Old and Newer methods for Bayesian updating

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Old and Newer methods for Bayesian updating

• Roger Jelliffe, M.D.
• USC Lab of Applied Pharmacokinetics

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Four types of Bayesian updating

• Maximum Aposteriori Probability (MAP).
• Multiple Model (MM) Bayesian updating.
• Hybrid Bayesian (MAP MM) updating.
• Interacting Multiple Model (IMM) Bayesian
  updating

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Maximum Aposteriori Probability (MAP).

• Can reach out toward an unusual patient
• But the MAP point misses the true patient
• Held back toward the prior
• Also, only 1 point. No graphic view of
  uncertainties.
• What to do?

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2. Multiple Model (MM) Bayesian updating.

• Support points dont change. Values of support
  points stay the same
• Use Bayes theorem to compute the Bayesian
  posterior probability of each support point,
  given patients data
• Problem will not reach out beyond pop param
  ranges. May miss unusual patient. What to do?

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Pop model has definite boundaries
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3. Hybrid Bayesian posterior updating

• Start with MAP Bayesian. It reaches out, but not
  fully. Pop prior holds it back.
• Add new support points nearby, inside and
  outside, to precondition the pop model for the
  new patient data.
• Then do MM Bayesian on ALL the support points.
• We are implementing this now. Out soon.

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Test Case
Probabilities calculated on a 4x4 grid about
optimal 5 percent increase/decrease between grid
points
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4. Bayesian for very unstable patients
interacting multiple model (IMM)

• Limitation of all current Bayesian methods
  assume only 1 set of fixed parameters to fit the
  data.
• Sequential MAP or MM Bayesian same as fitting all
  at once.
• Relax this assumption. Let the true patient
  change during data analysis if more likely to do
  so.
• Hit evasive targets better. IMM.

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What individualized therapy has done

• Digoxin
• Lidocaine
• Aminoglycosides
• Vancomycin
• Busulfan
• Methotrexate

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What individualized therapy has done

• Digoxin

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What individualized therapy has done

• Lidocaine

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What individualized therapy has done

• Aminoglycosides

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Vinks et al. Aminoglycoside therapy 4
hospitals.(TDM 2163-73, 1999)

• Adaptive TDM (ATM) vs ordinary TDM
• Patients 105 127
• Inf on adm 48 62
• Peak conc 10.62.9 ug/ml 7.62.2 plt0.01
• Trough conc 0.70.6 1.41.3 plt.001
• Mortality 9/105 18/127 p.26
• Mort, inf on adm 1/48 9/62 p.023

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Other aminoglycoside outcomes

• ATM TDM
  
• Nephrotoxicity 2.9 13.4 plt.01
• Hospital stay 20.01.4d 26.32.9
  p.045
• Inf on adm 12.60.8d 18.01.4
  plt.001
• Cost (DFL) 13,1259,267 16,88217,721
  plt.05
• Inf on adm 8,8833,778 11,743 7,437
  plt.001

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What individualized therapy has done

• Vancomycin

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Vanco IV Options
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Vanco IV Options
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What individualized therapy has done

• Busulfan

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Bleyzac et al.Busulfan in 29 Ped BMT Pts

• Test Control
• PTS 29 29
• VOD 3.4 24.1
• Graft Failure 0.0 12.0
• Survival 82.8 65.5
• plt.05

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• COST EFFECIVENESS STUDY OF CYCLOSPORIN BAYESIAN
  MONITORING IN PEDIATRIC BONE MARROW
  TRANSPLANTATION

Nathalie BLEYZAC, Emmanuelle SAVIDAN, Claire
GALAMBRUN Hôpital DEBROUSSE, Hospices Civils de
Lyon
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Context

• Bone marrow transplantation
• Numerous complications including graft versus
  host disease (GVHD)
• GVHD prophylaxis Cyclosporine ATG

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Bone marrow transplantation Indications

• Malignant diseases
• Leukemia (ALL, AML, CML, JMML), non Hodgkin
  lymphoma
• Myelodysplastic syndromes
• Non malignant diseases
• Bone marrow failure, hemoglobinopathies
• Immunodeficiencies
• Metabolic disorders

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Cyclosporine PK/PD

• No dose-effect relationship
• Relationship between cyclosporine trough blood
  concentration and GVHD grades
• Existence of cyclosporine target blood
  concentrations specific to each type of graft and
  each pathology

