A new PKPD modelling approach allowing a granular Exposure-Response analysis
Mats Karlsson1, Divya Brundavanam1
1Department of Pharmacy, Uppsala University
Introduction: Exposure-response (ER), or Pharmacokinetic-Pharmacodynamic (PKPD), analysis is an important activity to form a basis for dosing strategy decisions, for example individualization strategies based on response titration, covariates or exposure measurements. Two standard assumptions in the PKPD models that are used for characterizing ER are (i) that drug exposure have a causal influence on the response, and (ii) that changes in response are independent of why exposure changes. While the violations of these assumptions have been recognized, a systematic approach to evaluate them has not presented. In this presentation, we assess the consequences of applying a standard PKPD model to a series of ER scenarios and contrast with a PKPD model with random effects (RE) correlation between PK and PD parameters (PKPDC) and with a new modelling approach, the partitioned effects (PE) model which allows separate models to characterize the ER for dose, covariate- and random effect-driven exposure changes. Methods: PKPD data for six steady-state scenarios were simulated (nrepl=500) following two randomized dose rates (1 or 2; nsubj=100; 2 PK & 2 PD obs/subj) and linear CL. Concentrations were linked to response via Emax models with a random effect in C50. Scenarios: “Base Case” (no RE correlation between PK and PD parameters), “Protein Binding” (unobserved variability in protein binding causes a negative CL-C50 correlation), “Disease Severity” (both CL and C50 increase with an unobserved disease severity) and “Renal Function” (both CL and C50 increase with renal function, but in analysis only CL-renal function relation is recognized). In scenario “Active Metabolite” the parent drug was observed, but the response driven by an active metabolite. In scenario “Reverse Causality”, the only relation was that the response variable was linked to the CL of the drug. In all analyses, the PKPD, PKPDC and PE models were simultaneously fit to PK and PD data. The PKPD model generates a single ER relation, the PKPDC two relations (dose and RE) and the PE two (dose and RE) or three (dose, covariate and RE), depending on whether the PK model has covariates or not. In this work, only scenario “Renal Function”, contained a covariate in the PK model. A PE model can be formulated as shown below, with Y_PK=f(?_PK,?_PK,Dose,Cov)+ e_PK Y_(PD,Dose)=g(?_(PD,Dose),?_(PD,Dose),f(?_PK,Dose) ), Y_(PD,Cov)=g(?_(PD,Cov),f(?_PK,Dose,Cov)) -g(?_(PD,Cov),f(?_PK,Dose)) Y_(PD,RE)=g(?_(PD,RE),f(?_PK,?_PK,Dose,Cov)) -g(?_(PD,RE),f(?_PK,Dose,Cov)) Y_PD=Y_(PD,Dose)+ Y_(PD,Cov)+ Y_(PD,RE )+ e_PD, Results: All three models characterized correctly the ER relation in the Base Case. For dose-related changes in exposure from C50/2 to C50, the prediction error for the 5 remaining scenarios were: PKPD: -2, 1, 1, -2, 21; PKPDC: 0, 0, 2, 0, 1; PE: 0, 0, 0, 0, 1. Corresponding random effect related prediction errors: PKPD: 9, -9, 1, 15, 13; PKPDC: 0, 0, 0, 5, -8; PE 1, 1, 4, 1, 0. Corresponding covariate related prediction errors (only “Renal Function”) PKPD: -27; PKPDC: -27; PE 0. When data were reduced to one PK and one PD observation per subject, only PKPD and PE models are estimable. The corresponding prediction errors to those above are: PKPD: -3, 1, 2, -5, 20; PE: 0, 0, 0, 0, 0 (Dose-related); PKPD: 9, -9, 2, 11, 13; PE: -1, -4, -2, 1, 8 (RE-related); PKPD: -27; PE: -3 (Covariate-related). The prediction errors above are driven by bias in PD parameters, most notably Emax and C50. While a single comparison is illustrated, it is representative of other comparisons in the range of observed concentrations (ca 25%-400% of C50). Conclusions: To correctly select individualization strategies based on response titration, covariates or exposure measurements (i.e., TDM), it is important to understand how dose-, covariate- and RE-driven differences in exposure influence response. Standard PKPD models do not provide such understanding and will provide biased predictions when these relations differ, as in the case of PKPD confounding, partially addressed covariate relations or incorrect causality assumptions. The PE model shows promise in offering a systematic approach to explore and estimate the necessary relations and provide an enhanced basis for causality diagnosis and individualization strategy decisions.