bayesian forecasting utilizing bleeding information to support … · 2019-06-18 · bayesian...
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Bayesian forecasting utilizing bleeding information to support dose individualization of factor VIII
João A. Abrantes1, Alexander Solms2, Dirk Garmann3, Elisabet I. Nielsen1, Siv Jönsson1, Mats O. Karlsson1
(1) Uppsala Pharmacometrics Research Group, Uppsala University, Uppsala, Sweden(2) Bayer, Berlin, Germany(3) Bayer, Wuppertal, Germany
28th PAGE meetingStockholm, Sweden, 12 June 2019
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Haemophilia A
• Congenital X-linked bleeding disorder
• Deficiency of coagulation factor VIII (FVIII)
• Characteristic phenotype: spontaneous bleeding events
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Severe haemophilia A
3
Endogenous plasma factor VIII activity <1 IU/dL
Severe (<1 IU/dL)
Clock time
8:30Wed
14:30 20:30 2:30Thu
8:30 14:30 20:30 2:30Fri
8:30 14:30 20:30 2:30Sat
8:30
Healthy subject
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FVIII replacement therapy
3[1] O'Hara J et al. Orphanet J Rare Dis. 2017;12(1):106
Prophylactic administration of 15-40 IU/kg 3x week
Clock time
8:30Wed
14:30 20:30 2:30Thu
8:30 14:30 20:30 2:30Fri
8:30 14:30 20:30 2:30Sat
8:30FVIIIinfusion
clinical and economic burden (~ €200 000/patient/year)[1]
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FVIII replacement therapy
3[1] Berntorp E. J Thromb Haemost. 2017;15(6):1103-5 [2] Iorio A et al. J Thromb Haemost. 2017;15(12):2461-5
PK-guided model-based dose individualization increasingly encouraged [1,2]
Clock time
8:30Wed
14:30 20:30 2:30Thu
8:30 14:30 20:30 2:30Fri
8:30 14:30 20:30 2:30Sat
8:30FVIIIinfusion
Treatment targetTrough FVIII >1 IU/dL
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3[1] Berntorp E. J Thromb Haemost. 2017;15(6):1103-5 [2] Iorio A et al. J Thromb Haemost. 2017;15(12):2461-5Clock time
8:30Wed
14:30 20:30 2:30Thu
8:30 14:30 20:30 2:30Fri
8:30 14:30 20:30 2:30Sat
8:30
Treatment targetTrough FVIII >1 IU/dL
Patient 4
Patient 2Patient 3
Patient 1
FVIIIinfusion
FVIII replacement therapyPK-guided model-based dose individualization increasingly encouraged [1,2]
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4
Population PK model(IIV on CL, V1, residual error)
V1 V2
LBW
LBW
Population PK model2-compartment model
PK-bleed-covariate modelDose-exposure-response relationship
CL: clearance; IIV: inter-individual variability; LBW: lean body weight; V1 and V2: central and peripheral volumes of distributionAbrantes et al. PAGE 27 (2018) Abstr 8646 [www.page-meeting.org/?abstract=8646]
CL
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5
Population PK model(IIV on CL, V1, residual error)
RTTE model(IIV on h(t))
h(t) = 3.0 · e-0.57 · (t - 1) · 1 − FVIIIFVIII + IF50 · eη
PK-bleed-covariate modelDose-exposure-response relationship
CL: clearance; IIV: inter-individual variability; V1: central volume of distributionAbrantes et al. PAGE 27 (2018) Abstr 8646 [www.page-meeting.org/?abstract=8646]
Bleed model Repeated time-to-event model
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6
Population PK model(IIV on CL, V1, residual error)
RTTE model(IIV on h(t))
Covariates
PK-bleed-covariate modelDose-exposure-response relationship
BMI: body mass index; CL: clearance; IIV: inter-individual variability; LBW: lean body weight; V1: central volume of distributionAbrantes et al. PAGE 27 (2018) Abstr 8646 [www.page-meeting.org/?abstract=8646]
CovariatesFull random effects modeling
• Age• Body weight, LBW, BMI• Race• von Willebrand factor levels• Number of spontaneous bleeds within 12
months pre-study• Pre-study treatment (prophylaxis/on-demand)• Number of target joints at study start• Study
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Aim
Use the PK-bleed-covariate model to contrast different sources of patient information in their ability to predict future occurrence of bleeds
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Wait…but why? Considering other sources of
patients’ information may ↑ accuracy in predictions and
cost-effectiveness
Current model-based dose individualization methods
are mainly PK-guided
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Clinical data
LEOPOLD I and II clinical trials[1-3]
• 121 patients with severe haemophilia A (≥12 years)• Prophylactic treatment with octocog alfa• 12 months
– 798 sparse FVIII activity observations– 530 bleeding events (~1% of all observed days)– 11 covariates(subset of data used to develop the PK-bleed-covariate model)
