Static Versus Dynamic Model Predictions of Competitive Inhibitory Metabolic Drug–Drug Interactions via Cytochromes P450: One Step Forward and Two Steps Backwards

Abstract

Background

Predicting metabolic drug–drug interactions (DDIs) via cytochrome P450 enzymes (CYP) is essential in drug development, but controversy has reemerged recently about whether in vitro–in vivo extrapolation (IVIVE) using static models can replace dynamic models for some regulatory filings and label recommendations.

Objective

The aim of this study was to determine if static and dynamic models are equivalent for the quantitative prediction of metabolic DDIs arising from competitive CYP inhibition.

Methods

Drug parameter spaces were varied to simulate 30,000 DDIs between hypothetical substrates and inhibitors of CYP3A4. Predicted area under the plasma concentration–time profile ratios for substrates (AUCr = AUC_{(presence of precipitant)}/AUC_{(absence of precipitant)}) were compared between dynamic simulations (Simcyp^® V21) and corresponding static calculations, giving an inter-model discrepancy ratio (IMDR = AUCr_dynamic/AUCr_static). Dynamic simulations were conducted using a ‘population’ representative and a ‘vulnerable patient’ representative with maximal concentration (C_max) or average steady-state concentration (C_avg,ss) as the inhibitor driver concentrations. IMDRs outside the interval 0.8–1.25 were defined as discrepancy between models.

Results

The highest rate of IMDR <0.8 and IMDR >1.25 discrepancies in the ‘population’ representative was 85.9% and 3.1%, respectively, when using C_avg,ss as the inhibitor driver concentration. Using the ‘vulnerable patient’ representative showed the highest rate of IMDR >1.25 discrepancies at 37.8%.

Conclusion

Static models are not equivalent to dynamic models for predicting metabolic DDIs via competitive CYP inhibition across diverse drug parameter spaces, particularly for vulnerable patients. Caution is warranted in drug development if static IVIVE approaches are used alone to evaluate metabolic DDI risks.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40262-024-01457-1.

Key Points

Static models are not equivalent to dynamic models for predicting drug–drug interactions via competitive inhibition across diverse drug variations, particularly for vulnerable patients.

Caution is warranted in drug development if static approaches are used alone to evaluate metabolic drug–drug interaction risks.

Introduction

“Every complex problem has a solution which is simple, direct, plausible—and wrong.” (H. L. Mencken 1880–1956).

Concomitant drug therapy, as a way to improve the treatment of a given disease, or for the treatment of several diseases in the same patient, carries the risk of drug–drug interactions (DDI). Metabolic DDIs caused by the inhibition of cytochrome P450 enzymes (CYP) may result in adverse effects due to high drug exposure. Conversely, partial or complete loss of therapeutic effects via low drug exposure may follow the induction of CYP enzymes [1]. During drug development, screening for metabolic DDIs via CYP is routine using a battery of in-vitro assays and there are several regulatory guidelines on these [2–4]. These data determine whether dedicated clinical studies are warranted to quantify interaction potential, to further define risks to patients, and to guide prescribing information.

Logistically, testing all possible permutations of drug combinations for metabolic DDIs with clinical studies is impossible. Hence, in-vitro to in-vivo extrapolation (IVIVE) approaches are used to fill some of the knowledge gaps. The magnitude of a metabolic DDI is determined by comparing the area under the plasma–concentration time curve (AUC) of a ‘victim’ drug in the absence and presence of a ‘perpetrator’ drug. This gives the AUC ratio, defined as AUCr = AUC_{(presence of perpetrator)}/AUC_{(absence of perpetrator)}. The AUCr is >1 when a perpetrator increases the systemic exposure of a victim, such as the inhibition of drug metabolising enzymes, and between 0 and 1 when a perpetrator decreases the systemic exposure of a victim, most notably with the induction of drug metabolism [5]. Prediction of AUCr for any pair of victim and perpetrator drugs via IVIVE is not restricted to a single approach. An initial account of different strategies was provided by Einolf (2007), where various simple static equations, mechanistic static models, and dynamic ‘physiologically based pharmacokinetic’ (PBPK) modelling were discussed [6].

Mechanistic static models are typically used in early drug development to estimate metabolic DDI potential for victims and perpetrators known to be selective for major CYP enzymes [7]. Since clinical PK data may not be known at this stage, in addition to experimental in-vitro kinetic data, many assumptions are needed for static models regarding possible in-vivo drug concentrations. Even when clinical PK data are available, it is not always possible to know the exact drug concentration at the interaction sites, such as in the enterocytes and hepatocytes. Therefore, all IVIVE models for metabolic DDIs, whether static or dynamic, employ surrogate ‘driver concentrations’ to predict AUCr.

The mechanistic static model described in the FDA and ICH guidance for predicting inhibitory metabolic DDIs recommend using maximum unbound hepatic inlet concentration, predicted from the maximal unbound inhibitor concentration in the systemic plasma at steady state and the rate and extent of intestinal absorption, as the driver concentration for enzyme inhibition in the liver [2, 3]. Its use was also explored in a series of publications that compared the various mechanistic static models [6, 8, 9]. While this driver concentration is not a representative substitute for the time-variable perpetrator concentration, it reduces the risk of false-negative predictions. Thus, static models are not generally used to make quantitative predictions of metabolic DDIs, but rather, to serve as a tool to flag even minor AUCr deviations from unity ensuring future patient safety.

