocyte Activity and Therapeutic Modulation of Sclerostin by Extending a Multiscale Systems Model. CPT: Pharmacometrics & Systems Pharmacology, (Sept), . Presented at ACoP; Arlington, VA; -October ; Copies available at: metrumrg.com/publications Mechanistic Model Results OB (P1NP) OC (CTx) ROB RANK RANKL OPG PTH TGFβ lat TGFβ act RUNX2 BCL CREB TGFβ act Denos Teri Teri = teriparatide, SCLER = sclerostin, WNT = Wnt gene, OPG = osteoprogerin, RANK/L = Receptor activator of nuclear factor κ Β / - ligand, PTH = parathyroid hormone, CREB = cAMP response element binding protein, BCL = B-cell lymphoma 2, RUNX2 = Runt-related transcription factor 2, TGF-β = transforming growth factor beta (active and latent forms), ROB = responding osteoblasts, Denos = denosumab, OB = osteoblasts, P1NP = procollagen type 1 amino-terminal propeptide, OCY= osteocytes, SCLER mAb= monoclonal antibody against sclerostin, OC = osteoclasts, CTX = cross-linked C-telopeptide FN, LS, TH BMD= femoral neck, lumbar spine, and total hip bone mineral density Stimulatory eect Inhibitory eect Binding / Activation Binding / Inhibition Removal from system Implicit eect SCLER OCY WNT SCLER β-catenin SCLER SCLER mAb WNT FN, LS, TH BMD Figure 4: MSM schematic. Changes in OB and OC, described by changes in turnover markers P1NP and CTx, directly influence regional changes in BMD. Figure adapted from Fig 2 in Ref 1 Anabolic therapies (teriparatide and sclerostin mAb) are described by a two compart- ment disposition to enforce a time-delay for modeling activity: d dt DELAY = kin DELAY · OB OB baseline ! λ OB - kout DELAY · DELAY d dt BMD = kin · DELAY - OC OC baseline ! λ OC · kout · BMD kin DELAY = kout DELAY and kin = kout · BMD baseline Denosumab and combination therapy effects described by a single compartment: d dt BMD = kin · OB OB baseline ! λ OB - OC OC baseline ! λ OC · kout · BMD kin = kout · BMD baseline LUMBAR SPINE kout (1/hrs) gamOC (unitless) gamOB (unitless) kout DELAY (1/hrs) SCLER 0.000145 0.065 0.758 0.00246 DENO 0.0000740 0.0791 0.0793 - TERI 0.000554 0.0169 0.271 0.00100 COMBO 1.86 · DENO 1.28 · DENO 1 · DENO - TOTAL HIP kout (1/hrs) gamOC (unitless) gamOB (unitless) kout DELAY (1/hrs) SCLER 0.000145 0.0653 0.225 0.00246 DENO 0.000108 0.0552 0.0793 - TERI 0.000139 0.131 0.298 0.00100 COMBO 0.971 · DENO 1.28 · DENO 1 · DENO - FEMORAL NECK kout (1/hrs) gamOC (unitless) gamOB (unitless) kout DELAY (1/hrs) SCLER 0.000145 0.0653 0.131 0.00246 DENO 0.000119 0.0515 0.0793 - TERI 0.0000663 0.212 0.496 0.00100 COMBO 1.08 · DENO 1.30 · DENO 1 · DENO - Table 1: Estimated BMD Parameters TTE Model Results The candidate model with the lowest DIC value had the structure: h ij (t) = h 0j exp β BMD 0,j log BMD 0 / \ BMD 0 + β BMD cfb,j (BMD cfb,ij (t)) + β postMenoAge postMenoAge ij (t) - \ postMenoAge + β radFracture I radFracture,ij + β BMI BMI ij - \ BMI + E drug,ij log h 0j BMD 0,j BMD cfb,j N log c h 0 , \ BMD 0 , \ β BMD cfb , Ω h0 , Ω BMD0 , Ω BMD CFB for the i th trial and j th treatment arm. Estimated parameter values (mean, 95%CI): β BMD 0 ( 1 g/cm 2 )=0.396(-2.40; 3.18), β BMD cf b,ij ( 1 g/cm 2 )=4.83(-0.540; 10.2) , β radFracture (unitless)= -0.200(-0.379; -0.0221) β postMenoAge ( 1 yrs )=0.0249(0.0117; 0.0376) , β BMI ( 1 kg/m 2 )= -0.199(-0.0509; 0.0111), β bisphosphates (unitless)= -0.696(-0.833; -0.556), β PTH/teriparatide (unitless)= -0.894(-1.22; -0.578), β denosumab (unitless)= -0.898(-1.21; -0.579), β