## Abstract

Simcyp, a population-based simulator, is widely used for evaluating drug-drug interaction (DDI) risks in healthy and disease populations. We compare the prediction performance of Simcyp with that of mechanistic static models using different types of inhibitor concentrations, with the aim of understanding their strengths/weaknesses and recommending the optimal use of tools in drug discovery/early development. The inclusion of an additional term in static equations to consider the contribution of hepatic first pass to DDIs (AUC*R*_{hfp}) has also been examined. A second objective was to assess Simcyp's estimation of variability associated with DDIs. The data set used for the analysis comprises 19 clinical interactions from 11 proprietary compounds. Except for gut interaction parameters, all other input data were identical for Simcyp and static models. Static equations using an unbound average steady-state systemic inhibitor concentration (*I*_{sys}) and a fixed fraction of gut extraction and neglecting gut extraction in the case of induction interactions performed better than Simcyp (84% compared with 58% of the interactions predicted within 2-fold). Differences in the prediction outcomes between the static and dynamic models are attributable to differences in first-pass contribution to DDI. The inclusion of AUC*R*_{hfp} in static equations leads to systematic overprediction of interaction, suggesting a limited role for hepatic first pass in determining inhibition-based DDIs for our data set. Our analysis supports the use of static models when elimination routes of the victim compound and the role of gut extraction for the victim and/or inhibitor in humans are not well defined. A fixed variability of 40% of predicted mean area under the concentration-time curve ratio is recommended.

## Introduction

Drug-drug interactions (DDIs) have an impact on the exposure of a substrate (victim) drug via inhibition/induction of its metabolic pathways by a coadministered inhibitor/inducer (perpetrator) drug. Regulatory guidelines (European Medicines Agency, 2010: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2010/05/WC500090112.pdf; U.S. Food and Drug Administration, 2012: Drug Interaction Studies—Study Design, Data Analysis, Implications for Dosing, and Labeling Recommendations, http://wwwfdagov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM292362pdf) recommend that initial DDI risk assessments should be done using in vitro data, because they have been shown to predict interaction within 2-fold of that observed for reversible P450 inhibition-based (Brown et al., 2005; Ito et al., 2005; Obach et al., 2006), time-dependent inhibition-based (Kanamitsu et al., 2000a; Mayhew et al., 2000; Yamano et al., 2001), and induction-based (Ripp et al., 2006; Shou et al., 2008) DDIs. Improved DDI predictions are possible by incorporating in vitro data into mechanistic static or physiologically based models.

AUC ratios have traditionally been estimated with static equations. The prediction accuracy of these models relies on use of an appropriate surrogate for the inhibitor concentration at the active site of the enzyme. Although the use of an unbound inhibitor concentration is considered to be most relevant (Einolf, 2007), the U.S. Food and Drug Administration recommends use of total inhibitor concentration to avoid false-negative results. Average steady-state systemic concentration (*I*_{sys}), maximum steady-state systemic concentration (*I*_{max}), and hepatic inlet concentration (*I*_{inlet}) have all been evaluated for use (Ito et al., 2004) in static models. For an orally administered inhibitor, *I*_{inlet} is an appropriate measure of drug exposure to enzyme during the absorption phase of the inhibitor in the absence of transporter involvement. However, because the absorption phase is short compared with the dosing interval for a once-daily drug, the use of *I*_{inlet} may lead to overestimation of DDI risk, especially for a short half-life inhibitor. The use of *I*_{sys,} on the other hand, could underestimate DDI risk (Ito et al., 2004) because it neglects the higher-than-systemic inhibitor concentration associated with hepatic first pass, especially for high-clearance substrates.

In recent years, Simcyp (Simcyp Limited, Sheffield UK; http://www.simcyp.com), a dynamic, population-based model has been used to predict DDI risk over the entire PK profile of a substrate with dynamically varying inhibitor concentrations. Simcyp enables inclusion of inhibitory metabolites, simultaneous mechanisms of interaction (e.g., inhibition and induction), dose staggering, multiple inhibitors, and inhibition of multiple enzymes. By incorporating sources of variability (enzyme/transporter polymorphism, demography, and differences in ethnicities/disease states), Simcyp aids the design of DDI studies and helps identify individuals who are at extreme risk of DDIs (Cubitt et al., 2011) in a population defined in its database. However, confidence in DDI and variability estimates can be confounded by the large uncertainties associated with the input data in early stages (Fig. 1). Prediction performance of static and dynamic approaches depends on the quality of in vitro data and on the certainty in understanding elimination/metabolic routes and gut extraction for a substrate. Failure to understand the role of transporters or to identify the existence of inhibitory metabolites, concurrent inhibition/induction, compensatory elimination mechanisms, or active metabolites that are potential victims of DDIs can confound predictions. In the preclinical stage, uncertainties in the predicted clearance of victim/inhibitor and/or predicted inhibitor dose can further limit prediction accuracy. In addition, non-P450, renal, and biliary routes identified for the victim in preclinical species may be irrelevant to humans.