Dynamic, or PBPK models, have a plethora of advantages over static models, such as incorporating active metabolites, dose staggering investigations, assessing multiple perpetrators simultaneously, time-dependence, and providing prediction ranges to cover ‘worst case scenarios’ [10, 11]. Importantly, PBPK models use time-variable concentrations of perpetrator and victim drugs in various organs and the systemic circulation as driver concentrations (hence the name ‘dynamic’). One key strength of PBPK models is the ability to incorporate inter-individual variability and as a result are able to identify individuals at high DDI risk by extrapolating in special populations [12]. Some PBPK software, such as Simcyp^®, incorporate covariates known to influence metabolic clearance and the proportional importance of clearance pathways, including CYP enzyme polymorphisms [13], age [14], eliminating organ function [14], and pathologies related to changes in the gut wall abundance of enzymes and transporters that may influence the first pass effect [15]. This allows for DDI risk assessments in patient populations likely to receive the drug combinations and to improve prescribing in the absence of clinical studies, that is, ‘blind spots’ in prescribing when no formal dosing guidance is available [16, 17].

Clinical DDI studies are the most robust approach for predicting DDIs as they provide direct in-vivo evidence, accounting for interindividual variability. Due to logistical constraints, information from IVIVE approaches is used to guide clinical studies towards the major metabolic routes which are likely to be the source of the DDI. However, even in routine clinical DDI studies, vulnerable individuals with respect to the highest level of a DDI are unlikely to be present in said studies. Hence, the use of stochastic models that integrate the likelihood of physiological variability is essential to identify individuals at the highest risk of a DDI, especially when these models are used to support regulatory filling and labelling information.

While the different purposes of the static and dynamic approaches are outlined by regulatory agencies, discourse remains in the literature about their equivalence for some DDI predictions [10, 18]. This focuses on the argument that more physiologically relevant driver concentrations are required for static models, most commonly the unbound average steady-state concentration of the perpetrator. Some studies have claimed that static models give comparable predictions to dynamic models [10, 18], and that their evidence enhances “confidence in the use of mechanistic static models to inform enrolment for DDI clinical studies, support DDI study design and enable label recommendations (dose adjustment, avoid concomitant use, or no warnings)” [10]. Hence, after more than two decades of progress, the idea that static models can replace dynamic models for quantitative IVIVE of metabolic DDIs, at least in the simplest case of competitive inhibition of a single CYP enzyme, is making a comeback.

Importantly, such comparisons between the IVIVE approaches rely on observed data from a limited number of existing drugs, which, by definition, cannot address drug parameter spaces that differ from the existing drugs, or for parameters that were unavailable in the datasets examined for the comparisons. Therefore, caution should be exercised in applying the ‘equivalence’ conclusion to new regulatory submissions, particularly when the parameter spaces for the victim and perpetrator drugs are at the edges of existing drug parameter space. The literature does not adequately address all theoretically conceivable parameter spaces for drug pairs where the static and dynamic models may show discrepancies. It is crucial to understand such discrepancies, if they exist, and to quantify which drug parameter spaces could be driving such discrepancies.

This report is a large-scale simulation study investigating the drug parameter spaces that influence the predictions of inhibitory metabolic DDIs via CYP enzymes. Since dynamic models already have clear advantages over static models in the previously mentioned scenarios (e.g., active metabolites), further testing for discrepancies between the models in these cases is unwarranted [10, 11]. Therefore, the current exercise focused on the scenario where comparable results between static and dynamic models are still debated and might be expected: the competitive inhibition of CYP3A4 between a single inhibitor and a single selective probe substrate. Patient risk, defined as more than 1.25-fold AUCr predicted by static model versus dynamic model, and sponsor risk, defined as <0.8-fold AUCr predicted by static model versus dynamic model, were assessed for the population average, and for groups of patients that, according to stochastic predictions from dynamic models, might be at higher DDI risk.

Methodology

The premise of this study was to change the parameters of an existing drug to generate new, theoretical drugs and then simulate a DDI study on these compounds using both static and dynamic models. These compounds (both perpetrator and victim) were generated in a PBPK simulator Simcyp^® (V21, Certara Predictive Technologies, Sheffield, UK) by altering drugs present in the Simcyp^® compound library. Simcyp^® was also used as the dynamic model for DDI predictions; henceforth, any reference to dynamic models refers only to the models used in Simcyp^®. The mechanistic static model for reversible inhibition (Eqs. 1–5) [2–4, 19, 20] was used for the static predictions and calculations were conducted using either the maximum (C_max) or average (C_avg,_ss) concentration in plasma for predicting the inhibitor concentration in the liver (Eqs. 4a and 4b).

$$AUCR=\left(\frac{1}{A_g\times \left(1,-,F_g\right)+F_g}\right)\times \left(\frac{1}{A_h\times f_m+\left(1,-,f_m\right)}\right)$$ 1

A (Eqs. 2 and 3) is the effect of reversible inhibition and subscripts ‘g’ and ‘h’ denote the effect in the gut and liver, respectively. F_g is the fraction of the substrate escaping gut metabolism in the absence of an inhibitor and f_m is the fraction of hepatic clearance of the substrate mediated by the CYP enzyme that is subject to inhibition.

$$A_g=\frac{1}{1+\frac{{[I]}_g}{K_{i,u}}},$$ 2

$$A_h=\frac{1}{1+\frac{{[I]}_h}{K_{i,u}}}.$$ 3

[I] (Eqs. 4 and 5) is the inhibitor concentration at the relevant site which is denoted by ‘g’ for gut, and ‘h’ for liver. K_i,u is the unbound inhibition constant for the relevant CYP enzyme.

