Requirements to Establishing Confidence in Physiologically Based Pharmacokinetic (PBPK) Models and Overcoming Some of the Challenges to Meeting Them

Physiologically based pharmacokinetic (PBPK) models provide a mechanistic framework in which to integrate compound and system data for prospective predictions of drug exposure in humans [1, 2]. When scientifically well-founded, the mechanistic basis of PBPK models can help reduce the uncertainty and increase confidence in extrapolations outside the studied scenarios or studied populations. PBPK models are therefore increasingly applied during preclinical and clinical development [1, 3‐7]. During preclinical drug development, PBPK can support candidate drug selection and decision making by aiding an understanding of the mechanisms driving drug exposure [8]. During clinical drug development, PBPK modelling can drive internal decisions and support regulatory submissions [9‐11]. An increasing number of regulatory submissions over the last decade culminated in the recent draft guidelines by both the European Medicines Agency (EMA) [12] and the US Food and Drug Administration (FDA) [13], highlighting the growing relevance of PBPK in the pharmaceutical industry today. A recent publication from the Simcyp Consortium members [7] provided a perspective on the qualification and verification of PBPK platforms/models intended for regulatory submission. Despite the strengths of PBPK modelling approaches, most of the high-impact regulatory applications that resulted in labelling recommendations or study waivers have tended to be drug–drug interaction (DDI)-related [14]. Establishing confidence in PBPK models for non-DDI applications such as pediatric starting dose selection, organ impairment and absorption-related applications is challenged by the difficulty in developing mechanistically credible PBPK models or to verify and validate their prediction performance, either because drug elimination pathways cannot be well-characterized, or, when characterized, there is poor in vitro–in vivo correlation (IVIVC). This is especially true for transporter-dependent or non-cytochrome P450 (CYP)-mediated elimination pathways. The lack of a sufficient number of clinical datasets to resolve parameter non-identifiability has further limited model verification and validation. This work presents a systematic assessment of the current challenges to establishing confidence in PBPK models with respect to parameter estimation and model verification in each of the three major areas of PBPK application—absorption prediction, exposure prediction in a target population, and DDI risk assessment during drug development. These three areas cover most of the regulatory submissions. This paper also focuses on overcoming parameter non-identifiability issues through hypothesis testing, using case examples related to absorption.

In a workshop on modelling and simulation hosted by the EMA and the European Federation of Pharmaceutical Industries and Associations (EFPIA), representatives from industry, academia, and regulatory agencies proposed a framework where the degree of regulatory scrutiny, level of documentation, and the need for early dialogue is proportional to the impact of the modelling activity on regulatory decision making [15, 16]. Thus, regulatory submissions may be classified as high, medium or low impact depending on the ability of the work to replace, justify or describe an evidence base. For example, PBPK models that support regulatory filing for labelling negotiations or study waivers are considered ‘high impact’ applications. In general, these tend to be DDI-related. Pediatric starting dose selection or the study design may be considered an example of an application with moderate impact.

PBPK models are generally built in commercial platforms such as GastroPlus (http://​www.​simulations-plus.​com), PK-Sim^® (http://​www.​open-systems-pharmacology.​org/​) or Simcyp (http://​www.​simcyp.​com) that come with their own compound and population libraries. The EMA guidelines require qualification of these platforms [12]. PBPK platform qualification is defined as a version-specific evaluation to demonstrate its reliability for one or several intended purposes. It involves ensuring proper implementation of computational functionalities, accurate mathematical representation of the physiological processes, reliable system parameters for the library of populations, model verification for the library compounds, transparency regarding the source of system and compound data as well as assumptions in the system, version controlling, quality-controlled software installation, and evaluation of the predictive performance for high-impact applications for the intended purpose using a large, independent, diverse dataset.

Boxes 1 and 2 summarize the key questions that are addressed through PBPK modelling and simulations for some high-impact DDI applications. They also outline the modelling strategies employed to address these questions, as well as the possible outcomes that may be expected for regulatory submissions. Box 3 summarizes the key questions addressed by PBPK for moderate-impact non-DDI applications. The PBPK modelling strategy for an application depends on the impact level and the nature of the question that needs to be addressed. In general, the modelling strategy for a high-impact application involves the following:

A description of PBPK model qualification and verification is presented elsewhere [18]. However, in this current work, we distinguish between model verification and validation. While verification is a necessary step in a modelling exercise, in which model-simulated exposure is compared with independent clinical data (datasets that were not used in the model development steps), validation refers to the evaluation of the predictive performance of the model and may be part of either platform qualification or a regulatory submission.