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LEOPOLD: Long-Term Efficacy Open-Label Program in Severe Hemophilia A Disease[1] Saxena K et al. Haemophilia. 2016;22(5):706-12. [2] Kavakli K et al. J Thromb Haemost. 2015;13(3):360-9. [3] Ljung R et al. Haemophilia. 2016;22(3):354-60
Evaluations based on observed data
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Bleeding forecasting workflow
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Bayesian forecasting + calculation of Pi(bleeding)
JuneM T W T F S S1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 5
EBEs patient i Day 1 Day 1, 2 Day 1 … n-1
Pi(bleeding) patient i Day 2 Day 3 Day nn: last day of patient i in the studyPi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
EBEs: empirical Bayes estimates (individual parameters, eg. individual clearance or individual bleeding hazard)Pi(bleeding) = 1 - 𝑒𝑒− ∫t
t+24 hi t dt, where t is the end of the Bayesian forecasting observation period
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Bleeding forecasting workflow
9
Bayesian forecasting + calculation of Pi(bleeding)
JuneM T W T F S S1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 5
EBEs patient i Day 1 Day 1, 2 Day 1 … n-1
Pi(bleeding) patient i Day 2 Day 3 Day nn: last day of patient i in the studyPi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
EBEs: empirical Bayes estimates (individual parameters, eg. individual clearance or individual bleeding hazard)Pi(bleeding) = 1 - 𝑒𝑒− ∫t
t+24 hi t dt, where t is the end of the Bayesian forecasting observation period
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Bleeding forecasting workflow
9
Bayesian forecasting + calculation of Pi(bleeding)
JuneM T W T F S S1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 5
EBEs patient i Day 1 Day 1, 2 Day 1 … n-1
Pi(bleeding) patient i Day 2 Day 3 Day nn: last day of patient i in the studyPi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
EBEs: empirical Bayes estimates (individual parameters, eg. individual clearance or individual bleeding hazard)Pi(bleeding) = 1 - 𝑒𝑒− ∫t
t+24 hi t dt, where t is the end of the Bayesian forecasting observation period
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Bleeding forecasting workflow
9
Bayesian forecasting + calculation of Pi(bleeding)
JuneM T W T F S S1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 5
EBEs patient i Day 1 Day 1, 2 Day 1 … n-1
Pi(bleeding) patient i Day 2 Day 3 Day nn: last day of patient i in the studyPi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
EBEs: empirical Bayes estimates (individual parameters, eg. individual clearance or individual bleeding hazard)Pi(bleeding) = 1 - 𝑒𝑒− ∫t
t+24 hi t dt, where t is the end of the Bayesian forecasting observation period
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Bleeding forecasting workflow
9
Bayesian forecasting + calculation of Pi(bleeding)
JuneM T W T F S S1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 n
EBEs patient i Day 1 Day 1, 2 Day 1 … n-1
Pi(bleeding) patient i Day 2 Day 3 Day nn: last day of patient i in the studyPi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
EBEs: empirical Bayes estimates (individual parameters, eg. individual clearance or individual bleeding hazard)Pi(bleeding) = 1 - 𝑒𝑒− ∫t
t+24 hi t dt, where t is the end of the Bayesian forecasting observation period
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Information scenarios
10
“PK”, “Bleed”, and “All”
PKPK observations
BleedBleeding observations
AllPK, bleeding observations
and covariates
PK
PK
PK
PK
+ covariates
Infusion No bleed BleedPK PK sampling
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Time-varying bleeding probabilistic forecast
11Pi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
Illustrative patient
Pred
icte
d
PKBleed
All
Time of bleedFVIII infusion
P i(b
leed
ing)
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Predictive performance assessment
• Pi(bleeding) was compared with the actual occurrence or non-occurrence of a bleed on the forecasted day– Separation plots[1]
– Receiver operating characteristic (ROC) analyses[2]
– Precision-recall analyses[3]
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Pi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h[1] Greenhill B et al. American Journal of Political Science. 2011; 55 991-1002. [2] Fawcett T. Pattern recognition letters. 2006; 861-874. [3] Saito T, Rehmsmeier M. PLoS One. 2015;10(3):e0118432
