FormalPara Key Points

By fully utilizing the results from clinical drug trials, a newPK-mediated clinical drug–drug interaction risk assessment scale was established, which can accurately predict DDI outcomes.

A series of parameters, including the in vivo metabolic fraction, intestinal availability, and the inhibition constants of inhibitors were calculated. These parameters, compared to results from in vitro experiments, can be more reliably applied in contexts such as PBPK models.

1 Introduction

In clinical practice, over half the patients require the simultaneous use of two or more medications. Drug–drug interactions (DDIs) have always been an issue of special concern in clinical use because they can affect the exposure of the affected (victim) drug in the body, potentially leading to serious or even fatal adverse reactions [1, 2]. Reducing the toxic side effects caused by fluctuations in drug concentrations without delaying the treatment cycle is hindered by the lack of a highly efficient, feasible, accurate, and reliable method, aside from therapeutic drug monitoring tailored to specific medications. Although clinical DDI trials yield the most accurate risk results, the myriad of possible interaction combinations during the actual use of drugs make it impractical to assess all potential drug interactions in clinical trials.

Leveraging the results from existing clinical drug interaction studies to extrapolate DDIs has been recently proposed [3, 4] and has proven to be highly effective in clinical practice for predicting potential interactions [5]. This method utilizes midazolam as a standard drug and calculates the apparent inhibition ratio (IR) of the perpetrator drug based on clinical DDI trial results associated with midazolam. Subsequently, the contribution ratio (CR) of the affected drug has been determined in clinical DDI trials involving potent perpetrator drugs.

Using these two parameters, it is possible to extrapolate the exposure changes caused by other drug combinations using equation \(1/(1-\text{IR}\times \text{CR})\), allowing clinical trial data to rapidly and accurately guide the optimization of clinical prescriptions. However, this method still has shortcomings in the application of clinical DDI risk assessment because of three important issues. The first issue is the influence of intestinal metabolic sites on DDIs. This issue has been neglected. However, it is particularly pertinent for cytochrome P450 (CYP) 3A4, where the contribution of intestinal enzyme-mediated metabolism is significant and should not be overlooked [6]. Such an oversight could potentially compromise the precision of pharmacokinetic (PK) extrapolations. For substrates such as tacrolimus and sirolimus, the intestinal extraction exceeds 75% [7, 8]. Loue and Tod [5] utilized the methodology developed by Ohno et al. [3] and predicted DDIs when the aforementioned substrates were co-administered with CYP3A4 inhibitors. This prediction revealed significant discrepancies in both underestimation and overestimation. Clinical trials have demonstrated that an oral dose of 800 mg of posaconazole can lead to an 8.9-fold increase in the area under the curve (AUC) of sirolimus [9], whereas the method predicted only a 3.6-fold increase.

The second issue is that the IR of the perpetrator drug is calculated at a specific dosage, even though the effects of varying the perpetrator drug dosage on the substrate can differ significantly. For instance, a daily dose of 100 mg of fluconazole can cause a 2.1-fold increase in the AUC of triazolam, whereas a daily dose of 200 mg can elevate this value 4.4-fold [10]. In the context of complex clinical dosage adjustments, relying solely on the IR value does not fulfill the requirements for risk assessment.

The third issue is that the IR of the perpetrator drug and the CR of the victim drug lack concrete physiological significance and are not differentiated according to the type of inhibition exerted by the inhibitor. This limitation constrains the application scenarios for the parameter values. Hisaka et al. [4] examined the correlation between these parameters and the mechanistically meaningful parameters derived from in vitro experiments. This method could potentially replace in vitro experiments to obtain drug interaction parameters for use in physiologically based PK (PBPK) models to predict DDIs in special populations.

To address these issues, this study exploited the extensive available clinical trial data of drugs. Based on a mechanistic static model, the study fits parameters related to DDIs, including the metabolic fraction, intestinal permeability, inhibition constant of competitive inhibitors, inactivation efficiency of time-dependent inhibitors, and unbound concentration of the perpetrator drug at the enzyme-binding site. A framework was established to assess the clinical risks posed by drug combinations, enabling rapid and reliable quantitative assessment of DDIs during clinical use. Recommendations for their use are made based on these results.

2 Methods

2.1 Experimental Drugs

This study considered the CYP3A4 enzyme, which is frequently involved in DDIs, as a paradigm that included CYP3A4 substrates and inhibitors. By referencing the indicator drugs recommended on the US Food and Drug Administration (FDA) website [11] and reviewing previously published data [12,13,14,15], common CYP3A4 substrates and inhibitors were collected. Information was gathered regarding the main elimination pathways, metabolic profiles, types of CYP3A4 enzyme inhibition, and CYP3A4 selectivity of these drugs. The drugs were selected according to the following criteria. Substrates needed to be administered orally; with data available from clinical DDI trials involving two or more CYP3A4 inhibitors, resulting in an AUC ratio (AUCR) ≥1.15; primarily cleared by hepatic metabolism with assumed negligible renal clearance; with linear PK characteristics. Inhibitors needed to be administered orally; with clinical DDI trials performed with midazolam and other CYP3A4 substrates, yielding an AUCR ≥ 1.15; and with data of the type of CYP3A4 inhibition.

