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## 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 – PowerPoint PPT presentation

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Title: Old and Newer methods for Bayesian updating

1
Old and Newer methods for Bayesian updating
• Roger Jelliffe, M.D.
• USC Lab of Applied Pharmacokinetics

2
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

3
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?

4
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5
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?

6
Pop model has definite boundaries
7
3. Hybrid Bayesian posterior updating
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.

8
Test Case
Probabilities calculated on a 4x4 grid about
optimal 5 percent increase/decrease between grid
points
9
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.

10
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11
What individualized therapy has done
• Digoxin
• Lidocaine
• Aminoglycosides
• Vancomycin
• Busulfan
• Methotrexate

12
What individualized therapy has done
• Digoxin

13
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14
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15
What individualized therapy has done
• Lidocaine

16
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17
What individualized therapy has done
• Aminoglycosides

18
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19
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20
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21
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

22
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

23
What individualized therapy has done
• Vancomycin

24
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25
Vanco IV Options
26
Vanco IV Options
27
What individualized therapy has done
• Busulfan

28
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

29
• COST EFFECIVENESS STUDY OF CYCLOSPORIN BAYESIAN
MONITORING IN PEDIATRIC BONE MARROW
TRANSPLANTATION

Nathalie BLEYZAC, Emmanuelle SAVIDAN, Claire
GALAMBRUN Hôpital DEBROUSSE, Hospices Civils de
Lyon
30
Context
• Bone marrow transplantation
• Numerous complications including graft versus
host disease (GVHD)
• GVHD prophylaxis Cyclosporine ATG

31
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

32
Cyclosporine PK/PD
• No dose-effect relationship
• Relationship between cyclosporine trough blood
• Existence of cyclosporine target blood
concentrations specific to each type of graft and
each pathology

33
Cyclosporine therapeutic monitoring Empirical
strategy
More than one week is sometimes needed before
finding the optimal dosage regimen
34
Cyclosporine therapeutic monitoring MAP
Bayesian monitoring strategy
• 3 dose control per week / 2 first weeks
• USCPACK linear PK (? CsA)
• human neuronal network

35
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

36
Methods (2) Efficacy of cyclosporine Bayesian
TDM
• Choice of efficacy endpoint
• ? Incidence of severe acute GVHD
• (grades III and IV )
• ? Relapses

37
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

38
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

39
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

40
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

41
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

42
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

43
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

44
Results (1) Strategy efficacy incidence of
GVHD
• Strategy A
• Between 1999 and 2004
• Strategy B
• Mean

45
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.

46
Results (3) Resources consumed (costs in
euros)
The additional cost for one severe acute GVHD is
approximately 102 250 euros
47
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

48
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

49
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