The unique strength of PBPK modelling and simulations lies in its mechanistic basis. To leverage this strength, it is important to establish confidence in a mechanistically credible model that is validated for a particular purpose. This calls for a good understanding of mechanisms relevant to the question being addressed. The requirements to establish confidence in the application-relevant mechanisms depends on the type of application. For the three broad areas of PBPK application (absorption and formulation-related applications, extrapolation from a base population to pediatrics or special populations, and DDI) that cover most of the regulatory submissions, these requirements are presented in Fig. 1.

Absorption and formulation-related applications of PBPK modelling include (1) prediction of oral drug absorption by integrating drug permeability, dissolution, particle size and controlled/modified-release rates and formulation selection based on the model-predicted absorption; (2) prediction of the effects of food and/or proton pump inhibitors (PPI) on drug absorption; and (3) demonstration of bioequivalence of formulations through numerical or mechanistic IVIVC to support biowaivers. In this article, gut bioavailability (F_g) is defined as the product of fraction absorbed (f_abs) and fraction escaping intestinal loss (f_g), and is further illustrated in electronic Supplementary Figure 1. Intestinal loss (1 − f_g) is the loss of a drug due to gut metabolism or transporter-mediated intestinal efflux. These definitions are intended to appreciate the distinction between gut bioavailability and fraction escaping gut metabolism, often used interchangeably in the literature. At doses where intestinal efflux can be considered saturated, gut metabolism is assumed to be the sole contributor to intestinal loss. Confidence in absorption-related predictions is expected to be high when quantitative assessment of f_abs is reliable. For small molecule drugs that are sufficiently lipophilic (neutral or basic with log P > 1.8) to allow assumption of good permeability, the in vivo relevance of in vitro solubility and dissolution play a key role in the quantitative prediction of f_abs. In addition, knowledge of mechanisms contributing to gut bioavailability other than absorption, e.g. efflux and gut metabolism should either be known to be irrelevant (e.g. NCE is not a substrate of efflux transporters or enzymes expressed in the gut) or, when relevant, should be quantitatively assessed. For example, if gut metabolism is known to be relevant for the NCE, then quantifying the metabolic contribution of the gut requires metabolite measured in intravenous and oral routes. For CYP3A substrates, reasonable quantification is possible even with in vitro data [19]. For non-CYP drivers of gut metabolism, the availability of PK data following intravenous administration is indispensable in the quantitative mechanistic understanding of gut bioavailability. In the absence of intravenous data, for poorly soluble compounds, it is difficult to characterize the mechanisms relevant for absorption-related applications.

Application of PBPK to extrapolate drug exposure from a base population (usually healthy, adult, Caucasian) to other populations (pregnant, obese, smokers, hepatically/renally impaired, pediatric, elderly and different ethnicities) requires a mechanistic understanding of the drug PK in the base population, as well as a knowledge of how these mechanisms are altered in the target population (population in which the prediction is desired). This requires that the metabolic and elimination pathways, as well as the site contributing to each of the metabolic pathways (Electronic Supplementary Figure 2) are well-characterized. A combination of clinical DDI and PK data can also provide fraction metabolized (f_m). If an NCE is a transporter substrate, the in vivo contribution of the transporter to its elimination should be additionally well-understood. A good recovery of the in vivo clearance in the base population from in vitro intrinsic clearance (CL_int) is then necessary to adjust for differences in protein levels in the target population and will ensure that unique mechanisms relevant to the target population can be accounted for. When multiple CYP enzymes are responsible for the metabolism, pathway contributions should be verified through drug interaction studies and human absorption, distribution, metabolism and elimination (ADME)/mass balance studies when they become available. If only a single major CYP is involved in the metabolism in the base and target populations, CL_int may be derived from observed clearance in an intravenous PK study in the base population. A low variability in clinical PK (approximately 30% coefficient of variation) in the base population will allow for a robust estimation of parameters. In addition, for an oral drug whose gut bioavailability is < 1, the contribution of absorption, efflux or gut metabolism to gut bioavailability should be well-understood, as described for absorption-related applications. This will allow for appropriate corrections in parameters by accounting for differences between the base population and target populations.