$${[I]}_h=f_{u.p}\times \left(C_{\text{max}}+\left(f_a\times F_g\times k_a\times \text{Dose}\right)/Q_h/R_B\right),$$ 4a

$${\left[I\right]}_h=f_{u.p}\times \left(C_{\text{avg},\text{ss}}+\left(f_a\times F_g\times k_a\times \text{Dose}\right)/Q_h/R_B\right),$$ 4b

$${\left[I\right]}_g=f_a\times k_a\times \text{Dose}/Q_{\text{en},}$$ 5

f_u.p is the unbound fraction of the inhibitor in plasma, C_max is the maximal total (free and bound) inhibitor concentration in the plasma at steady state, f_a is the inhibitor fraction absorbed after oral administration, k_a is the first order absorption rate constant of the inhibitor, Q_en is the blood flow through enterocytes, Q_h is the hepatic blood flow, R_B is the blood-to-plasma concentration ratio. To maximise comparability between static and dynamic models, instead of using 18 L/h Q_en and 97 L/h Q_h as suggested in the regulatory guidance for a 70-kg individual, 23.9 L/h Q_en and 101.4 L/h Q_h, corresponding to the healthy volunteer population representative (80.7 kg) in Simcyp^®, were used also for the mechanistic static model calculations. The AUCr values from static and dynamic models were then compared to identify the presence of discrepancies between the two models. Practically, we tested the effect of a range of values of different input parameters on the discrepancies between models. In this study, the dynamic model is taken as a baseline to which the static model is compared. The input parameters used in the static models (listed in Eqs. 1–5) were obtained from the dynamic simulations, allowing for a direct comparison between models.

Compound Profiles

The theoretical compounds used in this study were generated by changing parameters of ‘template’ compounds that exist in Simcyp^® (Table 1). For the inhibitor/perpetrator compound, ketoconazole was used for this purpose as it is a drug that has been highly validated in clinical DDI studies as a CYP3A inhibitor. Midazolam was used as the template for substrate/victim drugs. These compounds were also chosen as midazolam has a predominant (>95%) fractional metabolism by the CYP3A4 enzyme. This allowed us to test the simplest scenario where a single inhibitor had a predominant inhibition on both intestinal and hepatic metabolic pathways for a single substrate.

Table 1.

Substrate and inhibitor parameters used for dynamic and static DDI simulations

	Substrate	Inhibitor
Dosing regimen	5-mg single oral dose on day 120a at 9 a.m.	400 mg QD at 9 a.m., or 200 mg BID at 9 a.m. and 9 p.m.b
MW (g/mol)	325.8	531.4
LogPo:w	3.53	4.04
Compound type	Monoprotic base	Diprotic base
pKa	6	2.94, 6.51
fu.p	0.032	0.029
B/P	0.603	0.62
Distribution model	Minimal PBPKb	Minimal PBPKb
Vss (L/kg)	0.88	0.05–31.5c
Absorption model	First order absorption	First order absorption
fa	1	1
ka (h–1)	3	0.05–6c
fuGut	1	0.06–1c
Fg	0.1–1c	1
Fh	0.26–0.85c	1
fmCYP3A4	96.61%	NA
CYP3A4 Ki (μM)	NA	0.015–7.68c
fumic	NA	0.97

BID twice daily, B/P blood-to-plasma ratio, fa fraction absorbed after oral administration, F_g fraction escaping gut metabolism, F_h fraction escaping hepatic metabolism, fu_Gut unbound fraction of drug in enterocytes, fu_mic fraction of unbound drug in the in vitro microsomal incubation,  f_u.p fraction unbound in plasma, k_a absorption rate constant, k_i inhibition constant, MW molecular weight, NA not applicable, PBPK physiologically based pharmacokinetics, QD once daily, V_ss volume of distribution at steady state

^aA long simulation run time was used to ensure that theoretical inhibitors with high V_ss values had adequate time to reach steady-state concentrations in the plasma

^b“The Simcyp minimal PBPK model consists of three well-stirred compartments, predicting the systemic, portal vein, and liver concentrations” [21]

^cRanges of inhibitor dosing regimen, V_ss, k_a, fu_Gut and CYP3A4 K_i, and substrate F_h and F_g were explored. Discrete values simulated are shown in Table 2

Simulations were conducted using a representative individual unless otherwise stated. The pharmacokinetic properties of the inhibitor were varied over the ranges noted in Table 2. For each simulation the dynamic simulation was run for long enough to ensure that the inhibitor had reached steady state, and a single dose of substrate was then administered. The parameters (C_max, C_avg,ss) used to describe the inhibitor in the static model were taken from the relevant dynamic simulation.

Table 2.

Description of explored parameter for the substrate and inhibitor compounds and the range of parameter values evaluated

Parameters	Values
	1	2	3	4	5	6	7	8	9	10
Inhibitor
Absorption rate constant – ka (h−1)	0.05	0.1	0.2	0.4	0.8	1	2	3	4	6
Inhibition constant for CYP3A4 – Ki (μM)	0.015	0.03	0.06	0.12	0.24	0.48	0.96	1.92	3.84	7.68
Volume of distribution at steady state – Vss (L/kg)	0.05	0.25	1.25	6.25	31.25
Unbound fraction of drug in enterocytes – fuGut	0.06	1
Dosing regimen	QD400	BID200
Substrate
Fraction escaping hepatic metabolism –Fha	0.26	0.58	0.85
Fraction escaping intestinal metabolism – Fgb	0.1	0.3	0.5	0.7	1

BID twice daily, QD once daily

^aChange in substrate F_h was achieved by either decreasing or increasing both the maximum rate of metabolism and the Michaelis-Menten constant for the CYP3A4 route of elimination by 4-fold

^bChange in substrate F_g was achieved by varying the CYP3A4 enzyme abundance in the intestine for the population; this did not affect the F_g of the inhibitor

In addition, we have also varied the substrate metabolism to give substrates with different values of F_g and fraction escaping hepatic metabolism (F_h); changing the F_h did slightly (< 1%) affect the fmCYP3A4 but this was accounted for in the static model calculations. Varying the F_g and the F_h was crucial in understanding whether first-pass metabolism in the gut or liver caused any discrepancy between models. The inhibitor and substrate parameters that were altered used physiologically realistic ranges to ensure our findings are applicable to real-world scenarios.