2.2 Development of the Mechanistic Static Model Method

Clinical DDI trials facilitate the acquisition of exposure change multiples, specifically the AUCR. The size of the AUCR is contingent on the binding affinity, potency, concentration, and extent of metabolic clearance of the substrate via CYP3A4 [16]. When the concentration of the substrate is below the Michaelis–Menten constant (Km), it is presumed that metabolic clearance by CYP3A4 is concentration independent. Furthermore, considering the presence of the CYP3A4 enzyme within the intestinal tract, the fraction of intestinal permeability affected by DDIs is considered into account [17].

$$\text{AUCR}=\frac{\text{AUC}^{\prime}}{\text{AUC}}=\frac{1}{\frac{1-{F}_{g}}{\left(1+\frac{{\left[I\right]}_{g,u}}{{k}_{i,u}}\right)}+{F}_{g}} \times \frac{1}{\frac{{f}_{m}}{\left(1+\frac{{\left[I\right]}_{H,u}}{{k}_{i,u}}\right)}+\left(1-{f}_{m}\right)}$$
(1)

If the inhibition type of the perpetrator drug is competitive inhibition, the change in the AUCR of the victim drug exposure can be calculated as:

If the inhibition type of the perpetrator drug is time dependent, the change in AUCR of the victim drug exposure can be expressed as:

$$\text{AUCR}=\frac{{\text{AUC}}^{\prime}}{\text{AUC}}=\frac{1}{\frac{1-{F}_{g}}{\left(1+\frac{{\left[I\right]}_{g,u}}{{k}_{\text{deg},g}} \times \frac{{k}_{\text{inact}}}{{K}_{I,u}}\right)}+{F}_{g}} \times \frac{1}{\frac{{f}_{m}}{1+\left(\frac{{\left[I\right]}_{H,u}}{{k}_{\text{deg},H}}\times \frac{{k}_{\text{inact}}}{{K}_{I,u}}\right)}+\left(1-{f}_{m}\right)}.$$
(2)

In Eqs. (1) and (2), \({\text{AUC}}^{\prime}\) represents the AUC of the victim drug after being affected by the perpetrator drug, \({F}_{g}\) represents intestinal availability, namely \({f}_{a}\times {f}_{g}\), \({f}_{m}\) represents the fraction of victim drug metabolized by enzymes (default refers to CYP3A4 enzyme), \({k}_{i,u}\) represents the inhibition constant for an unbound competitive inhibitor, \({k}_{\text{inact}}\) represents the maximal inactivation rate of time-dependent inhibitors, \({K}_{I,u}\) represents the unbound inactivator concentration at half \({k}_{\text{inact}}\), \({[I]}_{g,u}, {[I]}_{H,u}\) represent the unbound concentrations of the inhibitor in the liver and intestine, and \({k}_{\text{deg},g}, {k}_{\text{deg},H}\) represent the intestinal (\({\text{CYP}3\text{A}}_{\text{h}}\), 0.000321 min−1) and hepatic (\({\text{CYP}3\text{A}}_{\text{g}}\), 0.000481 min−1) degradation rates of CYP3A enzymes [18,19,20]. For a detailed derivation, please refer to the Electronic Supplementary Material (ESM).

It is evident from Eqs. (1) and (2) that the AUCR obtained from clinical DDI trials can be considered the result of the combined effects of four unknown parameters: intrinsic clearance (Fg), fraction metabolized (fm) of the substrate, the unbound concentration of the inhibitor ([I]u), and inhibition constant (Ki) or the ratio of inactivation rate constant to inhibition constant (kinact/KI). It is necessary to use a standard drug to establish the values of these parameters, as detailed in the process outlined in Fig. 1.

Fig. 1
figure 1

Workflow of the approach. AUCR area under the curve ratio, CYP cytochrome P450, DDI drug–drug interaction

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2.3 Standard Drug

This study requires the selection of a standard drug and setting initial values for the Fg and fm of this drug. In clinical trials, the sponsors typically use a single oral dose of midazolam to assess its inhibitory or inductive effects on CYP3A4. In vivo studies have confirmed that midazolam is a highly specific CYP3A4 substrate, undergoing clearance solely through CYP3A4 metabolism [21, 22]. The search terms “midazolam” and “CYP3A4” and “metabolite”, “midazolam” and “fraction gut” or “intestinal availability” were utilized in the PubMed search engine to query the published \({f}_{\text{m},\text{CYP}3\text{A}4}\) and \({F}_{g}\) values for midazolam. The search results are provided in Tables 1 and 2. The \({\text{f}}_{\text{m},\text{CYP}3\text{A}4}\) and \({F}_{g}\) values of the standard drug midazolam in this study were 0.92 and 0.55, respectively (the average values from the literature cited in Tables 1, 2).

Table 1 Summary of published results on the proportion of midazolam metabolized by CYP3A4
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Table 2 Summary of published results on the bioavailability of midazolam for intestinal use
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2.4 Human Data Sources

The results of the clinical drug interaction trials in this study were derived from clinical trials registered on the ClinicalTrials.gov website (https://clinicaltrials.gov/). Data were obtained by searching for clinical pharmacology review reports on the FDA website and Cortellis Drug Discovery Intelligence database or through the published literature that reported trial outcomes. Data on the drug concentration–time curve incorporated in the study were digitized following recommended practices [23] using GetData Graph Digitizer version 2.26.0.20 (https://getdata-graph-digitizer.software.informer.com/download/). The extracted PK curves data from clinical trials at clinical doses were imported into Certara Phoenix WinNonlin 8.1 for compartmental modeling and non-compartmental analysis to calculate the values of PK parameters including AUC, ka, and apparent clearance. The oral bioavailability of the drugs was cited from the publicly available Human Oral Bioavailability Database (http://modem.ucsd.edu/adme/databases/databases_bioavailability.htm) [24, 25].

2.5 Determination of Unbound Inhibition Concentration for the Inhibitors

Because CYP3A4 is present in both the liver and small intestine, it is necessary to determine the unbound inhibitor concentration in these organs. As shown in Fig. 2, after absorption in the gastrointestinal tract, inhibitors are metabolized or transported through the small intestinal mucosa and enter the liver via the portal vein and hepatic artery.