calcitonin (unitless)= -1.73(-4.92; 0.333), β MK-677 (unitless)= -0.658(-2.62; 0.812), β strontium ranelate (unitless)= -0.764(-1.69; 0.0518), Ω h0 =0.746(0.562; 0.967), Ω BMD0 =3.34(0.0835; 8.99), Ω BMD CFB =9.76(6.04; 15.2) and reference values of 0.8, 20, and 27.1 for BMD, post-menopausal age, and BMI, respectively. individual predictions percent of patients with fractures study 1 zoledronic acid study 1 placebo study 2 placebo study 2 teriparatide study 3 strontium ranelate study 4 teriparatide study 4 alendronate study 5 teriparatide study 6 denosumab study 6 ibandronate study 7 strontium ranelate study 7 placebo study 8 placebo study 8 risedronate study 9 zoledronic acid study 10 alendronate study 10 risedronate study 11 minodronate study 11 placebo study 12 denosumab study 12 placebo study 12 alendronate study 13 placebo study 13 risedronate study 14 placebo study 14 risedronate study 15 placebo study 15 risedronate study 16 alendronate study 16 placebo study 17 alendronate study 17 placebo study 18 denosumab study 19 strontium ranelate study 19 placebo study 20 placebo study 20 teriparatide study 21 placebo study 21 alendronate study 22 placebo study 22 risedronate study 23 zoledronic acid study 23 placebo study 24 zoledronic acid study 24 teriparatide study 25 alendronate study 25 risedronate study 26 placebo study 26 denosumab study 27 placebo study 27 teriparatide study 28 alendronate study 28 placebo study 29 alendronate study 29 MK677 study 29 placebo study 30 alendronate study 30 risedronate study 30 placebo study 31 alendronate study 31 risedronate study 32 alendronate study 33 alendronate study 34 alendronate study 34 risedronate study 35 alendronate study 36 denosumab study 36 alendronate study 37 alendronate study 37 placebo study 37 calcitonin study 38 placebo study 38 alendronate study 39 zoledronic acid study 39 placebo 0 10 20 30 40 50 < 0.843 g/cm^2 0.843 0.947 g/cm^2 0.947 1.05 g/cm^2 > 1.05 g/cm^2 0.80 0.85 0.90 0.95 1.00 0.80 0.85 0.90 0.95 1.00 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time (years) Probability of no fracture 5%ile 95%ile median observed Fracture Risk for Patients Stratifed by Baseline BMD Individual Predictions A B Figure 5: Posterior predictions for the NHANES dataset (A) and the metadataset (B). “Individual” predictions = prediction of hypothetical new observations within the same trial. For B, black = observed fracture; red = posterior median; blue = 90% credible intervals 0.00 0.25 0.50 0.75 1.00 0 1 2 3 4 5 6 7 8 9 10 Time (years) Probability of no fracture combination denosumab pbo teriparatide Simulated Fracture Risk Populationlevel Predictions (90% PI) 100 105 110 115 120 0 3 6 12 18 24 36 time (months) % of baseline combination denosumab teriparatide lumbar spine BMD +/90% CI 2 year treatment A B Figure 6: Simulations using MSM to model predicted changes in BMD (A). Solid lines represent the mean; shading represents simulated error around individual parameters in the model. The median posterior predicted fracture rate is shown (B); Shading represents 90% prediction intervals. Conclusion The MSM predicted regional changes in BMD within the range of clinical variability in most treatment arms. The candidate TTE fracture model that best described the metadataset was the model that included BMD expressed as change from baseline, baseline BMD and an additional drug effect as covariates.