Study Design

As depicted in Fig. 1, a factorial study was simulated. In this design, the range of values for each parameter are varied independently across all possible permutations. This factorial scheme ensures that all possible parameter combinations are evaluated, providing a comprehensive overview of the behaviour of static and dynamic models across the simulated parameter space.

Fig. 1.

A simplified schematic representation of the study design used. The top level represents ‘Sim,’ the overall simulation. Each subsequent level represents parameters and possible values for said parameter evaluated in this study. This pattern continues for all possible parameters represented by ‘Parameter X’. Each simulation result is generated from the various combinations of the different values for each parameter. Refer to Table 2 for every explored parameter and their individual values. BID twice daily, QD once daily

The current exercise focused on a simple scenario (single substrate competitively inhibited by a single inhibitor) where mechanistic static models might be expected to give comparable results to dynamic models. More complex scenarios (e.g., including inhibitory metabolites, temporal changes in administration, etc.) were not evaluated. Initial simulations were conducted using a population representative to compare static and dynamic models using the parameters in each dynamic simulation as input to the corresponding static model. The obtained static model results for each scenario were also compared with results from the dynamic model obtained using the 95th percentile of a population of 300 individuals (age 20–50; 50% female); this was done to mimic vulnerable individuals with respect to the highest level of a DDI and compare model discrepancies in said individuals.

To maximise comparability, the simple first order absorption model was chosen over the ADAM model and a minimal distribution PBPK model was used in the dynamic simulations, as we are purely interested in DDI prediction potential. Static models evaluate DDI potential at steady state, therefore, the theoretical inhibitors were allowed to reach steady state before the theoretical substrates were administered to the virtual population. For each simulation, the comparison was done for both static model driver concentrations, C_max and average inhibitor concentration at steady-state (C_avg,ss)

The total number of all possible permutations explored with regards to the parameters and their individual values was 30,000. Since manually running the simulations and collecting data would have been time consuming, this process was automated through the Simcyp^® R-Package. The R-Package enables running of the Simcyp^® Simulator, modifying compound parameters, and generating output data within R [22]. Leveraging this platform, a workflow was designed through the R-Package which allowed it to systematically change compound parameters, run the simulations, and collect relevant input data for the static mechanistic model for all possible parameter combinations. We have also implemented the static mechanistic model within R, which enabled the calculation of the static AUCr, and the comparison to the corresponding dynamic AUCr automatically.

Calculations and Data Analysis

The input parameters for the static models as seen in Eqs. 1–5 were identical to the ones in the dynamic models, allowing for comparability between said models. In each dynamic simulation and the corresponding static model prediction, an AUCr was calculated. The results for comparison are presented as the ratio AUCr_dynamic/AUCr_static. This ratio is referred to as the inter-model discrepancy ratio (IMDR) in the rest of the paper. An IMDR of 1 indicates that the prediction from the static and dynamic models are equivalent. IMDRs outside the interval (0.8–1.25) were considered a discrepancy between models. A ratio >1.25 represents a risk to patients using the static mechanistic model, a ratio <0.8 indicates a risk to the sponsor in that the mechanistic static model predicts an interaction bigger than the dynamic PBPK model.

Results

In total, 30,000 dynamic simulations and corresponding static calculations were compared. The format used to visualise the results in Figs. 3, 4, 5, 6, and S1–S20 (found in the electronic supplementary material [ESM]) is explained in Fig. 2.

Fig. 3.

A 3D representation of the parameter discrepancy space between static (C_avg,ss) and dynamic models when the inhibitor is administered in the 200 mg BID, Inhibitor fu_Gut: 1, and Substrate F_h: 0.26 scenario. Each row and column represent different Inhibitor V_ss and Substrate F_g values, respectively. The F_g values increase from left to right, while V_ss values increase from bottom to top. The discrepancy metric (IMDR) values are shown on the individual plot y-axis, and are colour coded according to the legend. k_a (x-axis) and K_i (z-axis) of the inhibitor range from 0.05 to 6 h^–1 and from 0.015 to 7.68 µM, respectively, as shown on the central plot schematic. BID twice daily, F_g fraction escaping gut metabolism, fu_Gut unbound fraction of drug in enterocytes, F_h fraction escaping hepatic metabolism, IMDR inter-model discrepancy ratio, k_a absorption rate constant, k_i inhibition constant, V_ss volume of distribution at steady state

Fig. 4.

A 3D representation of the parameter discrepancy space between static (C_avg,ss) and dynamic models when the inhibitor is administered in the 400 mg QD, Inhibitor fu_Gut: 0.06, and Substrate F_h: 0.26 scenario. Each row and column represent different Inhibitor V_ss and Substrate F_g values, respectively. The F_g values increase from left to right, while V_ss values increase from bottom to top. The discrepancy metric (IMDR) values are shown on the individual plot y-axis, and are colour coded according to the legend. k_a (x-axis) and K_i (z-axis) of the inhibitor range from 0.05 to 6 h^–1 and from 0.015 to 7.68 µM, respectively, as shown on the central plot schematic. F_g fraction escaping gut metabolism, fu_Gut unbound fraction of drug in enterocytes, F_h fraction escaping hepatic metabolism, IMDR inter-model discrepancy ratio, k_a absorption rate constant, k_i inhibition constant, QD once daily, V_ss volume of distribution at steady state

Fig. 5.