Fig. 2
figure 2

Process of digestion and absorption of orally administered drugs. Drug bioavailability is collectively determined by the absorption fraction in the gastrointestinal tract, intestinal mucosal metabolism permeability fraction, and hepatic metabolism permeability fraction. The drug is initially absorbed from the intestinal lumen into epithelial cells. The amount of the absorbed drug is represented as \({f}_{a}\times {k}_{a}\times D\) f[27]. The drug then enters the hepatic portal vein through the intestinal mucosal layer. A portion of the drug may be transported back to the gut by transporters. Hepatic inlet drugs are supplied by both the portal vein and hepatic artery; the sum of these two parts is considered as the drug concentration within the liver. CYP cytochrome P450, D represents the oral dose, \({f}_{a}\) absorption fraction, \({f}_{h}\) represents the fraction of non-metabolic elimination in the liver, \({k}_{a}\) absorption rate constant

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Although the free concentrations of inhibitors in the intestinal mucosa and around hepatic enzymes cannot be directly obtained from in vivo measurements, research by Ito et al. [26, 27] suggests that the free concentration of inhibitors in the intestinal mucosa and liver can be represented as the sum of the gastrointestinal absorbed fraction and systemic circulation concentration. Studies have compared the accuracy of drug interaction predictions based on static concentrations at the aforementioned sites, calculated using either \({C}_{\text{max}}\) (maximum systemic circulation concentration) or \({C}_{\text{ave}}\) (average systemic circulation concentration) derived from in vitro experiments [28,29,30]. Using the average concentration as the effective concentration of the inhibitor appears to provide a more conservative conclusion for risk assessment. This study based on the in vivo result, employed the free concentration at the portal vein inlet, denoted as \({\left[I\right]}_{g,u}\), to represent the free concentration of inhibitors in small intestinal mucosa, as determined in Equation (3). Similarly, the free concentration at the hepatic inlet was used to denote the free hepatic inhibitor concentration \({[I]}_{H,u}\), as shown in Eq. (4):

$$\begin{array}{c}{\left[I\right]}_{g,u,\text{ave}}={f}_{up}\times {C}_{\text{ave}}+{f}_{ub}\times \left(\frac{{k}_{a}\times {f}_{a} \times D}{{Q}_{pv}}\right),\end{array}$$
(3)
$$\begin{array}{c}{\left[I\right]}_{H,u,\text{ave}}={f}_{up}\times {C}_{\text{ave}}+{f}_{ub}\times \left(\frac{{k}_{a} \times {f}_{a} \times D}{{Q}_{h}}\right),\end{array}$$
(4)
$$\begin{array}{c}{f}_{ub}=\frac{{f}_{up}}{\text{BpR}},\end{array}$$
(5)
$$\begin{array}{c}{C}_{\text{ave}}=\frac{\text{AUC}}{\tau }.\end{array}$$
(6)

In the above equations, \({Q}_{h}\) represents the liver blood flow (96.6 L/h) [31, 32], \({Q}_{pv}\) represents the portal vein blood flow (73 L/h), which is approximately 75% of the hepatic blood flow, \({f}_{up}\) represents the free fraction of the test drug in plasma, \({f}_{ub}\) represents the free fraction of the test drug in the blood, \({k}_{a}\) represents the oral absorption rate of the test drug (h−1), BpR is the blood-to-plasma ratio, and τ is the dosing interval.

2.6 Calculation of In Vivo \({{\varvec{F}}}_{{\varvec{g}}}\) Value for the Substrates

Intestinal availability refers to the fraction of drugs that pass through the epithelial cells of the small intestinal mucosa and enter the portal vein. Currently, there are four methods to estimate the in vivo value of \({F}_{g}\). The first method is the comparison of the results of DDI studies following intravenous administration with the results obtained after oral administration [33]. The second method relies on grapefruit juice as a complete inhibitor of intestinal CYP3A4 enzymes. The DDI results of test drugs with grapefruit juice can effectively estimate the in vivo \({F}_{g}\) value [34]. The third method uses mathematical modeling approaches to derive the in vivo \({F}_{g}\) value from the body’s drug-time curves [35]. The fourth method infers the intestinal availability indirectly by obtaining information, such as bioavailability (F) and total clearance rate from the drug-time curves following both intravenous and oral administration of a drug [36].

In this study, the drugs included in the calculations were primarily metabolized and cleared by the liver, with negligible renal clearance. The total oral clearance rate, denoted as \({\text{CL}}_{\text{tot}}\), can be approximated as equivalent to the hepatic clearance rate, \({\text{CL}}_{\text{h}}\). Hence, intestinal availability, \({F}_{g}\), can be expressed as follows:

$$\begin{array}{c}{F}_{g}={f}_{a}\times {f}_{g}=\frac{F}{{f}_{h}}=\frac{F}{1-\frac{{\text{CL}}_{\text{tot}}}{{Q}_{h}}},\end{array}$$
(7)

where F represents the oral bioavailability of the test drug, which can be obtained from the drug concentration–time curve of intravenous/oral administration and \({\text{CL}}_{\text{tot}}/F\) is obtained through a compartmental analysis of drug concentration–time curves in vivo. The in vivo \({F}_{g}\) values of the affected drugs can be calculated using Eq. (7).

2.7 Determination of Specific Parameters for In Vivo DDIs

Upon obtaining the results of the clinical drug interaction trials between the study inhibitors and midazolam, and the concentrations of the inhibitors, the in vivo \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values were calculated using Eqs. (1) and (2). Following the workflow depicted in Fig. 1, after determining the in vivo \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values of the inhibitors, data from a series of clinical drug interaction studies performed with inhibitors that are highly selective for CYP3A4 were used to estimate the in vivo \({f}_{m,\text{CYP}3\text{A}4}\) values for a range of substrates used in combination with these inhibitors.

