Old and Newer methods for Bayesian updating Roger Jelliffe, M.D. USC Lab of Applied Pharmacokinetics 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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? 11/14/2018 USC LAPK

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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? 11/14/2018 USC LAPK

Pop model has definite boundaries 11/14/2018 USC LAPK

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. 11/14/2018 USC LAPK

Test Case Probabilities calculated on a 4x4 grid about optimal 5 percent increase/decrease between grid points 11/14/2018 USC LAPK

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. 11/14/2018 USC LAPK

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What individualized therapy has done Digoxin Lidocaine Aminoglycosides Vancomycin Busulfan Methotrexate 11/14/2018 USC LAPK

What individualized therapy has done Digoxin 11/14/2018 USC LAPK

11/14/2018 USC LAPK

11/14/2018 USC LAPK

What individualized therapy has done Lidocaine 11/14/2018 USC LAPK

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What individualized therapy has done Aminoglycosides 11/14/2018 USC LAPK

11/14/2018 USC LAPK

11/14/2018 USC LAPK

11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

What individualized therapy has done Vancomycin 11/14/2018 USC LAPK

11/14/2018 USC LAPK

Vanco IV Options 11/14/2018 USC LAPK

Vanco IV Options 11/14/2018 USC LAPK

What individualized therapy has done Busulfan 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

COST EFFECIVENESS STUDY OF CYCLOSPORIN BAYESIAN MONITORING IN PEDIATRIC BONE MARROW TRANSPLANTATION Nathalie BLEYZAC, Emmanuelle SAVIDAN, Claire GALAMBRUN Hôpital DEBROUSSE, Hospices Civils de Lyon 11/14/2018 USC LAPK

Context Bone marrow transplantation Numerous complications including graft versus host disease (GVHD) GVHD prophylaxis: Cyclosporine ± ATG 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

Cyclosporine therapeutic monitoring : Empirical strategy YES NO  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 More than one week is sometimes needed before finding the optimal dosage regimen 11/14/2018 USC LAPK

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” 11/14/2018 USC LAPK

Methods (1) Strategies compared : Costs considered : Direct costs : 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 11/14/2018 USC LAPK

Methods (2): Efficacy of cyclosporine Bayesian TDM Choice of efficacy endpoint : → Incidence of severe acute GVHD (grades III and IV ) → Relapses 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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 . 11/14/2018 USC LAPK

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% 11/14/2018 USC LAPK

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. 11/14/2018 USC LAPK

Results (3) : Resources consumed (costs in euros) The additional cost for one severe acute GVHD is approximately 102 250 euros 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK

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% 11/14/2018 USC LAPK

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 11/14/2018 USC LAPK