“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].

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 Cavg,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 Fg values. However, independent of permutations, every explored parameter (excluding ka and Ki) was shown to have discrepancies; 9 out of 10 and 6 out of 10 Ki and ka 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 Cavg,ss as a driver concentration. The use of Cmax 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 Cmax 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 Cmax were somewhat more predictable). When using Cmax, IMDR >1.25 discrepancies only occurred at Fg 0.1 and 0.3, and only when the perpetrator had a high inhibitory impact on gut metabolism (fuGut = 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 Cavg,ss or Cmax as the driver concentration, respectively. Most discrepancies fell into the IMDR < 0.8 interval, which is entirely expected when using Cmax in the static formulas. Cmax 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 Cavg,ss will lead to mostly comparable results to dynamic models, as stated in other literature [10]. Indeed, the use of Cavg,ss decreased the rate of discrepancies in comparison to Cmax (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 Fg was increased, cases where gut metabolism was absent (Fg: 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.

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 Cavg,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 Cavg,ss or Cmax 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.