A 3D representation of the parameter discrepancy space between static (C_avg,ss) and dynamic models when the inhibitor is administered in the 400 mg QD, Inhibitor fu_Gut: 1, and Substrate F_h: 0.26 scenario. Each row and column represent different Inhibitor V_ss and Substrate F_g values, respectively. The F_g values increase from left to right, while V_ss values increase from bottom to top. The discrepancy metric (IMDR) values are shown on the individual plot y-axis, and are colour coded according to the legend. k_a (x-axis) and K_i (z-axis) of the inhibitor range from 0.05 to 6 h^–1 and from 0.015 to 7.68 µM, respectively, as shown on the central plot schematic. F_g fraction escaping gut metabolism, fu_Gut unbound fraction of drug in enterocytes, F_h fraction escaping hepatic metabolism, IMDR inter-model discrepancy ratio, k_a absorption rate constant, k_i inhibition constant, QD once daily, V_ss volume of distribution at steady state

Fig. 6.

A 3D representation of the parameter discrepancy space between static (C_avr,ss) and dynamic models using the PopRep AUCr (average individual) (A) and 95th AUCr percentile (vulnerable individual) (B), when the inhibitor is administered in the 200 mg BID, Inhibitor fu_Gut: 0.06, and Substrate F_h: 0.85 scenario. Each row and column represent different Inhibitor V_ss and Substrate F_g values, respectively. The F_g values increase from left to right, while V_ss values increase from bottom to top. The discrepancy metric (IMDR) values are shown on the individual plot y-axis, and are colour coded according to the legend. k_a (x-axis) and K_i (z-axis) of the inhibitor range from 0.05 to 6 h^–1 and from 0.015 to 7.68 µM, respectively, as shown on the central plot schematic. AUCr area under the plasma–concentration time curve ratio, BID twice daily, F_g fraction escaping gut metabolism, fu_Gut unbound fraction of drug in enterocytes, F_h fraction escaping hepatic metabolism, IMDR inter-model discrepancy ratio, k_a absorption rate constant, k_i inhibition constant, PopRep population representative, V_ss volume of distribution at steady state

Fig. 2.

A basic 3D plot used to show discrepancies between models. IMDR is the inter-model discrepancy ratio. An IMDR of > 1.25 shows up as red zones and represents patient risk, IMDR of 0.8–1.25 shows up as green zones signifying no discrepancies between models, and IMDR of < 0.8 shows up as yellow zones indicating sponsor risk. k_a (x-axis) and K_i (z-axis) of the inhibitor range from 0.05 to 6 h^–1 and from 0.015 to 7.68 µM, respectively.

We have colour coded patient risk with red as this is the worst-case scenario representing a lower DDI prediction using the static model in comparison with the dynamic model and therefore has the potential of missing an interaction. On the other hand, yellow zones represent risk to sponsors, since the use of static models in these cases may lead to unnecessary clinical DDI studies. Figure 2 is the basis for every other figure; in each case when this figure is seen, the X, Y, and Z axes remain the same.

As outlined in Table 3, there is a high prevalence of discrepancies between models, with some scenarios showing discrepancies as high as ~86% of the simulations conducted. The total discrepancies between models were 67% when using C_avr,ss as a driver concentration for mechanistic static models, with patient risk discrepancies making up only a small fraction of that total. The best-case scenarios considering patient risk included scenarios where the inhibitor binding in the intestine was highest (fu_Gut inhibitor = 0.06). The case where the second highest overall correspondence between models occurred is the scenario where we also see the highest prevalence of patient risk, as seen in Fig. 3.

Table 3.

Summary of discrepancies between static (C_avr,ss) and dynamic models

Simulation scenario				No. of simulations within boundaries (%)
Inhibitor dosing regimen	Substrate Fh	Inhibitor fuGut	Corresponding figure	IMDR > 1.25	1.25 > IMDR > 0.8	0.8 > IMDR
QD400	0.26	0.06	Figure 4	10 (0.4)	634 (25.4)	1856 (74.2)
QD400	0.26	1	Figure 5	37 (1.5)	1288 (51.5)	1175 (47)
QD400	0.58	0.06	Figure S1	0 (0)	428 (17.1)	2072 (82.9)
QD400	0.58	1	Figure S2	15 (0.6)	1004 (40.2)	1481 (59.2)
QD400	0.85	0.06	Figure S3	0 (0)	352 (14.1)	2148 (85.9)
QD400	0.85	1	Figure S4	14 (0.6)	837 (33.4)	1649 (66)
BID200	0.26	0.06	Figure S5	0 (0)	720 (28.8)	1780 (71.2)
BID200	0.26	1	Figure 3	77 (3.1)	1364 (54.5)	1059 (42.4)
BID200	0.58	0.06	Figure S6	0 (0)	556 (22.2)	1944 (77.8)
BID200	0.58	1	Figure S7	68 (2.7)	1142 (45.7)	1290 (51.6)
BID200	0.85	0.06	Figure S8	0 (0)	511 (20.4)	1989 (79.6)
BID200	0.85	1	Figure S9	67 (2.7)	1028 (41.1)	1405 (56.2)
Total				288 (1.0)	9864 (32.8)	19848 (66.2)

Figures S1–S9 can be found in the electronic supplementary material

BID twice daily, F_h fraction escaping hepatic metabolism, fu_Gut unbound fraction of drug in enterocytes, IMDR inter-model discrepancy ratio, QD once daily

When the inhibitor was dosed at 200 mg BID and the substrate F_h was fixed at 0.26, differences between the static and dynamic model were seen in all of the graphs (Fig. 3). IMDRs < 0.8 were observed when substrate F_g was high (> 0.5) but at low F_g values ratios < 0.8 and > 1.25 were observed. Ratios > 1.25 were observed when inhibitor k_a was low. In this scenario the highest IMDR value (1.93) out of all simulations was observed when the following parameters were used: (Inhibitor K_i: 0.48 μM, k_a: 0.05 hr⁻¹, V_ss: 31.25 L/Kg, and Substrate F_g: 0.1). When the inhibitor was dosed at 200 mg BID, the trend between F_g, V_ss, and the IMDR is similar for each discrete substrate F_h value used (Figs. S13 & S16 in the ESM).

