Two new user-friendly methods to assess pharmacometric parameter identifiability on categorical and continuous scales.

Parameter identifiability methods assess whether the parameters of a model are uniquely determined by the observations. While the success of a model fit can provide some information on this, it can be valuable to determine identifiability before any fit has been attempted, or to separate identifiability from other issues. Two concepts that lean themselves well for identifiability analysis and have been underutilized are the sensitivity matrix (SM) and the Fisher information matrix (FIM). This paper presents two newly developed methods, one based on the SM and one based on the FIM. Both methods can assess local identifiability for a wide set of models, can be used with limited effort, and are freely available. The methods require the proposed model in the form of a set of differential equations, the parameter values, and the study design as input. They can be used a priori, as they do not need observed values or a successful model fit. Traditional methods provide a single categorical (yes/no) answer to the question of identifiability. In many cases, this is not very informative, and identifiability depends on study design (e.g., dose levels or observation times) and parameter values. Indicators on a continuous scale characterizing the level of identifiability would provide more detailed and relevant information, for example, to guide model development. Our two methods provide both categorical and continuous indicators. Both methods indicate which parameter combinations are difficult to identify by calculating the directions in parameter space that are least identifiable. The methods were validated with an example problem.

Navigating the landscape of parameter identifiability methods: A workflow recommendation for model development.

In pharmacometric modeling, it is often important to know whether the data is sufficiently rich to identify the parameters of a proposed model. While it may be possible to assess this based on the results of a model fit, it is often difficult to disentangle identifiability issues from other model fitting and numerical problems. Furthermore, it can be of value to ascertain identifiability beforehand. This paper compares four methods for parameter identifiability, namely Differential Algebra for Identifiability of SYstems (DAISY), the sensitivity matrix method (SMM), Aliasing, and the Fisher information matrix method (FIMM). We discuss the characteristics of the methods and apply them to a set of applications, consisting of frequently used PK model structures, with suitable dosing regimens and sampling times. These applications were selected to validate the methods and demonstrate their usefulness. While traditional identifiability analysis provides a categorical result [PLoS One, 6, 2011, e27755; CPT Pharmacometrics Syst Pharmacol, 8, 2019, 259; Bioinformatics, 30, 2014, 1440], we argue that in practice a continuous scale better reflects the limitations on the data and is more informative. The methods were generally consistent in their evaluation of the applications. The Fisher information matrix method seemed to provide the most consistent answers. All methods provided information on the parameters that were unidentifiable. Some of the results were unexpected, indicating identifiability issues where none were foreseen, but could be explained upon further analysis. This illustrated the usefulness of identifiability assessment.

Pharmacokinetics and pharmacodynamics of finerenone in patients with chronic kidney disease and type 2 diabetes: Insights based on FIGARO-DKD and FIDELIO-DKD.

AIMS: To perform dose-exposure-response analyses to determine the effects of finerenone doses. MATERIALS AND METHODS: Two randomized, double-blind, placebo-controlled phase 3 trials enrolling 13 026 randomized participants with type 2 diabetes (T2D) from global sites, each with an estimated glomerular filtration rate (eGFR) of 25 to 90 mL/min/1.73 m2 , a urine albumin-creatinine ratio (UACR) of 30 to 5000 mg/g, and serum potassium ≤ 4.8 mmol/L were included. Interventions were titrated doses of finerenone 10 or 20 mg versus placebo on top of standard of care. The outcomes were trajectories of plasma finerenone and serum potassium concentrations, UACR, eGFR and kidney composite outcomes, assessed using nonlinear mixed-effects population pharmacokinetic (PK)/pharmacodynamic (PD) and parametric time-to-event models. RESULTS: For potassium, lower serum levels and lower rates of hyperkalaemia were associated with higher doses of finerenone 20 mg compared to 10 mg (p < 0.001). The PK/PD model analysis linked this observed inverse association to potassium-guided dose titration. Simulations of a hypothetical trial with constant finerenone doses revealed a shallow but increasing exposure-potassium response relationship. Similarly, increasing finerenone exposures led to less than dose-proportional increasing reductions in modelled UACR. Modelled UACR explained 95% of finerenone's treatment effect in slowing chronic eGFR decline. No UACR-independent finerenone effects were identified. Neither sodium-glucose cotransporter-2 (SGLT2) inhibitor nor glucagon-like peptide-1 receptor agonist (GLP-1RA) treatment significantly modified the effects of finerenone in reducing UACR and eGFR decline. Modelled eGFR explained 87% of finerenone's treatment effect on kidney outcomes. No eGFR-independent effects were identified. CONCLUSIONS: The analyses provide strong evidence for the effectiveness of finerenone dose titration in controlling serum potassium elevations. UACR and eGFR are predictive of kidney outcomes during finerenone treatment. Finerenone's kidney efficacy is independent of concomitant use of SGLT2 inhibitors and GLP-1RAs.

Finerenone Dose-Exposure-Response for the Primary Kidney Outcome in FIDELIO-DKD Phase III: Population Pharmacokinetic and Time-to-Event Analysis.

BACKGROUND: Finerenone is a nonsteroidal selective mineralocorticoid receptor antagonist that recently demonstrated efficacy in delaying chronic kidney disease progression and reducing cardiovascular events in patients with chronic kidney disease and type 2 diabetes in FIDELIO-DKD, where 5734 patients were randomized 1:1 to receive either titrated finerenone doses of 10 or 20 mg once daily or placebo, with a median follow-up of 2.6 years. METHODS: Nonlinear mixed-effects population pharmacokinetic models were used to analyze the pharmacokinetics in FIDELIO-DKD, sparsely sampled in all subjects receiving finerenone. Post-hoc model parameter estimates together with dosing histories allowed the computation of individual exposures used in subsequent parametric time-to-event analyses of the primary kidney outcome. RESULTS: The population pharmacokinetic model adequately captured the typical pharmacokinetics of finerenone and its variability. Either covariate effects or multivariate forward-simulations in subgroups of interest were contained within the equivalence range of 80-125% around typical exposure. The exposure-response relationship was characterized by a maximum effect model estimating a low half-maximal effect concentration at 0.166 µg/L and a maximal hazard decrease at 36.1%. Prognostic factors for the treatment-independent chronic kidney disease progression risk included a low estimated glomerular filtration rate and a high urine-to-creatinine ratio increasing the risk, while concomitant sodium-glucose transport protein 2 inhibitor use decreased the risk. Importantly, no sodium-glucose transport protein 2 inhibitor co-medication-related modification of the finerenone treatment effect per se could be identified. CONCLUSIONS: None of the tested pharmacokinetic covariates had clinical relevance in FIDELIO-DKD. Finerenone effects on kidney outcomes approached saturation towards 20 mg once daily and sodium-glucose transport protein 2 inhibitor use provided additive benefits.