Most of the applications of PBPK modelling and simulations in regulatory submissions are related to DDI, in which an NCE is either assessed as a victim/perpetrator of enzyme (CYP and non-CYPs)/transporter inhibition or CYP induction when coadministered with other drugs. To establish confidence in the utility of PBPK modelling for assessing an NCE as a victim drug, the metabolic and elimination pathways, as well as the site contributing to each of the metabolic pathways, should be well-characterized, as described for extrapolation to the target population. If the NCE is a transporter substrate, the contribution of transporter to elimination of the NCE should be additionally well-understood. For NCE as a perpetrator, it is enough to have the model-simulated profiles of drug exposure at interaction sites (gut, liver or kidney) derived from clinical data at steady-state and reliable in vitro data for inhibition and/or induction parameters. If the perpetrator drug also relies on the affected pathway for its own metabolism, then the fraction metabolized by an affected enzyme in the organ of interest (f_{m,isoform,organ}) is additionally required for the affected enzyme to account for potential auto-inhibition/induction. Thus, the requirements shown in Fig. 1 may be adapted to fit the purpose of the PBPK model, depending on the mechanisms relevant for a given drug and the availability of clinical data for model building.

In general, for all three major applications of PBPK, the fewer the mechanisms impacting the drug exposure (drug dissolution, and metabolic and elimination pathways), the fewer the associated parameters, and therefore overall uncertainty, and the greater the confidence in model predictions. Thus, Biopharmaceutics Classification System (BCS) I compounds for which elimination is driven by single (or major) CYP-mediated metabolism are likely to be associated with the least parameters, least overall parameter uncertainty, and therefore the highest confidence in prospective predictions (Electronic Supplementary Figure 3), as exposure of these compounds is not likely to be limited by absorption or impacted by transporters. Therefore, the only drug parameters needed for a BCS I perpetrator drug, for example, are parameters related to drug clearance, enzyme inhibition or induction potency of the drug. However, biowaivers are granted for BCS Class I drugs even without modelling. BCS Class II–IV drugs with their solubility- and/or permeability-limited, transporter-dependent exposure are subject to absorption and DDI challenges that can be addressed with PBPK. Applications include absorption [20, 21], PPI effect [22], food effect prediction [23, 24], bioequivalence assessment through IVIVC for getting a biowaiver for formulation bridging, and DDI assessment [25‐30], to name a few. A comprehensive list of applications is covered by Shebley et al. [7].

When mechanisms that are relevant to an application of interest can be identified, associated parameters well-established, and the PBPK model built in a qualified platform is verified and validated (if necessary) against clinical data, then confidence in the predictive performance of the model is said to be high. However, there are several barriers to establishing confidence in the mechanisms related to an application. These are presented in Fig. 2.

To cover for uncertainty in measured parameters, a sensitivity analysis on model parameters is first performed to identify the most sensitive parameters on which to conduct an uncertainty analysis. The impact of uncertainty in sensitive model parameters that cannot be precisely measured on endpoints of interest is assessed by varying the sensitive parameters over a range of plausible values for compound-related parameters, and over the 5th to 95th percentile of distributions for system parameters [40], based on what is known about the mechanism, rather than being arbitrary.

Parameter non-identifiability presents the greatest challenge for a proper characterization of underlying mechanisms. One way to overcome non-identifiability is to measure one or more of the non-identifiable parameters that can be reliably measured and combine with the composite parameter estimated from clinical data, to obtain the other non-identifiable parameter. Depending on the number of non-identifiable parameters in the composite parameter, the number that can be reliably measured, and the availability of relevant clinical data, complete deconvolution of the composite parameters may not be possible.