When the inhibitor dose was 400 mg QD, the results were similar to those of the 200 mg BID simulations across most of the input parameter space. However, there were some notable differences. Figure 4 shows a range of parameter spaces where IMDR > 1.25 was observed with a substrate F_g = 1. The differences between the models decrease at higher values of substrate F_h (refer to Table 3). Thus, discrepancies between the models given IMDR > 1.25 are predominantly observed with compounds undergoing high first-pass extraction (either in the gut or liver).

Figure 5 shows the second scenario where we observe discrepancies between models at k_a > 0.4 h^–1 and F_g >0.3. This scenario is the biggest deviation from the trends we saw with BID200, fu_Gut: 1 simulations. Firstly, no discrepancies occurred at any of the V_ss: 0.25 L/kg permutations, whereas with BID200 every V_ss permutation with F_g 0.1 and 0.3 had patient risk discrepancies. This is also the case when we change the substrate F_h to 0.58 and 0.85. Secondly, we also see an IMDR > 1.25 at F_g 0.5, and F_g 0.7, which both occurred in combination with V_ss 0.05 L/kg. What is interesting is that at V_ss 0.05 L/kg, we see these discrepancies in exactly the same K_i & k_a permutations, which took place at K_i: 0.60 and k_a: 0.40, K_i: 0.120 and k_a: 0.40, and K_i: 0.240 and k_a: 0.80. Similarly to Fig. 4, patient risk discrepancies occur identically at substrate F_g: 1, as the only difference between scenarios is the intestinal inhibition which is not a factor when there is no intestinal metabolism for the substrate. Apart from this, similar trends to the BID200 scenarios are followed with other discrepancies being localised at the lower range of the k_a values, albeit with much lower IMDR peaks.

The inclusion of population variability is an important feature of dynamic PBPK models. Figure 6 shows the IMDR for an average individual and for an individual who was at the 95th percentile of a simulated virtual population (age 20–50; 50% female, n = 300). The static model input parameters were kept the same in both panels of Fig. 6. For the average individual (Panel A), the static model resulted in significantly higher DDI predictions than the dynamic model in 79.4% of simulations (Table 4). This is clearly not the case for the 95th percentile individual (Panel B), which shows a reduction in sponsor risk discrepancies, but also a 37.8% increase in patient risk discrepancies.

Table 4.

Summary of discrepancies between static (C_max) and dynamic models using the PopRep AUCr (average individual) and 95th AUCr percentile (vulnerable individual), for the BID200, FuGut: 0.06, and F_h: 0.85 scenario

AUCr source	IMDR > 1.25	1.25 > IMDR > 0.8	0.8 > IMDR	% of IMDR > 1.25 discrepancies	% of 0.8 > IMDR discrepancies
PopRep	0	103	397	0	79.4
95th percentile	189	143	168	37.8	33.6

AUCr area under the plasma–concentration time curve ratio, BID twice daily, C_max maximum concentration, fu_Gut unbound fraction of drug in enterocytes, F_h fraction escaping hepatic metabolism, IMDR inter-model discrepancy ratio, PopRep population representative

The comparison between models was also performed using C_max as the driver concentration for the static models, the summary of which is shown in Table 5. Comparing it to when C_avr,ss was used as a driver concentration, these results show an ~8% increase in total discrepancies between static and dynamic predictions. This increase is expected as the C_max will be higher than the C_avr,ss and so will tend to increase the magnitude of DDI predicted by the static model. Comparing Fig. S17 (in the ESM), which uses C_max as a driver for the static model, to Fig. 3 (using C_avg,ss as a driver for the static model), the results are comparable with more IMDRs > 1.25 at lower substrate F_g. At high F_g there are more predictions with IMDR < 0.8 at low V_ss when C_max is used as driver compared with C_avg,ss. The highest IMDR was 1.93 regardless of driving concentration.

Table 5.

Summary of discrepancies between static (C_max) and dynamic models

Simulation scenario				No. of simulations within boundaries
Inhibitor dosing regimen	Substrate Fh	Inhibitor fuGut	Corresponding figure	IMDR > 1.25	1.25 > IMDR > 0.8	0.8 > IMDR
QD400	0.26	0.06	Figure S10	0 (0%)	360 (14.4%)	2140 (85.6%)
QD400	0.26	1	Figure S11	12 (0.5%)	806 (32.2%)	1682 (67.3%)
QD400	0.58	0.06	Figure S12	0 (0%)	292 (11.7%)	2208 (88.3%)
QD400	0.58	1	Figure S13	13 (0.5%)	672 (26.9%)	1815 (72.6%)
QD400	0.85	0.06	Figure S14	0 (0%)	273 (10.9%)	2227 (89.1%)
QD400	0.85	1	Figure S15	12 (0.5%)	627 (25.1%)	1861 (74.4%)
BID200	0.26	0.06	Figure S16	0 (0%)	543 (21.7%)	1957 (78.3%)
BID200	0.26	1	Figure S17	68 (2.7%)	1030 (58.8%)	1402 (56.1%)
BID200	0.58	0.06	Figure S18	0 (0%)	460 (18.4%)	2040 (81.6%)
BID200	0.58	1	Figure S19	63 (2.5%)	922 (36.9%)	1515 (60.6%)
BID200	0.85	0.06	Figure S20	0 (0%)	449 (18%)	2051 (82.0%)
BID200	0.85	1	Figure S21	62 (2.5%)	869 (34.7%)	1569 (62.8%)
Total				230 (0.8%)	7303 (24.3%)	22467 (74.9%)

Figures S10–S21 can be found in the electronic supplementary material

BID twice daily, C_max maximum concentration, F_h fraction escaping hepatic metabolism, fu_Gut unbound fraction of drug in enterocytes, IMDR inter-model discrepancy ratio, QD once daily

Discussions

“when interpreting the results of interaction studies, it is important to consider not only the mean of the interaction effect but also the observed and the theoretically conceivable extreme effects in individual subjects”

(Krayenbuhl et al., 1999)

This quote comes from scientists of the Swiss regulatory agency more than two decades ago in response to the tragic DDI cases of mibefradil causing fatal torsade de pointes [23, 24]. The statement clearly indicates the ‘focus’ of DDI investigations during drug development—the most vulnerable patients.