2.8 Validation of Specific Parameters for In Vivo DDIs

To verify the accuracy and reliability of a series of in vivo DDI specificity parameters derived using the methodology outlined in this article for the assessment of interaction risks, cross-validation was performed using a validation set composed of clinical trials that did not incorporate the calculated parameters. Employing the basic static method described in the FDA DDI guidelines [37], we validated the discrepancies between the calculated specificity parameters for substrates and inhibitors for risk assessment and their observed values, intending to examine their reliability. Furthermore, this study incorporated the in vivo DDI specificity parameters calculated herein into Eqs. (1) and (2) to forecast the outcomes of clinical drug interactions, and compared these predictions with the actual measured values to assess predictive accuracy. The magnitude of the discrepancies was quantified using the geometric mean fold error (GMFE) and root mean square error (RMSE).

$$\begin{array}{c}GMFE={10}^{\frac{\sum \left|\text{log}\frac{\text{predicted DDI}}{\text{actual DDI}}\right|}{\text{number of predictions}}}\end{array}$$
(8)
$$\begin{array}{c}RMSE=\sqrt{\frac{\sum {\left(\text{predicted DDI}-\text{actual DDI}\right)}^{2}}{\text{number of predictions}}}\end{array}$$
(9)

2.9 Establishment of the PBPK model

The feasibility of using the drug interaction specificity parameters obtained from this study instead of in vitro experimental results for predicting DDIs using PBPK models was investigated. Physiologically based PK models were constructed for both the substrates and inhibitors using PK-Sim and MoBi (Open Systems Pharmacology Suite 10, available at www.open-systems-pharmacology.org), referencing model information from the OSP-PBPK-Model-Library (https://github.com/Open-Systems-Pharmacology/OSP-PBPK-Model-Library). The validated PBPK models were then used to simulate the PK profile changes of the substrate when combined with an inhibitor, which was subsequently compared with the observed clinical PK curves. The details of the model development are in the ESM.

2.10 Clinical DDI Risk Scale Evaluation

Currently, the risk of drug-induced interactions is categorized as strong, moderate, and weak, based on AUCR when co-administered with a probe drug. Such a basic qualitative classification is insufficient for risk assessment in complex clinical scenarios. In this study, by computing in vivo DDI specificity parameters, we introduced two novel metrics for evaluating the risk associated with CYP3A4 enzyme interactions: the risk index (RI) for substrates and the potency index (PI) for inhibitors, which serve as scales for risk measurement. The RI is defined as the maximal fold increase in the AUC of the substrate co-administered with a potent enzyme inhibitor (see Eq. 10). The PI is defined as the maximal theoretical fold increase in the AUC of the most sensitive enzyme substrate to the inhibitor at a given dose (see Eqs. 11 and 12).

$$\begin{array}{c}RI=\frac{1}{\frac{1-{F}_{g}}{10}+{F}_{g}}\times \frac{1}{\frac{{f}_{m}}{10}+\left(1-{f}_{m}\right)}\end{array}$$
(10)

For competitive inhibitors:

$$\begin{array}{c}PI=\left(1+\frac{{\left[I\right]}_{H,u}}{{k}_{i}}\right)\times \left(1+\frac{{\left[I\right]}_{G,u}}{{k}_{i}}\right).\end{array}$$
(11)

For time-dependent inhibitors:

$$\begin{array}{c}PI=\left(1+\frac{{\left[I\right]}_{H,u}}{{k}_{\text{deg},h}}\times \frac{{k}_{\text{inact}}}{{K}_{I}}\right)\times \left(1+\frac{{\left[I\right]}_{G,u}}{{k}_{\text{deg},g}}\times \frac{{k}_{\text{inact}}}{{K}_{I}}\right).\end{array}$$
(12)

3 Results

3.1 Inclusion of Experimental Drugs and Human Data

We included 33 marketed drugs that are primarily metabolized by CYP3A4 (Table 3) along with 20 commonly marketed drugs that inhibit CYP3A4 (Table 4). Clinical drug interaction studies for these drugs were identified by searching the FDA’s Drug Approvals and Databases (https://www.fda.gov/drugs) and querying the PubMed database with the keywords “[drug name]” and “drug interaction study” and “healthy volunteers”. A total of 53 in vivo drug interaction outcomes were included as a training set for the method to calculate DDI-specific parameters (Tables S1 and S2 of the ESM). Furthermore, 89 in vivo drug interaction outcomes were included as a validation set to verify the reliability of the predicted parameters, which can be found in Table S3 of the ESM.

Table 3 CYP3A4 substrates included in this study
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Table 4 CYP3A4 inhibitors included in this study
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3.2 Unbound Concentration for the Inhibitors and In Vivo Fg Values for the Substrates

According to Eqs. (3)–(6), the inhibitor concentration is related to the drug dosage, absorption constant, fraction absorbed, AUC, and free fraction, among other factors. Data on the drug concentration–time curve incorporated in the study were extracted using GetData Graph Digitizer version 2.26.0.20, and Certara Phoenix WinNonlin version 8.1 was utilized for non-compartmental analysis and compartment model fitting to obtain the AUC and ka values for specific inhibitor doses (Table S4 of the ESM). The unbound fraction was obtained by querying the Cortellis Drug Discovery Intelligence database. Based on Eqs. (3)–(6), the average concentration of the free inhibitor in the small intestinal mucosa and hepatic inlet at specific doses were calculated and are compiled in Table S5 of the ESM.

According to Eq. (7), the calculation of the \({\text{F}}_{\text{g}}\) for the substrates included in the study requires knowledge of the bioavailability and clearance rate of the substrate. We used the PK curves derived from the control group in clinical DDI trials where substrates are administered individually to perform compartmental model fitting, which yielded the \({\text{CL}}_{\text{tot}}/F\) of the substrate, approximating the hepatic clearance \({\text{CL}}_{\text{h}}/F\). The bioavailability was determined using the Human Oral Bioavailability Database summarized by Hou et al. [24, 25]. The calculated \({F}_{g}\) values for the substrates are listed in Table S6 of the ESM.