For applications that do require complete deconvolution (as in the example of food effect prediction in the previous section), hypothesis generation/testing with PBPK [8, 41, 42] can help deconvolute the relative contributions of intestinal loss factors. This begins with identifying CL_int and the tissue partition coefficient (K_p) factor (a multiplicative factor applied to all K_p in the PBPK model) that best fits the observed intravenous profile (Fig. 3). Assuming linear PK, as well as the constancy of hepatic clearance across different routes of administration, the best-fit parameters from the intravenous profile are fixed for oral PK simulations. Applying a bottom-up PBPK model, PK mechanisms underlying the observed oral PK profile can be identified using signature discrepancies of the simulated profile from the observed, as shown in Box 4 [2]. Signature discrepancies from observed data may be due to higher in vivo solubility than measured in vitro, drug-induced gastric empting delay, gut metabolism, enterohepatic recirculation, auto-inhibition/saturation of drug-metabolizing enzymes, auto-inhibition/saturation of uptake transporters and auto-inhibition/saturation of efflux transporters. The hypotheses generated by this approach may then be tested by suitable experimentation.

Hypothesis generation with PBPK can already be applied to preclinical intravenous and oral PK profiles to gain insight into the mechanisms underlying PK profiles in the preclinical species. When human intravenous and oral PK data become available, a similar systematic line-shape analysis with PBPK can check for the relevance of the mechanisms identified in preclinical species to humans. Two examples of hypotheses generation/testing with PBPK are illustrated in Boxes 5 and 6. Box 5 describes how hypothesis generation with PBPK helped distinguish gut metabolism from poor solubility for an NCE with gut bioavailability < 1. In this example, a compound that was believed to have solubility-limited absorption was shown to have no solubility limitation in vivo. The poor oral bioavailability of the drug could be attributed to gut metabolism. If clinical intravenous data are available, a quantitative in vivo gut bioavailability can then be estimated and employed in DDI assessment. In the absence of clinical intravenous data, dose proportional or supra-dose-proportional exposure observed in single ascending dose (SAD) and multiple ascending dose (MAD) FiH studies can support the hypotheses generated (solubility does not limit absorption) in preclinical species. This deconvolution of PK mechanisms has the potential to avert any unnecessary and costly formulation development to improve oral bioavailability. Box 6 describes the use of hypothesis generation for identifying gut metabolism [42] as the principal mechanism contributing to intestinal loss. The use of in vitro solubility and permeability, with the best-fit intravenous parameters, could simulate the maximum concentration (C_max), but not the AUC (Boxes 6c, d). Resolving parameter non-identifiability through hypothesis generation, testing and verification can ensure a high quality of prospective predictions for absorption-related applications.

In summary, regulatory submissions demand a rigorous application of the build-verify/refine-validate-predict/simulate modelling strategy and use of qualified platforms to address the key questions in the three broad categories of PBPK applications. In addition to building confidence in prospective predictions of PBPK models through the predict-learn-confirm process [43], understanding the mechanisms relevant to the question being addressed is highly desirable to leverage the unique strengths and mechanistic basis of PBPK models. However, there are barriers to establishing confidence in the mechanisms relevant to an application for the building and validation of models. Hypothesis generation/testing with PBPK models can provide useful insights into mechanisms underlying observed concentration-time profiles and pave the way for improved confidence in PBPK model predictions.

“Everything should be made as simple as possible, but not simpler” is a quote attributed to Einstein, which succinctly expresses the principle of Occam’s razor. The rationale behind this generic principle is that the number of assumptions generally tends to increase with the increasing complexity of models/hypotheses, and, at some point, a complex model could become too distant to whatever is being modelled. PBPK models or simpler? The choice should depend on the value addition brought on by PBPK over simpler methods for a particular drug in a particular application, given the challenges.

The steps involved in establishing confidence in PBPK models, and situations in which simpler models may be considered, are summarized in Fig. 4. To begin with, a fit-for-purpose PBPK model is built by identifying the key mechanisms that are relevant to the purpose of the application. Next, sensitive parameters pertinent to the identified mechanism should be estimated/derived from clinical data if possible. If the PK profile simulated by the model can be verified against an independent clinical dataset satisfying the acceptance criterion, then provided the requirements for establishing confidence in the model are met (Fig. 1), the model can be validated for its purpose before applying it for prospective prediction to an untested scenario. In the absence of satisfactory validation, it is possible that confidence in the key mechanism needs to be established, perhaps through hypothesis generation and testing.

