Principal Consultant, MIDD Platform Science Lead Pharmetheus AB Uppsala, Sweden
Disclosure(s):
Martin Bergstrand, PhD, ISOP member: No financial relationships to disclose
Objectives: To compare visual predictive check (VPC), prediction corrected VPC (pcVPC) [1] and rcVPC model diagnostics for their ability to visually characterize a models ability to capture underling exposure-response (ER) relationships for models with delayed effect onset.
Methods: The rcVPC is a novel model diagnostic based on the definition of a reference dataset with user defined independent variables (e.g. covariates, dose, inter dose interval and time) but otherwise with the same dimensions as the analysis dataset (introduced at PAGE 2024). We used a real life inspired PKPD examples for the comparison. Example 1 was a one compartment PK model with first order absorption and an indirect response PD model for body weight (BW). The drug plasma concentrations (PC) had an ihibitory effect on the production rate (KIN) through an Emax function. The data came from two studies: An MRD study with 5 doses levels (100 mg, 200 mg, 400 mg, 600 mg and 800 mg and 5 subjects/dose level) and 6 weeks of treatment and 4 weeks of follow up, and a Phase IIa study with 20 patients on 600 mg, for 16 weeks of treatment and 2 weeks of follow up. VPCs, pcVPCs and rcVPCs were used to plot BW and the change from baseline BW vs drug PC. Models featuring the true as well as misspecified ER relationships was evaluated with the model diagnostics. NONMEM version 7.5 in combination PsN was used for simulation and re-estimation purposes and all data post processing and graphical representation was done using R.
Results: The rcVPC model diagnostic normalized to change from baseline BW after 16 weeks of treatment allowed to visualize and diagnose the underlying ER without the influence of the delayed effect onset. Fitting a model with a linear ER relationship instead of the true Emax relationship did not result in any clearly identified model misspecifications with the traditional VPC or pcPVC model diagnostics. The rcVPC on the other hand clearly indicated the actual misspecified ER relationships in a way that was intuitive to interpret.
Conclusions: The possibility for a user defined set of reference characteristics (independent variables) with the rcVPC makes it not only a powerful model diagnostic but also a vehicle for efficient communication of modeling results to a wider audience. The rcVPC have been demonstrated to be especially useful for an intuitive evaluation of underlying ER relationships in the presence of delayed effect onset in a way that isn’t possible a traditional VPC or pcPVC plots.
Citations: [1] Bergstrand M, Hooker AC, Wallin JE, Karlsson MO. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J. 2011 Jun;13(2):143-51