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Cyclosporine therapeutic monitoring Empirical
strategy
More than one week is sometimes needed before
finding the optimal dosage regimen
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Cyclosporine therapeutic monitoring MAP
Bayesian monitoring strategy

• Home-made PK populations
• 3 dose control per week / 2 first weeks
• USCPACK linear PK (? CsA)
• human neuronal network

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Methods (1)

• Strategies compared
• Strategy A Bayesian monitoring (Debrousse
  hospitals)
• Strategy B empirical monitoring (all other
  French centers)
• Costs considered Direct costs
• directly linked to GVHD treatment
• costs of monitoring strategies

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Methods (2) Efficacy of cyclosporine Bayesian
TDM

• Choice of efficacy endpoint
• ? Incidence of severe acute GVHD
• (grades III and IV )
• ? Relapses

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Methods (3) Efficacy data collection

• Strategy A
• Data reported in a previous study patients
  transplanted from Nov. 1999 to Oct. 2004 at
  Debrousse hospital
• 85 children

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Methods (4) Efficacy data collection

• Strategy B
• Literature review Medline request combining
  bone marrow transplantation AND children AND
  GVHD restriction on last 6 years
• ? gt 100 papers
• Selection of studies showing criterion previously
  defined

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Methods (5) Efficacy data collection

• Strategy B
• Selection criterion
• Pediatric studies
• 15 patients
• Incidence of moderate and severe acute GVHD
  clearly indicated

• Exclusion criterion
• Rare pathologies
• Autologous graft
• Peripheral stem cell graft or umbilical cord
  blood graft if no data about BMT

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Methods (6) Efficacy data collection

• Strategy B
• 9 studies
• Warning cohorts differ from ours for different
  reasons
• Data synthesis
• Median percentages about moderate and severe
  acute GVHD incidence calculated from percentages
  reported in each study

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Methods (7)Costs considered

• Cost saved by using strategy A
• Overcost generated by the treatment of one severe
  GVHD
• Mean cost of treatment for a patient affected by
  severe GVHD mean cost of treatment for a
  patient without GVHD or I-II
• Cost of carrying out strategy A

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Methods (8) Costs considered

• Cost of carrying out strategy A
• Cyclosporine blood samples and dosages
• Equivalent in both strategies
• Bayesian monitoring
• Informatics material insignificant
• Staff 0.6 équivalent temps plein (ETP) of
  hospital pharmacist and 1.5 ETP of resident

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Methods (9) Costs considered

• Costs of treatment (severe acute GVHD / no GVHD)
  
• Cost of hospitalization
• Cost of drugs used
• Cost of stable and labile blood products
• Parenteral nutrition
• Biological and imaging investigations
• Calculated from 10 patients files

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Results (1) Strategy efficacy incidence of
GVHD

• Strategy A
• Between 1999 and 2004
• Grade I-II 48.2
• Grade III-IV 8.2
• Strategy B
• Mean
• Grade I-II 39.4
• Grade III-IV 22.4

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Results (2) Additional cost linked to severe
GVHD

• Number of patients concerned
• 26 BMT / year at Debrousse hospital of which
• 26 x 8.2 2.1 patients affected by severe
  acute GVHD each year.
• If cyclosporine was monitored according to
  classical strategy, it would be 26 22.4 5.8
  patients affected by severe acute GVHD each year,
  i.e. 3.7 more.

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Results (3) Resources consumed (costs in
euros)
The additional cost for one severe acute GVHD is
approximately 102 250 euros
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Results (4) Costs avoided by cyclosporine
Bayesian monitoring

• Cost of severe GVHD saved (3.7 x 102250)
• 378 325 euros
• Cost of carrying out strategy A
• 111 000 euros
• Overall cost saved by using strategy A
• 267 325 euros

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Results (5) Sensitivity analysis

• Strategy A remains cost-effective when resources
  varies
• Hospitalization cost length of stay of 50 130
  days
• Quantity of stable and labile blood products
  administered 2000 to 72 000 euros
• Severe GVHD incidence variance above 12.5

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Conclusion

• Cyclosporin MAP Bayesian monitoring strategy is
  cost-effective as it allows
• about 14 less severe acute GVHD
• about 270 000 euros of cost saving per year