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Page 1: acture Probability of no fr - Metrum Research Group · INSTITUTE LinkingaMechanisticModelofBoneMineralDensitytoaTime-To-EventModelofFracture Rena J. Eudy1, William R. Gillespie3,

INSTITUTE

Linking a Mechanistic Model of Bone Mineral Density to a Time-To-Event Model of FractureRena J. Eudy1, William R. Gillespie3, Matthew M. Riggs3, Marc R. Gastonguay1,2,3(1) Department of Biomedical Engineering, University of Connecticut, (2) Metrum Institute, (3) Metrum Research Group, LLC

Objectives1. To predict regional changes in bone mineral density (BMD) in patients with osteoporo-

sis on three classes of osteoporosis drugs, using a multiscale systems model (MSM)1of bone metabolism.

2. To implement a time-to-event (TTE) model of fracture in order to examine the effect ofmono- or combination therapy on the probability of fracture during long-term (10-yr)treatment.

MethodsTo develop the MSM, data were assembled from 27 documented clinical trials with

teriparatide, denosumab and/or combination therapy. Parameters were optimized usingthe R package minqa and changes in BMD were simulated using R package mrgsolve. The

final model was evaluated by sensitivity analysis.

Miller et al. 6−60mg Miller et al. 14−60mg_1 Miller et al. 30−60mg Miller et al. 14−60mg_2

Miller et al. 60mg Miller et al. 100−60mg Miller et al. 210mg Bone et al. 60mg

Roux et al. 60mg Leder et al. 60mg Brown et al. 60mg Kendler et al. 60mg

Bolognese et al. 60mg

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Figure 1: Trials with denosumab. Graphs show simulated (blue) overlaying data (red) and 95%CIs

PhRMA Web Synop et al. Orwoll et al. Miyauchi et al. Miyauchi_2 et al.

Cosman et al. Cosman_2 et al. Deal et al. Deal_2 et al.

Hwang et al. Saag et al. LY IND et al. Panico et al.

Leder et al. Muschitz et al. Yamamoto et al. Walker et al.

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Figure 2: Trials with teriparatide. Graphs show simulated (blue) overlaying data (red) and 95%CIs

The data used to develop the hazard model for fracture was comprised of:• A subset of individual-level data from the NHANES (2005-2008) database

• Summary-level BMD and fracture data from publications identified by specificsearch criteria (39 trials in total involving various treatments). The BMD timecourseused by the fracture model was simulated by the MSM.Candidate models were evaluated by DIC and PPC.

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0.75

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0.81

0.78

0.80

0.82

0.8250.8500.8750.900

0.790.800.810.820.830.84

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 0.0 2.5 5.0 7.5 10.0 0 1 2 3 0.0 0.5 1.0 1.5 0.0

00.2

50.5

00.7

51.0

0 0 1 2 3 4

0 1 2 3 0 1 2 3 0.00

0.25

0.50

0.75 0 1 2 3 0 1 2 3 0 1 2 3 0.0 0.5 1.0 1.5 2.0

0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 0.0 2.5 5.0 7.5 0 1 2 3 0 1 2 3 4 5 0.0 0.5 1.0 1.5 0 1 2 3

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.3 0.6 0.9 0.0 0.5 1.0 1.5 2.0 0 1 2 3 0.0 0.5 1.0 1.5 0.00