3.3 Calculation of In Vivo Apparent \({{\varvec{K}}}_{{\varvec{i}}}\) and \({{\varvec{k}}}_{\mathbf{i}\mathbf{n}\mathbf{a}\mathbf{c}\mathbf{t}}/{{\varvec{K}}}_{{\varvec{I}}}\) Values

To assess the potency of enzyme inhibitors, the current practice predominantly involves the use of in vitro systems, such as liver microsomes or human hepatocyte incubations. These systems test various concentration levels and standard substrates incubated with the enzyme, allowing the calculation of inhibition constants \({K}_{i}\) (for time-dependent inhibitors, the inactivation constant \({k}_{\text{inact}}/{K}_{I}\) is determined) [38, 39]. The results vary significantly depending on the incubation conditions. This study calculated the \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values based on human data obtained from the concomitant use of the inhibitor with midazolam, utilizing the model parameters in Table 5. The results are provided in Table S7 of the ESM.

Table 5 Model parameters used to calculate inhibitor \({K}_{i}\), \({k}_{\text{inact}}/{K}_{I}\), and substrate \({f}_{m,\text{CYP}3\text{A}4}\) values
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According to the FDA DDI guidance, when a drug is determined to be an enzyme inhibitor in vitro, the severity of the consequences of the drug inhibiting the enzyme is assessed using a basic model [40] by calculating the R-value of the inhibitor. To compare whether the inhibitor parameters from different sources could reliably estimate the risk of the inhibitor in clinical use, the R values were calculated (Eqs. 13–16) using the \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) calculated in this study, the average of in vitro experiments obtained from the literature [18, 41,42,43] (see Table S8 of the ESM) and the IR value calculated as described by Ohno et al. [3] with the same dataset (see Table S1 of the ESM). Finally, these three sets of R values were compared with the clinical DDI results of the corresponding inhibitors in the validation set [44]. The results are shown in Fig. 3A, B. The data clearly show that the R values calculated using the \({K}_{i}\) and \({\text{k}}_{\text{inact}}/{\text{K}}_{\text{I}}\) values obtained in this study had smaller errors with the clinical AUCR in the validation set. The findings indicate that it better reflects the clinical DDI risk caused by the inhibitors. Moreover, Fig. 3C, D show that the \({K}_{i}\) and \({\text{k}}_{\text{inact}}/{\text{K}}_{\text{I}}\) values calculated in this study were consistently closer to the overall mean of the inhibitory potency parameters of the corresponding inhibitors obtained in the literature than those derived from the IR values.

Fig. 3
figure 3

A Comparison of basic model fitting results using \({K}_{i}\) or \({k}_{\text{inact}}/{K}_{I}\) values (Eqs. 13–16) obtained from this study, the method of Ohno et al., and in vitro experimental results from the literature with the clinically observed area under the curve ratio (AUCR) values of the validation set (Table S3 of the ESM). B Geometric mean fold error (GMFE) and root mean square error (RMSE) for basic model fitting using \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values from this study, the method of Ohno et al., and in vitro experimental results from the literature compared with clinically observed AUCR values of the validation set (Table S3 of the ESM). C Distribution of \({K}_{i}\) values of competitive inhibitors from this study, the method of Ohno et al., and in vitro experimental results from the literature, the diamonds represent a series of in vitro experimental Ki values from the literature listed in Table S8 of the ESM with the average of these in vitro experimental results shown in red lines and the standard error represented by black error bars; hexagons represent Ki values obtained using the method described by Ohno et al.; and pentagrams represent Ki values calculated in this study. D Distribution of \({k}_{\text{inact}}/{K}_{I}\) values of time-dependent inhibitors from this study, the method of Ohno et al., and in vitro experimental results from the literature, the diamonds represent a series of in vitro experimental \({k}_{\text{inact}}/{K}_{I}\) values from the literature listed in Table S8 of the ESM with the average of these in vitro experimental results shown in red lines and the standard error represented by black error bars; hexagons represent \({k}_{\text{inact}}/{K}_{I}\) values obtained using the method described by Ohno et al.; and pentagrams represent \({k}_{\text{inact}}/{K}_{I}\) values calculated in this study

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For competitive inhibition:

$$\begin{array}{c}R1=1+\left[I\right]/{K}_{i}.\end{array}$$
(13)

For time-dependent inhibition:

$$\begin{array}{c}R2=1+{k}_{\text{obs}}/{k}_{\text{deg}},\end{array}$$
(14)
$$\begin{array}{c}{k}_{\text{obs}}={k}_{\text{inact}}\times [I]/{K}_{I.}\end{array}$$
(15)

The relationship between the IR and the boundary R values obtained by Ohno et al. [3] is as follows:

$$\begin{array}{c}R=1/\left(1-IR\right).\end{array}$$
(16)

3.4 Calculation of In Vivo \({{\varvec{f}}}_{{\varvec{m}},\mathbf{C}\mathbf{Y}\mathbf{P}3\mathbf{A}4}\) Values

Accurately calculating the fraction of metabolized \({f}_{m}\) of a target drug is critical for assessing the infinite risk of drug interactions in clinical settings [5, 45]. Common methods for determining the contribution of a drug through a specific metabolic pathway include in vitro system incubation, back-calculation from human results, and human radiolabeled absorption, distribution, metabolism, and excretion studies.

This study employed inhibitors with strong CYP3A4 selectivity in conjunction with the clinical DDI trial results for the included substrates. The in vivo values of the target CYP3A4 substrates \({f}_{m,\text{CYP}3\text{A}4}\) were calculated using the \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values derived from the model parameters in Table 5, and the corresponding in vivo \({F}_{g}\) values calculated above. The results are provided in Table S9 of the ESM. We separately examined the risks of clinical DDI effects on substrates assessed using fm values alone, and using both \({F}_{g}\) and \({f}_{m}\) values. These results were compared to the corresponding substrate AUCR results for the validation set. As shown in Fig. 4, considering both \({\text{F}}_{\text{g}}\) and \({\text{f}}_{\text{m}}\) values of the substrate provides a better representation of the potential risk of clinical DDI and reduce the likelihood of false negatives.

