A Bayesian PK/PD model for synergy A case study Fabiola La Gamba, Tom Jacobs, Christel Faes 23/06/2016 0 Importance of being uncertain
Case study To assess the safety resulting from the co-administration of a novel molecule with an existing, marketed treatment using in-vivo data Data sets: Historical study : Dose-response longitudinal data where only • the existing treatment is administered (55 rats in total) 11 synergy studies : Both existing and novel treatments are • administered. One specific dose combination in each study: (Non-clinical) My PhD Biostatistics A Bayesian PK/PD model for synergy; a case study 23/06/2016 1
Case study To assess the safety resulting from the co-administration of a novel molecule with an existing, marketed treatment using in-vivo data Data sets: Historical study : Dose-response longitudinal data where only • the existing treatment is administered (55 rats in total) 11 synergy studies : Both existing and novel treatments are • administered. One specific dose combination in each study: (Non-clinical) My PhD Biostatistics A Bayesian PK/PD model for synergy; a case study 23/06/2016 2
Case study To assess the safety resulting from the co-administration of a novel molecule with an existing, marketed treatment using in-vivo data Data sets: Historical study : Dose-response longitudinal data where only • the existing treatment is administered (55 rats in total) 11 synergy studies : Both existing and novel treatments are • administered. One specific dose combination in each study: (Non-clinical) My PhD Biostatistics Study 1 2 3 4 5 6 7 8 9 10 11 Existing treatment 10 2.5 10 0.63 10 0.16 2.5 0.63 0.16 0.04 0.04 dose (mpk) Novel treatment 40 40 10 40 2.5 40 10 10 10 10 40 dose (mpk) A Bayesian PK/PD model for synergy; a case study 23/06/2016 3
Case study To assess the safety resulting from the co-administration of a novel molecule with an existing, marketed treatment using in-vivo data Data sets: Historical study : Dose-response longitudinal data where only • the existing treatment is administered (55 rats in total) 11 synergy studies : Both existing and novel treatments are • administered. 20 rats in each study, 5 for each treatment group: (Non-clinical) My PhD Biostatistics Existing Treatments treatment only combination (Non-clinical) My PhD Biostatistics Novel Vehicle treatment only A Bayesian PK/PD model for synergy; a case study 23/06/2016 4