0.25

0.50

0.75

1.00

0.0 0.5 1.0 1.5 0.00

0.25

0.50

0.75

1.00

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

0.0 2.5 5.0 7.5 10.0 0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 0 1 2 3

Time (years)

g/cm

^2

Lumbar Spine Bone Mineral Density

study 1 0 − 2 yearsstudy 2 0 − 0.5 years

study 2 0 − 1 yearsstudy 2 0 − 1.5 years

study 3 0 − 5 yearsstudy 3 5 − 10 years

study 4 0 − 2.89 yearsstudy 4 0 − 3.12 years

study 5 0 − 0.5 yearsstudy 5 0.5 − 1 yearsstudy 5 0 − 1.5 years

study 6 0 − 1 yearsstudy 7 0 − 4 yearsstudy 8 0 − 1 yearsstudy 8 0 − 2 yearsstudy 8 0 − 3 yearsstudy 9 0 − 3 years

study 10 0 − 0.85 yearsstudy 11 0 − 0.5 yearsstudy 11 0.5 − 1 yearsstudy 11 1 − 1.5 years

study 11 2 − 3 yearsstudy 11 0 − 2 yearsstudy 12 0 − 1 yearsstudy 12 0 − 2 yearsstudy 12 0 − 3 yearsstudy 13 0 − 1 years

study 13 0 − 1.5 yearsstudy 13 0 − 2 yearsstudy 13 0 − 3 yearsstudy 14 0 − 2 yearsstudy 15 0 − 2 yearsstudy 16 0 − 4 yearsstudy 17 6 − 9 yearsstudy 17 0 − 3 yearsstudy 18 0 − 3 yearsstudy 19 0 − 5 years

study 20 0 − 1.5 yearsstudy 21 0 − 3 yearsstudy 22 0 − 2 yearsstudy 23 0 − 2 years

study 24 0 − 1.08 yearsstudy 25 0 − 1 yearsstudy 26 0 − 3 years

study 27 0 − 1.58 yearsstudy 27 0 − 1.5 years

study 28 0 − 1 yearsstudy 29 0 − 1.5 years

study 30 0 − 1 yearsstudy 31 0 − 2 yearsstudy 32 0 − 1 yearsstudy 33 0 − 2 yearsstudy 34 0 − 1 yearsstudy 35 0 − 1 yearsstudy 36 0 − 3 years

study 36 5 − 10 yearsstudy 37 0 − 2 yearsstudy 38 0 − 4 yearsstudy 39 0 − 3 years

0 10 20 30 40% of Patients Experiencing Fracture

Fracture Rate by Trial ArmA B

Figure 3: Metadata summary by trial of longitudinal changes in BMD (A) and fracture rate (B). Colors identifycorresponding treatment arms in plots A & B

1.) R. Eudy, M. Gastonguay, K. Baron, and M. Riggs. Connecting the Dots: Linking Osteocyte Activity and Therapeutic Modulation of Sclerostin by Extending a Multiscale Systems Model. CPT: Pharmacometrics& Systems Pharmacology, (Sept), 2015. Presented at ACoP6; Arlington, VA; 07-October 2015; Copies available at: metrumrg.com/publications

Mechanistic Model Results

OB (P1NP)

OC(CTx)

ROB

RANK

RANKL

OPG

PTH

TGFβlat

TGFβact

RUNX2

BCL

CREB TGFβact

Denos

Teri

Teri = teriparatide, SCLER = sclerostin, WNT = Wnt gene, OPG = osteoprogerin, RANK/L = Receptor activator of nuclear factor κ Β / - ligand, PTH = parathyroid hormone, CREB = cAMP response element binding protein, BCL = B-cell lymphoma 2, RUNX2 = Runt-related transcription factor 2, TGF-β = transforming growth factor beta (active and latent forms), ROB = responding osteoblasts, Denos = denosumab, OB = osteoblasts, P1NP = procollagen type 1 amino-terminal propeptide, OCY= osteocytes, SCLER mAb= monoclonal antibody against sclerostin, OC = osteoclasts, CTX = cross-linked C-telopeptide FN, LS, TH BMD= femoral neck, lumbar spine, and total hip bone mineral density