Fig. 4
figure 4

Relationship between substrate drug–drug interaction (DDI) sensitivity parameters and the clinical DDI area under the curve ratio (AUCR). A In vivo \({F}_{g}\) values and \({f}_{m}\) values of substrate determined using the study methodology were employed to assess the sensitivity of the substrate to DDIs: \(\text{AUCR}\approx 1/{(F}_{g}\times (1-{f}_{m})\). B In vivo \({f}_{m}\) values of substrates determined using the study methodology were used to assess substrate sensitivity to DDIs: \(\text{AUCR}\approx 1/(1-{f}_{m})\). The red color blocks represent false negatives, the gray color blocks represent false positives, and the green color blocks represent true positives/negatives

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3.5 Validation of Clinical Drug Interaction Simulation Results

Upon obtaining a reliable inhibitor \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values, and substrate \({F}_{g}\) and \({f}_{m}\) values, common methodologies for predicting clinical DDI risks include static and PBPK models [46]. Initially, we applied Eqs. (1) and (2) to the aforementioned data to predict clinical DDI outcomes within the validation set. Concurrently, we utilized the method developed by Ohno et al. [3] to predict DDI outcomes in the validation set, comparing each with clinically observed values. As depicted in Fig. 5, the predictions made using our method showed that 81% of the results varied within 1.5-fold of the clinically observed values, which is superior to the outcomes achieved using the method of Ohno et al. [3] (Fig. 5A, a). In scenarios involving high-risk clinical DDIs with AUCR > 2.5 (Fig. 5B, b) and cases where Fg < 0.5 (Fig. 5C, c), our method demonstrated superior accuracy. Under all circumstances, the overall prediction error of our method was less than that of the method of Ohno et al. [3] (Fig. 5D, d).

Fig. 5
figure 5

Comparison of in vivo drug–drug interaction simulation outcomes with values observed in clinical trials. This figure illustrates data of a comparative analysis between the results of in vivo drug–drug interaction simulations and actual measured values from clinical trials. The simulations were conducted using both \({K}_{i}\),\({k}_{\text{inact}}/{K}_{I}\), and \({f}_{m}\) values obtained from this study, and inhibition ratio (IR) and contribution ratio (CR) values derived from the method of Ohna et al. The comparison involves 89 clinical drug–drug interaction measured values from a validation set. The vertical axis represents the simulated area under the curve (AUCR) values and the horizontal axis displays the AUCR values observed in clinical trials. A Results of simulations using the method of Ohna et al. compared with clinical observed values. a Results of simulations using the method from this study compared with clinical observed values. B Subset of the validation set with AUCR > 2.5, comparing simulations based on the method of Ohna et al. with clinically observed values. b Subset of the validation set with AUCR > 2.5, comparing simulations from this study against clinical observed values. C Subset of the validation set with intrinsic clearance (Fg) < 0.5, comparing simulations based on the method of Ohna et al with clinically observed values. c Subset of the validation set with Fg < 0.5, comparing simulations from this study with clinical observed values. D Comparison between the geometric mean fold error (GMFE) of the results simulated in this study and those by Ohna et al. relative to clinical observed values. d Comparison of the root mean square error (RMSE) between the simulation results of this study and those by Ohna et al. relative to clinical observed values

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To describe the impact of temporal variation in the in vivo concentrations of inhibitors and substrates on the PK profile of the substrate due to DDIs, PBPK models are commonly utilized to simulate interaction combinations for which clinical trials have not been performed. Recent studies have analyzed new drug applications submitted to the FDA [47, 48]. These studies have revealed that 56–67% of these applications employ PBPK modeling to assess the risk of DDIs. These applications predominantly use Simcyp™ (https://www.certara.com/ software/simcyp-pbpk/), GastroPlus® (https://www.simulations-plus.com/software/gastroplus/), and PK-SIM® (https://www.open-systems-pharmacology.org/) software for PBPK modeling. Although built-in models and parameters for common inhibitors are available in these software packages, the inhibitory potency parameters are still largely derived from in vitro experimental results.

In this study, we established PBPK models for the investigational drugs using PK-SIM and MoBi. After optimization using human PK curves, we used the inhibitory potency parameters obtained from our research to simulate drug interactions in the validation set. Tables S10–S27 of the ESM list the clinical trial references used for training and test sets in the self-built models. Table S28 of the ESM lists the models from the OSP-PBPK-Model-Library cited in this study. Tables S29–S48 of the ESM list the parameter values and sources of all models, as well as parameters related to enzymes and transporters. See Figs. 3.10–3.35 for the goodness of fit of the model and sensitivity analysis results. The results demonstrated that utilizing the inhibitory parameters \({K}_{i}\) and \({k}_{\text{inact}}/{K}_{I}\) values derived from our study to fit the substrate concentration–time curves affected by the inhibitor yielded good agreement with the observed data, as illustrated in Fig. 6.