Three techniques were used
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Merged Pi(bleeding) data for all days for all patients
Patient Forecasted day Pi(bleeding) Bleed1 2 0.020 0
1 3 0.075 0
1 4 0.051 0
1 n 0.037 0
2 2 0.056 0
2 3 0.012 0
2 4 0.094 1
2 n 0.031 0
3 2 0.252 1
3 3 0.181 0
3 4 0.138 0
3 n 0.121 0
Separation plots
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Patient Forecasted day Pi(bleeding) Bleed2 3 0.012 0
1 2 0.020 0
2 n 0.031 0
1 n 0.037 0
1 4 0.051 0
2 2 0.056 0
1 3 0.075 0
2 4 0.094 1
3 n 0.121 0
3 4 0.138 0
3 3 0.181 0
3 2 0.252 1 13
Rows ordered according to the ascending order of Pi(bleeding)Separation plots
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Highlighted rows corresponding to days when bleeds actually occurred
Patient Forecasted day Pi(bleeding) Bleed2 3 0.012 0
1 2 0.020 0
2 n 0.031 0
1 n 0.037 0
1 4 0.051 0
2 2 0.056 0
1 3 0.075 0
2 4 0.094 1
3 n 0.121 0
3 4 0.138 0
3 3 0.181 0
3 2 0.252 1
Separation plots
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Low Pi(bleeding) High Pi(bleeding)
Separation plots
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14Pi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 h
bleed dayno-bleed day
Ordered Pi(bleeding)
P i(b
leed
ing)
0.15
0.10
0.05
0.00
Low Pi(bleeding) High Pi(bleeding)
Separation plots
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Separation plotsBleed and All associated with higher relative Pi(bleeding)
Pi(bleeding): individual forecasted probability of having a bleed in the upcoming 24 hSeparation plots showing all predicted days for all patients. Since the occurrence of bleeds was rare (~1.2% of forecasted days), vertical bars corresponding to bleed days were emphasized.
bleed dayno-bleed day
Ordered Pi(bleeding)
P i(b
leed
ing)
Pi(bleeding)
• Bleed days more often associated with higher Pi(bleeding) in Bleed and All than in PK
• PK information and covariates did not substantially improve the predictive performance
PK (PK observations)
Bleed (bleeding observations)
All (PK observations, bleeding observations and covariates)
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Receiver operating characteristic (ROC) analysisBleeds were a main component driving the forecast of future bleeds
True positive rate = true positivespositives , false positive rate = false positives
negatives
PK
BleedAll
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Precision-recall analysisBleeds were a main component driving the forecast of future bleeds
Precision = true positivestrue positives + false positives (low precision observed for all information scenarios as expected); recall = true positive rate = true positives
positives
PK
BleedAll
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Some limitations
• Evaluation based on a subset of data used to develop the model
• Study design, for instance:– PK sampling times– Patients well protected against bleeds
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• An integrated PK-bleed-covariate model approach can be used to forecast the occurrence of bleeds under prophylactic treatment
• Three techniques confirmed that past bleeding information is a main component driving the forecast of future bleeds
• Further steps to optimize the proposed tool for FVIII dose adaptation are required
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What have we learnt?
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Acknowledgements
Uppsala PharmacometricsResearch Group
Apotekare Gunnar Hylténs stiftelse
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João A. Abrantes1, Alexander Solms2, Dirk Garmann3, Elisabet I. Nielsen1, Siv Jönsson1, Mats O. Karlsson1
(1) Uppsala Pharmacometrics Research Group, Uppsala University, Uppsala, Sweden(2) Bayer, Berlin, Germany(3) Bayer, Wuppertal, Germany
28th PAGE meetingStockholm, Sweden, 12 June 2019
Bayesian forecasting utilizing bleeding information to support dose individualization of factor VIII
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Varying the observation period lengthThe longer the observation period for EBEs estimation the better
Prediction errori= Bleedforecast – Bleedobserved where Bleedforecast and Bleedobserved are the number of forecasted and observed bleeds during the whole individual study period. Bleeding risk was categorized as: low risk, if patients did not bleed during the study (N=33); moderate risk, 1-4 bleeds (N=49); and high risk, ≥5 bleeds (N=39)
Information scenario: Bleed
Overprediction
Underprediction
S3