Stimulatory effectInhibitory effect

Binding / ActivationBinding / Inhibition

Removal from systemImplicit effect

SCLER

OCY

WNTSCLER

β-catenin

SCLER

SCLER mAb

WNT

FN, LS, THBMD

Figure 4: MSM schematic. Changes in OB and OC, described by changes in turnover markers P1NP and CTx,directly influence regional changes in BMD. Figure adapted from Fig 2 in Ref 1

• Anabolic therapies (teriparatide and sclerostin mAb) are described by a two compart-ment disposition to enforce a time-delay for modeling activity:

d

dtDELAY = kinDELAY ·

(OB

OBbaseline

)λOB− koutDELAY · DELAY

d

dtBMD = kin · DELAY −

(OC

OCbaseline

)λOC· kout · BMD

kinDELAY = koutDELAY and kin = kout · BMDbaseline

• Denosumab and combination therapy effects described by a single compartment:

d

dtBMD = kin ·

(OB

OBbaseline

)λOB−(

OC

OCbaseline

)λOC· kout · BMD

kin = kout · BMDbaseline

LUMBAR SPINEkout (1/hrs) gamOC (unitless) gamOB (unitless) koutDELAY (1/hrs)

SCLER 0.000145 0.065 0.758 0.00246DENO 0.0000740 0.0791 0.0793 -TERI 0.000554 0.0169 0.271 0.00100

COMBO 1.86 · DENO 1.28 · DENO 1 · DENO -TOTAL HIP

kout (1/hrs) gamOC (unitless) gamOB (unitless) koutDELAY (1/hrs)SCLER 0.000145 0.0653 0.225 0.00246DENO 0.000108 0.0552 0.0793 -TERI 0.000139 0.131 0.298 0.00100

COMBO 0.971 · DENO 1.28 · DENO 1 · DENO -FEMORAL NECK

kout (1/hrs) gamOC (unitless) gamOB (unitless) koutDELAY (1/hrs)SCLER 0.000145 0.0653 0.131 0.00246DENO 0.000119 0.0515 0.0793 -TERI 0.0000663 0.212 0.496 0.00100

COMBO 1.08 · DENO 1.30 · DENO 1 · DENO -

Table 1: Estimated BMD Parameters

TTE Model ResultsThe candidate model with the lowest DIC value had the structure:

hij (t) = h0j exp

(βBMD0,j log

(BMD0/BMD0

)+

βBMDcfb,j (BMDcfb,ij (t)) +

βpostMenoAge

(postMenoAgeij (t)− postMenoAge

)+

βradFractureIradFracture,ij + βBMI

(BMIij − BMI

)+ Edrug,ij

)log(h0j , βBMD0,j

, βBMDcfb,j

)∼ N

((log(h0

), BMD0, βBMDcfb ,Ωh0,ΩBMD0,ΩBMD CFB

))for the i th trial and j th treatment arm.

Estimated parameter values (mean, 95%CI):βBMD0

( 1g/cm2 ) = 0.396(−2.40; 3.18), βBMDcfb,ij

( 1g/cm2 ) = 4.83(−0.540; 10.2) ,

βradFracture(unitless) = −0.200(−0.379; −0.0221) βpostMenoAge( 1yrs

) = 0.0249(0.0117; 0.0376) ,

βBMI(1

kg/m2 ) = −0.199(−0.0509; 0.0111), βbisphosphates(unitless) = −0.696(−0.833; −0.556),

βPTH/teriparatide(unitless) = −0.894(−1.22; −0.578), βdenosumab(unitless) = −0.898(−1.21; −0.579),

βcalcitonin(unitless) = −1.73(−4.92; 0.333), βMK-677(unitless) = −0.658(−2.62; 0.812),