Fig. 6
figure 6

Integration of inhibitor parameters calculated using the study methodology in a physiologically based pharmacokinetic model to predict drug interactions. a Fluconazole 100 mg twice daily (BID) for 2 days and zolpidem 5 mg at day 2, clinical results from [98]. b Ketoconazole 200 mg BID for 3 days and alprazolam 1 mg once daily (QD) at day 3, clinical results from [97]. c Fluvoxamine 100 mg QD for 6 days and zolpidem 5 mg at day 6, clinical results from [99]. d Itraconazole 200 mg BID for 4 days and tacrolimus 3 mg at day 4, clinical results from [100]. E Voriconazole 400 mg BID at day 2, 200 mg BID for 3 days and tacrolimus 3 mg at day 5, clinical results from [101]. f Cimetidine 400 mg bid for 2 weeks and triazolam 0.5 mg at day 14, clinical results from [102]. g Diltiazem 60 mg three time daily (TID) for 2 days and triazolam 0.25 mg at day 2, clinical results from [103]. h Ritonavir 200 mg bid for 7 days and tadalafil 20 mg at day 3, clinical results from [104]. i Aprepitant 125 mg QD and bosutinib 500 mg, clinical results from [105], j Erythromycin 500 mg tid for 2 days and simvastatin 40 mg at day 2, clinical results from [106]. k Posaconazole 400 mg BID for 7 days and tacrolimus 0.05 mg/kg at 7 days, clinical results from [107]. l Clarithromycin 500 mg BID for 2 days and triazolam 0.125 mg at day 2, clinical results from [108]. m Saquinavir 1200 mg TID for 8 days and sildenafil 100 mg at 8 days, clinical results from [109]. n Azithromycin 500 mg QD for 3 days and sildenafil 100 mg at day 3, clinical results from [110]. o Roxithromycin 300 mg QD for 5 days and lovastatin 80 mg at day 5, clinical results from [111]. p Ranitidine 300 mg TID for 5 days and nifedipine 20mg at day 5, clinical results from [112]. q Nefazodone 100 mg BID for 9 days and alprazolam 1 mg bid for 6 days, clinical results from [113]. r Verapamil 80 mg tid for 2 days and simvastatin 40 mg at day 2, clinical results from [106]. The solid line represents the physiologically based pharmacokinetic fitted concentration–time curves of the victims affected by the perpetrators; the solid dots represent the measured values of victims concentration–time curves in clinical drug interaction trials; and the shading represents the arithmetic standard deviation of physiologically based pharmacokinetic simulations for the population

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3.6 Application of Clinical Drug Interaction Risk Scales

Currently, the clinical drug interaction risk quantification system established based on the method by Ohno et al. is widely used [49], sorting drugs according to their substrate CR and inhibitor IR value. However, the CR value does not differentiate between the contributions of intestinal and hepatic enzymes. At the same time, the IR value does not consider significant changes in the inhibitory potency caused by different doses of the inhibitor. The RI for substrates and PI for inhibitors established in this study address these issues. We placed the clinically measured values from the validation set into the AUCR risk intervals obtained after sorting drugs based on their RI and PI values (Fig. 7a) to investigate whether our risk scale can reliably reflect the clinical DDI risk levels and compared them with the AUCR risk intervals obtained using the method of Ohno et al. [3] (Fig. 7b). Using the RI and PI values as quantitative measures reduced the probability of false-negative assessments of clinical DDI risk from 15.73% to 5.6%. From the figure, it is evident that the IR-CR system led to an uneven distribution of risk intervals for AUCR. In the low-to medium-risk intervals, where the AUCR is < 3, alterations in IR and CR values by 0.5 have minimal impacts on the outcomes. However, in the higher risk intervals where AUCR is  3, a change of 0.5 in IR and CR values resulted in more than a twofold difference in outcomes, which is unsuitable for the preliminary assessment of DDI risk.

Fig. 7
figure 7

Application of clinical drug–drug interaction risk scales. A Comparison of drug–drug interaction risk stratification using a risk index (RI) and a potency index (PI) from this study with clinically observed values. B: Comparison of drug risk stratification using inhibition ratio (IR) and contribution ratio (CR) from Ohna et al. with clinically observed values. The vertical axis denotes the magnitude of the inhibitor’s PI or IR values. The horizontal axis indicates the magnitude of the substrate’s RI or CR values. Color mapping reflects the magnitude of area under the curve ratio (AUCR) values associated with the predicted RI and PI values. Dots symbolize the coordinate positions in the graph for 89 pairs of substrate and inhibitor combinations from the validation set, with the color mapping of the dots representing the clinical observed AUCR values. All axes are logarithmic; the RI is derived from Eq. 10; the PI is obtained from Eqs. 11 and 12; IR is calculated as IR = (1/AUCR+1)/CR, as proposed by Ohno et al., where CR is computed as CR = (1/AUCR+1)/IR per Ohno et al. and IR is calculated using equation IR = (1/AUCR + 1)/CR based on the training set data of this study, derived from the method proposed by Ohno et al., CR is determined using equation CR = (1/AUCR + 1)/IR based on the training set data of this study, also from the method by Ohno et al.

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In summary, this study included predicted AUCR values for 660 pairs of clinical drug interactions at specific inhibitor dosages, as illustrated in Fig. 8. In clinical use, these drugs allow for a clear pre-determination of safe co-administration with certain drugs based on RI or PI values, identifying combinations that may lead to high-risk DDIs. Moreover, for two potentially co-administered drugs, the fold increase in the AUC of one drug due to co-administration can be rapidly calculated, enabling precise dose adjustment recommendations. Similarly, assuming the inhibitor has linear PK characteristics, the free concentration of the inhibitor at the corresponding dose calculated in this study can be converted to concentrations at other doses. The fold increase in substrate AUC caused by adjusted doses of the inhibitor could be rapidly calculated. To facilitate the application of this method in clinical practice, we developed a simplified program based on Microsoft Excel 2021, as detailed in the mini-program in the ESM.

Fig. 8
figure 8

Matrix plot of the predicted fold increase in substrates area under the curve (AUC) due to inhibitors at specific dosages. The z-axis denotes the magnitude of the predicted AUC ratio (AUCR) values. The left axis arranges the substrates according to their risk index values. The right axis organizes the inhibitors by their potency index values at specific dosages. bid twice daily, pred predicted, tid three times daily

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4 Discussion and Conclusions

Pharmacokinetic-mediated DDIs are among the primary causes of clinically relevant adverse drug reactions [50]. Studies indicate that DDIs in the USA result in an annual range of emergency department visits from 2600 to 220,000, impacting between 1.9 and 5 million hospitalized patients [51, 52]. These events, preventable and avoidable [53], often occur because of a lack of accessible tools and assessment databases for clinical pharmacists to promptly mitigate and provide adjustment recommendations [54]. The concomitant use and overlay of post-marketing drugs are complex and variable, making it impossible to fully assess and investigate DDIs in preclinical evaluations and clinical trials. The results of clinical drug interaction trials should be more fully utilized to serve as vital reference material for clinical pharmacists to assess the myriad of DDIs in clinical practice. This study took advantage of abundant clinical drug interaction trial data to calculate critical DDI-specific parameters, such as \({K}_{i}\),\({k}_{\text{inact}}/{K}_{I}\),\({f}_{m}\), and \({F}_{g}\), for effective and accurate extrapolation of interaction results, and to establish a quantitative clinical DDI risk assessment framework. Compared with previously published studies, this study achieved an accurate prediction of the DDI outcome of the inhibitors with the substrates at any dose.