Case study To assess the safety resulting from the co-administration of a novel molecule with an existing, marketed treatment using in-vivo data Data sets: Historical study : Dose-response longitudinal data where only • the existing treatment is administered (55 rats in total) 11 synergy studies : Both existing and novel treatments are • administered (Non-clinical) My PhD Biostatistics Study variables: Existing treatment dose • Novel treatment dose (only in synergy studies) • Continuous safety biomarker, measured at the moment of oral • administration, and after 1, 2, 3, 4 hours A Bayesian PK/PD model for synergy; a case study 23/06/2016 5
How does the data look like? Example from study 1 (Non-clinical) My PhD Biostatistics Which model is the most suitable? A Bayesian PK/PD model for synergy; a case study 23/06/2016 6
A nice answer: PK-PD model 𝑒𝐵 𝑓𝑗𝑢 i =1, …, S ( subjects) = −𝑙 𝑏 𝐵 𝑓𝑗𝑢 PK Part : 𝑒𝑢 t=0, …, 4 (hours) one compartment model with oral 𝑒𝐷 𝑗𝑢 𝑒𝑢 = 𝑙 𝑏 𝐵 𝑓𝑗𝑢 − 𝑙 𝑓 𝐷 𝑗𝑢 absorption A 𝑓𝑗𝑢 =Existing treatment amount 𝐵 𝑜𝑗0 =Novel treatment dose PD part : 𝑗𝑢 , 𝜏 2 ) 𝑗𝑢 𝑆 𝑗𝑢 =Response: 𝑆 𝑗𝑢 ~𝑂(𝑆 𝑒𝑆 𝐽 𝑛𝑏𝑦 𝐷 𝑗𝑢 𝑗𝑢 𝑒𝑢 = 𝑙 𝑗𝑜 1 − 𝐽𝐷 50 +𝐷 𝑗𝑢 − 𝑙 𝑝𝑣𝑢 𝑆 indirect response 𝐷 𝑗𝑢 =Plasma concentration of the (turnover) model existing treatment (latent!) 𝑓 𝛾𝐵 𝑓𝑗0 𝐵 𝑜𝑗0 𝑗𝑢=0 = 𝑙 𝑗𝑜 /𝑙 𝑝𝑣𝑢 With: 𝐵 𝑓𝑗𝑢=0 = 𝐵 𝑓𝑗0 (𝑓𝑦𝑗𝑡𝑢𝑗𝑜 𝑢𝑠𝑓𝑏𝑢𝑛𝑓𝑜𝑢 𝑒𝑝𝑡𝑓); 𝐷 𝑗𝑢=0 = 0; 𝑆 Parameters : 𝑙 𝑏 ≥ 0 : Absorption constant 𝑙 𝑓 ≥ 0 : Elimination constant 𝑙 𝑗𝑜 ≥ 0 : Constant for response production 𝑙 𝑝𝑣𝑢 ≥ 0 : Constant for response loss 0 ≤ 𝐽 𝑛𝑏𝑦 ≤ 1 : Maximal inhibition attributed to drug 𝛾 : Interaction coefficient A Bayesian PK/PD model for synergy; a case study 23/06/2016 7
A nice answer: PK-PD model 𝑒𝐵 𝑓𝑗𝑢 i =1, …, S ( subjects) = −𝑙 𝑏 𝐵 𝑓𝑗𝑢 PK Part : 𝑒𝑢 t=0, …, 4 (hours) one compartment model with oral 𝑒𝐷 𝑗𝑢 𝑒𝑢 = 𝑙 𝑏 𝐵 𝑓𝑗𝑢 − 𝑙 𝑓 𝐷 𝑗𝑢 absorption A 𝑓𝑗𝑢 =Existing treatment amount 𝐵 𝑜𝑗0 =Novel treatment dose PD part : 𝑗𝑢 , 𝜏 2 ) 𝑗𝑢 𝑆 𝑗𝑢 =Response: 𝑆 𝑗𝑢 ~𝑂(𝑆 𝑒𝑆 𝐽 𝑛𝑏𝑦 𝐷 𝑗𝑢 𝑗𝑢 𝑒𝑢 = 𝑙 𝑗𝑜 1 − 𝐽𝐷 50 +𝐷 𝑗𝑢 − 𝑙 𝑝𝑣𝑢 𝑆 indirect response 𝐷 𝑗𝑢 =Plasma concentration of the (turnover) model existing treatment (latent!) 𝑓 𝛾𝐵 𝑓𝑗0 𝐵 𝑜𝑗0 𝑗𝑢=0 = 𝑙 𝑗𝑜 /𝑙 𝑝𝑣𝑢 With: 𝐵 𝑓𝑗𝑢=0 = 𝐵 𝑓𝑗0 (𝑓𝑦𝑗𝑡𝑢𝑗𝑜 𝑢𝑠𝑓𝑏𝑢𝑛𝑓𝑜𝑢 𝑒𝑝𝑡𝑓); 𝐷 𝑗𝑢=0 = 0; 𝑆 Parameters : 𝑙 𝑏 ≥ 0 : Absorption constant 𝑙 𝑓 ≥ 0 : Elimination constant 𝑙 𝑗𝑜 ≥ 0 : Constant for response production 𝑙 𝑝𝑣𝑢 ≥ 0 : Constant for response loss 0 ≤ 𝐽 𝑛𝑏𝑦 ≤ 1 : Maximal inhibition attributed to drug 𝛾 : Interaction coefficient A Bayesian PK/PD model for synergy; a case study 23/06/2016 8