βstrontium ranelate(unitless) = −0.764(−1.69; 0.0518),

Ωh0 = 0.746(0.562; 0.967), ΩBMD0 = 3.34(0.0835; 8.99), ΩBMD CFB = 9.76(6.04; 15.2)

and reference values of 0.8, 20, and 27.1 for BMD, post-menopausal age, and BMI, respectively.

individual predictionspercent of patients with fractures

study 1 zoledronic acidstudy 1 placebostudy 2 placebo

study 2 teriparatidestudy 3 strontium ranelate

study 4 teriparatidestudy 4 alendronatestudy 5 teriparatidestudy 6 denosumabstudy 6 ibandronate study 7 strontium ranelatestudy 7 placebo

study 8 placebostudy 8 risedronate

study 9 zoledronic acidstudy 10 alendronatestudy 10 risedronatestudy 11 minodronate

study 11 placebostudy 12 denosumab

study 12 placebostudy 12 alendronatestudy 13 placebo

study 13 risedronatestudy 14 placebo

study 14 risedronatestudy 15 placebo

study 15 risedronatestudy 16 alendronatestudy 16 placebostudy 17 alendronatestudy 17 placebostudy 18 denosumab

study 19 strontium ranelatestudy 19 placebostudy 20 placebostudy 20 teriparatide

study 21 placebostudy 21 alendronatestudy 22 placebostudy 22 risedronate

study 23 zoledronic acidstudy 23 placebostudy 24 zoledronic acid

study 24 teriparatidestudy 25 alendronatestudy 25 risedronatestudy 26 placebostudy 26 denosumab study 27 placebostudy 27 teriparatidestudy 28 alendronatestudy 28 placebostudy 29 alendronate

study 29 MK−677study 29 placebostudy 30 alendronatestudy 30 risedronatestudy 30 placebostudy 31 alendronatestudy 31 risedronatestudy 32 alendronatestudy 33 alendronatestudy 34 alendronatestudy 34 risedronatestudy 35 alendronatestudy 36 denosumab

study 36 alendronatestudy 37 alendronate

study 37 placebostudy 37 calcitonin study 38 placebostudy 38 alendronate

study 39 zoledronic acidstudy 39 placebo

0 10 20 30 40 50

< 0.843 g/cm^2 0.843 − 0.947 g/cm^2

0.947 − 1.05 g/cm^2 > 1.05 g/cm^2

0.80

0.85

0.90

0.95

1.00

0.80

0.85

0.90

0.95

1.00

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10Time (years)

Prob

abilit

y of

no

fract

ure

5%ile95%ilemedianobserved

Fracture Risk for Patients Stratifed by Baseline BMD Individual Predictions

A B

Figure 5: Posterior predictions for the NHANES dataset (A) and the metadataset (B). “Individual” predictions= prediction of hypothetical new observations within the same trial. For B, black = observed fracture; red =posterior median; blue = 90% credible intervals

0.00

0.25

0.50

0.75

1.00

0 1 2 3 4 5 6 7 8 9 10Time (years)

Prob

abilit

y of

no

fract

ure

combinationdenosumabpboteriparatide

Simulated Fracture Risk Population−level Predictions (90% PI)

100

105

110

115

120

0 3 6 12 18 24 36time (months)

% o

f bas

elin

e

combination denosumab teriparatide

lumbar spine BMD +/− 90% CI 2 year treatment

A B

Figure 6: Simulations using MSM to model predicted changes in BMD (A). Solid lines represent the mean;shading represents simulated error around individual parameters in the model. The median posterior predictedfracture rate is shown (B); Shading represents 90% prediction intervals.

ConclusionThe MSM predicted regional changes in BMD within the range of clinical variability in most treatment arms. The candidate TTE fracture model that best described the metadataset was the model that included BMDexpressed as change from baseline, baseline BMD and an additional drug effect as covariates.