If the verification criterion is not satisfied, further model refinement may be necessary through parameter changes that uniquely improve the fit to the clinical data. If multiple parameter changes lead to the same outcome, the non-identifiability should be resolved through hypothesis generation and testing. If an hypothesis cannot be verified, then the mechanistic strengths of PBPK cannot be leveraged, and simpler methods supported by a totality of evidence approach should be preferred.

To illustrate the strategy laid out in Fig. 4, consider the example of a CYP3A-metabolized, poorly soluble, weak-base NCE for which a bottom-up PBPK model is built using in vitro solubility and dissolution data for predicting food effect. For a poorly soluble weak base, PBPK models are likely to predict an absorption limited by precipitation. The extent of supersaturation and precipitation depends on the difference between gastric and intestinal pH. Since food affects the gastric pH, the exposure of a poorly soluble weak base is expected to show a food effect. In the absence of established confidence in the mechanism of precipitation (impossible to verify due to non-identifiability), prospective predictions of food and PPI effects based on the PBPK model may lead to resource-intensive studies and futile study designs, costing valuable time and money. An alternative approach may be to first establish confidence in a PBPK model that is meant for food effect prediction. According to Fig. 1, establishing confidence in a PBPK model that is meant for absorption-related application requires an understanding of mechanisms contributing to gut bioavailability and a quantitative assessment of fraction absorbed and gut metabolism. The key mechanism that needs to be well-characterized from clinical data is intestinal precipitation due to poor solubility. This requires clinical intravenous PK data in addition to oral PK to quantify gut bioavailability (F_g = f_abs × f_g). Gut bioavailability is derived from oral bioavailability (F) and fraction escaping hepatic clearance (f_h) [F = f_abs × f_g × f_h]. The model is then verified with oral clinical PK data. Even if the verification criterion is met, there is still no confidence in the f_abs as it is non-identifiable from f_g. An hypothesis generation as illustrated in Boxes 5 and 6 can distinguish poor in vivo solubility from gut metabolism as the driver of intestinal loss. If the extent of gut metabolism can be verified in the clinic (by comparing the amount of metabolite formed in intravenous vs. oral routes), then the non-identifiability is resolved and the PBPK model can be used for food effect prediction using the model-generated in vivo solubility. Otherwise, a simpler approach by which confidence in the extent of absorption is based on a platform of evidence from preclinical and clinical data may be adopted. Figure 5 illustrates such a platform of evidence for a drug for which hypothesis testing with preclinical PK profiles shows that solubility does not limit exposure. This may be supported by a lack of impact of an enabling formulation on drug exposure, as well as by dose proportionality in toxicological studies in preclinical species. Later in the clinic, dose proportionality or supra-dose proportionality observed in SAD and MAD studies, and a short time to reach C_max in oral PK profiles, can add to the evidence that the exposure of the compound is possibly not limited by solubility. Furthermore, a supra-dose-proportional exposure with higher interindividual variability in C_max compared with AUC is probably indicative of gut metabolism, distinct from solubility limitation. When a PPI study of a compound with omeprazole, a drug known to induce gastroparesis [44], shows lower C_max but the same AUC, it may be deduced that the compound behaves like a BCS Class I drug with no solubility- or permeability-limited absorption. Thus, as a drug progresses through the value chain, it is possible to build a platform of evidence to confirm that the drug does not have solubility/dissolution-limited absorption and therefore may not show a food effect.

PBPK models are unique in their ability to integrate all available compound and system knowledge for a meaningful prediction of absorption, DDI and drug exposure in an untested scenario or in an unstudied population. Yet, its full potential cannot be unleashed unless confidence in the mechanisms that are relevant to an application are well-established. This paper highlights the importance of leveraging all preclinical knowledge to generate hypotheses that can be verified when clinical data become available. If a hypothesis can be verified, then the learning can be incorporated into building a mechanistically credible PBPK model, which is likely to have better predictive performance. In the absence of sufficient clinical datasets to resolve parameter non-identifiability, hypothesis testing offers a great opportunity to maximize the confidence in PBPK model predictions. Continued efforts in improving in vitro assays, gaining a better understanding of the factors driving drug exposure and its variability in different individuals and populations, and improving confidence in system parameters are all imperative to broaden the scope of PBPK applications. As PBPK models continue to evolve, building on the collective experience of the scientific community, wider acceptance from regulatory agencies is anticipated in the future.