An international gathering of experts in Basel in 1999 tried to capture all the scientific knowhow on the issue of preventing such cases, and a consensus was published that summarised the state of art, including practical measures that should be considered during drug development [25, 26]. Applications of in vitro data using in silico models under the framework of IVIVE-PBPK were discussed alongside more pragmatic (simplified) approaches [7]. The following decade witnessed a series of efforts comparing various models and assumptions [6, 8, 27]. Regulatory guidance documents were published that took advantage of accumulated evidence over these years and capturing the strategies in identifying and dealing with metabolic DDIs in various forms, such as pragmatic decision trees [2, 3]. However, during these efforts, some aspects related to distinguishing between the average patient and the theoretically conceivable most vulnerable patient, have been forgotten. Hence, literature discussing the issue of ‘static versus dynamic DDI models’ mainly focused on predictions for the average patient.

Some comparisons between static and dynamic DDI models erroneously assume that a one-fits-all quantitative value for AUCr is adequate for DDI risk assessments. However, the issue is not the average, but the most sensitive patient, with an indication of likelihood. Such individuals are not found in most clinical trials. For this reason, a stochastic model that incorporates the likelihood of existing physiological variations is needed to define individuals at highest DDI risk in support of regulatory filings. Furthermore, the dynamic approach helps design clinical studies, such as exploring different dosing strategies or deciding on inclusion/exclusion criteria in various populations [14]. Indeed, regulatory bodies such as the FDA are increasingly encouraging companies to “broaden eligibility criteria in clinical trials to ensure that the study population better reflects the patient population” [28].

Static versus Dynamic Comparison: Average Individual

In this study, the static mechanistic models, irrespective of driver concentration, consistently failed to provide predictions comparable to the dynamic models, even when looking at the average individual. Consequently, this puts into question the suitability of static models for designing DDI studies or making labelling recommendations, even for a single representative or average patient. Firstly, the overall structural integrity of the static models is questionable when looking at IMDR > 1.25 discrepancies. While there was little increased patient risk when using static models (< 1% of our observed cases), these cases still have severe implications on the reliability of static models. When using C_avg,ss as a driver concentration for the static model, 288 of the 30,000 tested permutations resulted in patient risk discrepancies. Some of these permutations resulted in IMDR values of ~2, meaning that the static AUCr was half of the dynamic AUCr prediction. If these permutations were real drugs, this may risk patient harm if only static models were used for predictions.

Another issue is the lack of predictability where these discrepancies occur, particularly at lower F_g values. However, independent of permutations, every explored parameter (excluding k_a and K_i) was shown to have discrepancies; 9 out of 10 and 6 out of 10 K_i and k_a values, respectively, were also involved in some premutation that caused discrepancies. If the scenarios where the IMDR >1.25 discrepancies are localised cannot be predicted, then it may be dangerous to use them and assume a ‘one-model-fits-all’ principle. Furthermore, this was not the case only for C_avg,ss as a driver concentration. The use of C_max in the static models also resulted in cases where predicted substrate exposure in the presence of an inhibitor was significantly lower than the dynamic model. This brings into question the widely accepted assumption that the static models always provide conservative estimates of DDIs and can be relied on to avoid false-negative predictions. While static models are designed to be conservative using parameters like C_max for inhibitor concentration in the liver, in our study there were specific scenarios where dynamic models predict higher DDI risks. These scenarios involve inhibition of gut wall metabolism, particularly when inhibitors accumulate after repeated dosing. The dynamic model used in this study estimates the inhibitor concentration in the enterocytes from the concentration in the portal vein and unbound fraction in the intestinal tissue whereas the mechanistic static model predicted the inhibitor concentration in the gut wall from the oral dose and the rate and extent of intestinal absorption from an individual dose only. As the dynamic model considers the possibility that systemic accumulation of the inhibitor may increase the inhibitor concentration not only in the liver but also in the gut wall, the dynamic model can predict higher inhibitor concentrations in the gut wall than the static model for high accumulation inhibitors (as demonstrated in Fig. S22, see ESM). However, it is important to note that our study lacks evidence to conclusively claim that the dynamic model gives accurate DDI risk predictions in these cases; nevertheless, other studies have demonstrated confidence in using PBPK models such as Simcyp^® for assessing DDI potential of CYP-mediated interactions [29]. Thus, while static models are generally assumed to be worst-case scenarios, there are clear situations where this may not hold true (noting that discrepancies between models when using C_max were somewhat more predictable). When using C_max, IMDR >1.25 discrepancies only occurred at F_g 0.1 and 0.3, and only when the perpetrator had a high inhibitory impact on gut metabolism (fu_Gut = 1). Studies that recommend using static models due to their simpler computational needs, ease of use, and ease of interpretation [10] work under the assumption that static models can only show realistic or conservative DDI estimates. However, with the evidence provided in this study, this assumption should be reviewed when suggesting appropriate IVIVE approaches for competitive inhibition DDI predictions. As this study did not look into mechanism-based inhibition and induction interactions, no conclusions can be made for those instances.

