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
1. 2. 3. 4. 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 don’t change. Values of support points stay the same – Use Bayes’ theorem to compute the Bayesian posterior probability of each support point, given patient’s 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
4x4 added grid points (MAP with red circle) 0.32 0.315 0.31 0.305 0.3
Vs1
MM probability (MAP with red circle) 0.35
0.3
0.25
0.2
prob
0.295 0.29 0.285 0.28
0.15
0.1
0.05 0.275 0.27 1.18 0 1.2 1.22 1.24 1.26 1.28 Ks1 1.3 1.32 1.34 1.36 1.38
-3
0
2
4
6
x 10
8 grid index
10
12
14
16
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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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MAP,MM
IMM
Errors in tracking serum conc: Sequential 8/11/2008 USC LAPK MAP, MM, and IMM Bayesian posteriors
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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 21:63-73,
1999)
• • • • • • •
Adaptive TDM (ATM) vs ordinary TDM Patients 105 127 Inf on adm 48 62 Peak conc 10.6±2.9 ug/ml 7.6±2.2 p<0.01 Trough conc 0.7±0.6 1.4±1.3 p<.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
2.9%
20.0±1.4d 12.6±0.8d
13,125±9,267 8,883±3,778
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TDM
13.4%
26.3±2.9 18.0±1.4
• Nephrotoxicity
• Hospital stay – Inf on adm
p<.01
p=.045 p<.001
• Cost (DFL)
– Inf on adm
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16,882±17,721 p<.05
11,743± 7,437 p<.001
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What individualized therapy has done
• Vancomycin
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Vanco IV Options
4500 4000 3500 3000 2500 2000 1500 1000 500 0 Total Daily Dose
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Q 24 h - 12 Q 12 h - 12 Q 8 h - 12 Q 6 h - 12 Q 4 h - 12 Cont IV-12 Cont IV-22
Vanco IV Options
200 180 160 140 120 100 80 60 40 20 0
Q 24 h - 12 Q 12 h - 12 Q 8 h - 12 Q 6 h - 12 Q 4 h - 12 Cont IV- 12 Cont IV- 22 Peak Cen Tr Cen Peak Per
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What individualized therapy has done
• Busulfan
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Bleyzac et al. Busulfan in 29 Ped BMT Pts
PTS VOD Graft Failure Survival
Test Control 29 29 3.4% 24.1%* 0.0% 12.0% 82.8% 65.5% *p<.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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• Malignant diseases :
Bone marrow transplantation : Indications
Leukemia (ALL, AML, CML, JMML), non Hodgkin lymphoma
• Myelodysplastic syndromes • Non malignant diseases :
Bone marrow failure, hemoglobinopathies
• Immunodeficiencies • 8/11/2008 Metabolic disorders LAPK USC
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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
YES
or doses by 5 to 10% increment if trough blood concentration differ from target values (Cmin between 100 et 200ng/ml)
new measure of trough blood concentration to verify it is within target values range
NO
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 hospital’s)
– 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 → > 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)
Exams
Patients FRE LAT CRO FOUR GON BEL KON SAL FOUC Cost 15534 18154 14105 11005 5678 12895 4271 5087 2786 1257 3350
Blood Hospitalizat products ion costs
Cost 21364 10724 71630 16579 2003 24460 735 3831 3990 1295 2463 Cost 73950 190791 113883 81345 78387 107671 41412 60639 42891 42891 46958
Parenteral nutrition
Cost 1045 2445 1601 1067 1023 1436 311 800 556 311 495
Drugs
Cost 10585 2993 29870 2000 1150 9320 397 264 69 402 283
Total cost 122478 225107 231090 111995 88240 155782 47126 70621 50291 46156 53549
GRADE III/IV
median no GVHD
median
Overcost
9545
21997
60713
941
9037
102233
The additional cost for one severe acute GVHD is approximately 102 250 euros 8/11/2008 USC LAPK 46
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
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