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Old and Newer methods for Bayesian updating

Old and Newer methods for Bayesian updating. Roger Jelliffe, M.D. USC Lab of Applied Pharmacokinetics. Four types of Bayesian updating. Maximum Aposteriori Probability (MAP). Multiple Model (MM) Bayesian updating. Hybrid Bayesian (MAP + MM) updating.

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Old and Newer methods for Bayesian updating

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

  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 USC LAPK

  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? USC LAPK

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  5. 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? USC LAPK

  6. Pop model has definite boundaries USC LAPK

  7. 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. USC LAPK

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

  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. USC LAPK

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  11. What individualized therapy has done • Digoxin • Lidocaine • Aminoglycosides • Vancomycin • Busulfan • Methotrexate USC LAPK

  12. What individualized therapy has done • Digoxin USC LAPK

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  15. What individualized therapy has done • Lidocaine USC LAPK

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  17. What individualized therapy has done • Aminoglycosides USC LAPK

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  21. 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 USC LAPK

  22. Other aminoglycoside outcomes • ATM TDM • Nephrotoxicity 2.9% 13.4% p<.01 • Hospital stay 20.0±1.4d 26.3±2.9 p=.045 • Inf on adm 12.6±0.8d 18.0±1.4 p<.001 • Cost (DFL) 13,125±9,267 16,882±17,721 p<.05 • Inf on adm 8,883±3,778 11,743± 7,437 p<.001 USC LAPK

  23. What individualized therapy has done • Vancomycin USC LAPK

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  25. Vanco IV Options USC LAPK

  26. Vanco IV Options USC LAPK

  27. What individualized therapy has done • Busulfan USC LAPK

  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% *p<.05 USC LAPK

  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 USC LAPK

  30. Context • Bone marrow transplantation • Numerous complications including graft versus host disease (GVHD) • GVHD prophylaxis: Cyclosporine ± ATG USC LAPK

  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 USC LAPK

  32. Cyclosporine: PK/PD • No dose-effect relationship • Relationship between cyclosporine trough blood concentration and GVHD grades • Existence of cyclosporine target blood concentrationsspecific to each type of graft and each pathology USC LAPK

  33.  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 YES NO Cyclosporine therapeutic monitoring :Empirical strategy More than one week is sometimes needed before finding the optimal dosage regimen USC LAPK

  34. 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” USC LAPK

  35. 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 USC LAPK

  36. Methods (2):Efficacy of cyclosporine Bayesian TDM Choice of efficacy endpoint : → Incidence of severe acute GVHD (grades III and IV ) → Relapses USC LAPK

  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 USC LAPK

  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 → >100 papers • Selection of studies showing criterion previously defined USC LAPK

  39. 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 Methods (5):Efficacy: data collection USC LAPK

  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 USC LAPK

  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 USC LAPK

  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 USC LAPK

  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 USC LAPK

  44. 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% USC LAPK

  45. 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. USC LAPK

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

  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 USC LAPK

  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% USC LAPK

  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 USC LAPK

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