In all the simulated scenarios, both models only corresponded in 32.8% and 24.3% of the cases when using C_avg,ss or C_max as the driver concentration, respectively. Most discrepancies fell into the IMDR < 0.8 interval, which is entirely expected when using C_max in the static formulas. C_max is not a realistic concentration as it is not physiologically accurate and will give conservative metabolic DDI estimates regardless of model structure, increasing risk for sponsors who will see overinflated DDI predictions leading to unnecessary clinical DDI studies. However, our study helps dissuade the notion that C_avg,ss will lead to mostly comparable results to dynamic models, as stated in other literature [10]. Indeed, the use of C_avg,ss decreased the rate of discrepancies in comparison to C_max (66.2% and 74.9%, respectively), but this improvement is nowhere close to making the DDI predictions between static and dynamic models comparable. In our observations, this also occurred regardless of the extent of gut wall metabolism; while a general trend of increased correspondence between models was seen as the substrate F_g was increased, cases where gut metabolism was absent (F_g: 1) still resulted in a mean discrepancy rate of 47%. The inability of the static model to predict dynamically varying perpetrator concentrations continues to be its weakness, as the employed surrogate values are not a faultless substitute and in most cases result in an overpredicted AUCr in comparison to dynamic models. Most of these discrepancies fall into the sponsor risk category, meaning a high likelihood of false-positive predictions when using static models. Nevertheless, at pre-clinical testing stages these cautionary indications are not used to make go/no go decisions but are utilised as an early flag for conducting more in-vitro and in-vivo DDI studies.

Static versus Dynamic Comparison: DDI Sensitive Individual

Unlike previous studies which compared static and dynamic models for a representative average patient, the consequences of using static models to predict DDIs in virtual individuals who greatly deviate from the average was investigated. Expectedly, the results (Fig. 6) showed major discrepancies in AUCr when comparing the static model results for the average patient compared with a vulnerable individual (95th percentile of a simulated virtual population). Roughly 40% of the results showed a patient risk discrepancy, further supporting the argument that static models are inadequate for the purpose of studying DDI sensitive populations.

Real-world data further support this conclusion. A recent paper reported on high-impact regulatory cases where static models using C_avg,ss could be used to replace dynamic models for regulatory filing [10]. One of these high-impact cases was ibrutinib, a CYP3A4 substrate [30]. Independently applying the static and dynamic DDI models for the ibrutinib and ketoconazole interaction, we also found there to be no discrepancies between both models, and both models had accurately predicted the mean AUCr observed from clinical data [30]. However, while the dynamic simulation in a population of individuals was able to predict the range of AUCr observed in the clinical trial, the static model, using either C_avg,ss or C_max as a driver concentration, provided AUCr predictions that were significantly lower than the highest observed AUCr in the clinical data [30].

What makes this particularly noteworthy is that those advocating strongly for static models already acknowledge this strength of dynamic models. For example, “by incorporating population differences in physiology and enzyme/transporter expression, they allow simulations of virtual populations and explain pharmacokinetic differences due to genetic polymorphisms” [10] and “Another unique strength of PBPK modelling is its ability to extrapolate DDI effects in a healthy population to an unstudied population, which could be a target population or organ impaired population” [10]. This raises the question of why there is ongoing support to replace dynamic DDI models with static ones, when there are no cases where static models can fully replicate the utility of dynamic models. Such an approach is therefore ‘two steps backwards’ in the field of metabolic DDI predictions. Our position is that static calculations are the first step, and that dynamic models, with their stochastically included co-variates, are subsequently required to more realistically predict real-world scenarios, enabling DDI risk to be assessed in all patients, but particularly in the most vulnerable patients who are likely to receive the concurrent drugs.

Conclusion

Even if static and dynamic DDI models could give identical results for the average patient, dynamic models are still required for drug labelling to provide prescribing advice in high-risk individuals and patient populations not routinely studied in clinical trials. Therefore, replacing dynamic DDI tools with static models is unwarranted, as static models are unable to fulfil a primary reason for why metabolic DDI studies are conducted in the first place—to ensure patient safety in those most at risk.

Supplementary Information

Below is the link to the electronic supplementary material.

Declarations

Conflicts of Interest

Ivan Tiryannik, Aki T. Heikkinen, Iain Gardner, Masoud Jamei, Anthonia Onasanwo, and Amin Rostami-Hodjegan are paid employees of Certara Predictive Technologies and may hold shares in Certara. The authors indicate no other conflicts of interest.

Author Contributions

Conceptualisation: Amin Rostami-Hodjegan; Methodology: Ivan Tiryannik, Aki T. Heikkinen, Iain Gardner, Masoud Jamei, Amin Rostami-Hodjegan, Thomas M. Polasek; Software: Anthonia Onasanwo, Ivan Tiryannik; Formal analysis: Ivan Tiryannik; Investigation: Ivan Tiryannik, Aki T. Heikkinen, Iain Gardner; Data curation: Ivan Tiryannik; Writing – original draft: Ivan Tiryannik; Writing – review & editing: Aki T. Heikkinen, Iain Gardner, Masoud Jamei, Amin Rostami-Hodjegan, Thomas M. Polasek, Anthonia Onasanwo; Visualisation: Ivan Tiryannik.

Data and Code Availability Statement

The authors confirm that the visualised data supporting the findings of this study are available within the article and its supplementary materials. The individual simulation data sets are available from the corresponding author, Ivan Tiryannik, upon reasonable request. The code created for compound batch generation, analysis, and visualisation can be found on this public GitHub repository: https://github.com/ivantiryannik/Simcyp-R-BatchWorkflow.

Funding

Not applicable.

Ethics Approval

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Consent to Participate

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Consent for Publication

Not applicable.