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
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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 Bone et al. 60mg Roux 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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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.
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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.
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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.
1 2 3 4 5 6 7
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29 30 31 32 33 34 35
36 37 38 39
0.850.860.870.880.890.90
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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
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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
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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
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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.
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