Based on the reliable calculation of the in vivo DDI specific parameters, we have developed a Clinical Drug Interaction Risk Scale and the mini-program for clinical applications. If the RI value is < 2, the probability of adverse reactions due to PK DDIs in patients with special conditions, such as non-hepatic or renal dysfunction, is low. In such cases, intensive monitoring may not be necessary, and the primary focus should be on ensuring therapeutic effectiveness when co-medication. Conversely, if the RI value exceeds 2, it indicates that the drug is a more sensitive substrate for an enzyme. When co-administered with a high dose of enzyme inhibitor, the drug’s exposure in vivo increases significantly. Therefore, prescriptions should be carefully selected and managed when co-administration is necessary. The PI is determined using the intended clinical dose concentrations. If the inhibitor’s PI value is > 2, a quantitative assessment process must be initiated, in which the fold increase in the drug’s AUC when co-administered is calculated, and the reduction of the inhibitor concentration for an acceptable increase in substrate AUCR is determined. These actions specify the dose adjustment range for the inhibitor when co-administration with the drug. For example, ibrutinib, an orally active inhibitor targeting Bruton’s tyrosine kinase, undergoes significant first-pass and metabolic clearance, which are both mediated by CYP3A4 [55, 56]. Based on clinical trial results, which showed a 23-fold increase in AUC when co-administered with a daily dose of 400 mg of ketoconazole, its RI value was calculated as 22.7, classifying it as a high-risk victim drug. However, no clinical DDI trial data are currently available for this drug in combination with other CYP3A4 inhibitors. A clinical case reported in 2016 [57] described a 68-year-old patient with relapsed mantle cell lymphoma and hypertension who experienced severe diarrhea and dizziness, which led to unconsciousness and hospitalization 1 week after taking 560 mg of ibrutinib along with verapamil plus trandolapril 180 mg/2 mg. According to the risk assessment framework of this study, the PI value for a daily dose of verapamil of 180 mg was 4. Further quantitative predictions indicated that verapamil increased the AUC of ibrutinib three-fold, resulting in an exposure that exceeded the safe therapeutic window of ibrutinib. Employing the methodology of this study, if the daily dose of verapamil was reduced to 120 mg, the AUC of ibrutinib was predicted to increase by 2.27-fold. Therefore, for patients undergoing treatment with ibrutinib who require verapamil, the daily dose of verapamil should not exceed 120 mg. For drugs with wider therapeutic windows, an increase in exposure to inhibitors that does not exceed the therapeutic window is considered safe. The RI value for lovastatin is 17.68, and a daily verapamil dose of 240 mg can increase its AUC 3.5-fold. However, because of its broad therapeutic window, the combination of verapamil and lovastatin is not associated with adverse reactions [58, 59].

The methodology of this study involved the retrograde calculation of specific parameters for victim and perpetrator drugs based on human trial results. This is predicated on six assumptions. First, midazolam, a standard substrate for CYP3A4, is metabolized solely through CYP3A4-mediated clearance, with an \({\text{f}}_{\text{m CYP}3\text{A}4}\) of 0.92 and \({F}_{g}\) of 0.55. Second, the renal clearance of the included substrates is considered negligible. Third, the in vivo concentration of substrates is much lower than Km, thus the dosing does not affect the \({f}_{m\text{ CYP}3\text{A}4}\) value. Fourth, only the impact of CYP3A4 on interactions is considered, with CYP3A4 distributed in both intestinal epithelial cells and hepatocytes. Fifth, the free concentration of the inhibitor at the enzyme-binding site in intestinal epithelial cells is represented by the average concentration at the hepatic portal vein, and at the hepatocyte-binding site by the average concentration at the liver inlet. Sixth, for time-dependent inhibition, it is assumed that the free concentration of the inhibitor is much less than its KI. With these assumptions, the inhibitory constant of the inhibitor against CYP3A4 is calculated based on the concomitant administration results with midazolam. Subsequently, the human trial results of the combination of selective CYP3A4 inhibitors with other substrates were used to calculate the \({f}_{m\text{ CYP}3\text{A}4}\) of these substrates.

It is noteworthy that the prediction of DDIs in special populations requires particular attention. More reliable results could be obtained through verification using PBPK models, with a thorough understanding of drug clearance pathways, interactions with endogenous substances, and the physiological parameters of special populations. However, this approach is time consuming and labor intensive in clinical practice. When assessing the risk of drug interactions on the exposure of victim drugs in the real world, the method should be simple and accessible and yield reliable results to provide sufficient confidence when adjusting drug dosages. The assessment system in this study offers a certain level of simplicity compared with simulations using PBPK models and a degree of accuracy over the currently popular static models, making it a useful reference for clinicians and patients in adjusting medication prescriptions. However, this study still has several unresolved issues: for enzyme inhibitors, there are no inhibitors that selectively target only one enzyme. The common CYP3A4 inhibitors included in this study, along with their metabolites, exhibited varying degrees of induction or inhibition of other enzymes, such as CYP2D6 and CYP2C9. Although these interactions can be accurately predicted, the role of CYP3A4 in these interactions may have been overestimated. For victim drugs, after the metabolic clearance pathways are inhibited, renal clearance of the parent drug may compensate for the decrease in clearance rate. This study overlooked this aspect of clearance, which could potentially lead to an overestimation of risks. Moreover, victim drugs may exert inhibitory or inductive effects on metabolic enzymes, resulting in bidirectional interactions that affect the fit of the outcomes.