A nice answer: PK-PD model 𝑒𝐵 𝑓𝑗𝑢 i =1, …, S ( subjects) = −𝑙 𝑏 𝐵 𝑓𝑗𝑢 PK Part : 𝑒𝑢 t=0, …, 4 (hours) one compartment model with oral 𝑒𝐷 𝑗𝑢 𝑒𝑢 = 𝑙 𝑏 𝐵 𝑓𝑗𝑢 − 𝑙 𝑓 𝐷 𝑗𝑢 absorption A 𝑓𝑗𝑢 =Existing treatment amount 𝐵 𝑜𝑗0 =Novel treatment dose PD part : 𝑗𝑢 , 𝜏 2 ) 𝑗𝑢 𝑆 𝑗𝑢 =Response: 𝑆 𝑗𝑢 ~𝑂(𝑆 𝑒𝑆 𝐽 𝑛𝑏𝑦 𝐷 𝑗𝑢 𝑗𝑢 𝑒𝑢 = 𝑙 𝑗𝑜 1 − 𝐽𝐷 50 +𝐷 𝑗𝑢 − 𝑙 𝑝𝑣𝑢 𝑆 indirect response 𝐷 𝑗𝑢 =Plasma concentration of the (turnover) model existing treatment (latent!) 𝑓 𝛾𝐵 𝑓𝑗0 𝐵 𝑜𝑗0 𝑗𝑢=0 = 𝑙 𝑗𝑜 /𝑙 𝑝𝑣𝑢 With: 𝐵 𝑓𝑗𝑢=0 = 𝐵 𝑓𝑗0 (𝑓𝑦𝑗𝑡𝑢𝑗𝑜 𝑢𝑠𝑓𝑏𝑢𝑛𝑓𝑜𝑢 𝑒𝑝𝑡𝑓); 𝐷 𝑗𝑢=0 = 0; 𝑆 Parameters : 𝑙 𝑏 ≥ 0 : Absorption constant 𝑙 𝑓 ≥ 0 : Elimination constant 𝑙 𝑗𝑜 ≥ 0 : Constant for response production 𝑙 𝑝𝑣𝑢 ≥ 0 : Constant for response loss 0 ≤ 𝐽 𝑛𝑏𝑦 ≤ 1 : Maximal inhibition attributed to drug 𝛾 : Interaction coefficient A Bayesian PK/PD model for synergy; a case study 23/06/2016 9
A nice answer: PK-PD model 𝑒𝐵 𝑓𝑗𝑢 i =1, …, S ( subjects) = −𝑙 𝑏 𝐵 𝑓𝑗𝑢 PK Part : 𝑒𝑢 t=0, …, 4 (hours) one compartment model with oral 𝑒𝐷 𝑗𝑢 𝑒𝑢 = 𝑙 𝑏 𝐵 𝑓𝑗𝑢 − 𝑙 𝑓 𝐷 𝑗𝑢 absorption A 𝑓𝑗𝑢 =Existing treatment amount 𝐵 𝑜𝑗0 =Novel treatment dose PD part : 𝑗𝑢 , 𝜏 2 ) 𝑗𝑢 𝑆 𝑗𝑢 =Response: 𝑆 𝑗𝑢 ~𝑂(𝑆 𝑒𝑆 𝐽 𝑛𝑏𝑦 𝐷 𝑗𝑢 𝑗𝑢 𝑒𝑢 = 𝑙 𝑗𝑜 1 − 𝐽𝐷 50 +𝐷 𝑗𝑢 − 𝑙 𝑝𝑣𝑢 𝑆 indirect response 𝐷 𝑗𝑢 =Plasma concentration of the (turnover) model existing treatment (latent!) 𝑓 𝛾𝐵 𝑓𝑗0 𝐵 𝑜𝑗0 𝑗𝑢=0 = 𝑙 𝑗𝑜 /𝑙 𝑝𝑣𝑢 With: 𝐵 𝑓𝑗𝑢=0 = 𝐵 𝑓𝑗0 (𝑓𝑦𝑗𝑡𝑢𝑗𝑜 𝑢𝑠𝑓𝑏𝑢𝑛𝑓𝑜𝑢 𝑒𝑝𝑡𝑓); 𝐷 𝑗𝑢=0 = 0; 𝑆 Parameters : 𝑙 𝑏 ≥ 0 : Absorption constant 𝑙 𝑓 ≥ 0 : Elimination constant 𝑙 𝑗𝑜 ≥ 0 : Constant for response production 𝑙 𝑝𝑣𝑢 ≥ 0 : Constant for response loss 0 ≤ 𝐽 𝑛𝑏𝑦 ≤ 1 : Maximal inhibition attributed to drug 𝛾 : Interaction coefficient A Bayesian PK/PD model for synergy; a case study 23/06/2016 10
A nice answer: PK-PD model A 𝑓𝑗0 =Existing treatment dose PD part : 𝑗𝑢 𝑒𝑆 𝐽 𝑛𝑏𝑦 𝐷 𝑗𝑢 𝐵 𝑜𝑗0 =Novel treatment dose 𝑗𝑢 𝑒𝑢 = 𝑙 𝑗𝑜 1 − 𝐽𝐷 50 +𝐷 𝑗𝑢 − 𝑙 𝑝𝑣𝑢 𝑆 indirect response 𝛾 = Synergy coefficient, expressing (turnover) model the pharmacodynamic drug-drug 𝑓 𝛾𝐵 𝑓𝑗0 𝐵 𝑜𝑗0 interaction Simulated model Observed data Slower onset, larger decrease A Bayesian PK/PD model for synergy; a case study 23/06/2016 11
Recommend
More recommend