A comparison of dynamic and static models covering a wide range of inhibitors, substrates, and enzymes (Einolf, 2007) was disadvantaged by the use of inconsistent input parameters in the two models. A combined static model was compared with Simcyp for 30 DDIs involving midazolam and various CYP3A4 inhibitors (Fahmi et al., 2009). Wang (2010) compared the models for 54 interactions perpetrated by mechanism-based inhibitors of CYP3A4. Guest et al. (2011) used 35 DDIs to compare Simcyp V8's time-based model with its implementation of static models. All evaluations showed a comparable performance for the two models. Our objective was to use a diverse proprietary data set of 19 DDIs to compare the mechanistic static equations with Simcyp V11, ensuring consistent preclinical input parameters in the models, to understand the reasons for any differences in performance. To avoid the impact that the quality of PK predictions can have on the performance of the tools, clinically observed clearance and distribution parameters have been used for all the 11 AZ compounds. We have not tried to fit a dynamic model to the observed plasma data, as we position our evaluation at the end of the preclinical phase. We also examine the use of an additional term in static equations to consider the contribution from hepatic first pass to DDI. Together with an assessment of Simcyp's estimates of variability, we suggest an optimal use of DDI prediction tools in drug discovery/early development.

## Materials and Methods

#### Compounds Used in the Study.

The 11 proprietary compounds chosen for this retrospective analysis were either victims or perpetrators of reversible or time-dependent inhibition or induction of CYP3A4 or inhibition of CYP2D6. Clinical interaction studies that involved the inhibition of drug transporters were not included. The compounds selected are from seven disease areas, and their chemical space encompasses a medium to high molecular weight (350–592), logarithm of octanol-water partition coefficient (log*P*) ranging from approximately 1 to 5.6, and polar surface area from approximately 40 to 140 Å^{2}.

#### Clinical Pharmacokinetic and Drug Interaction Data.

Intravenous PK data were obtained from phase I studies. Clinical PK parameters obtained from study reports were calculated using compartmental or noncompartmental analysis. Metabolic clearance was estimated by subtracting any measured renal clearance from total clearance. Biliary clearance was not reported for any of the compounds studied. When intravenous data were not available, total clearance was obtained by taking the product of per oral clearance and bioavailability (based on the best estimated internal data). Fraction of compound metabolized (*f*_{m}) was obtained by subtracting from 1, the fraction of dose excreted as parent drug in urine. Clinical drug interaction data were collected from in-house clinical DDI trials. The study designs for the 19 interactions from 11 compounds are reported in Table 1. With the exception of AZ10 in the AZ10-carbamazepine interaction, the substrate (victim) dose was typically a single oral dose administered after several days of oral administration of the inhibitor (perpetrator) to ensure attainment of steady state. The duration of inhibitor administration was long enough to cover the elimination of the substrate drug. When the perpetrator was an inducer, it was administered for a sufficient duration to ensure both steady-state and maximum enzyme induction. Drug analyses were performed with validated liquid chromatography-tandem mass spectrometry. The AZ10-carbamazepine interaction study was done in psychiatric patients who were otherwise healthy. All other clinical studies were done in healthy volunteers. Studies have been performed in accordance with the Declaration of Helsinki. Informed consent was obtained from all individuals participating in the studies before initiation of the studies.

#### Determination of In Vitro Interaction Parameters.

In-house methods for the in vitro evaluation of cytochrome P450 reaction phenotyping and competitive and time-dependent inhibition as well as induction have been described previously (Zhou et al., 2011). The panel of recombinant P450s in P450 reaction phenotyping included the isoforms CYP1A2, -2C9, -2C19, -2D6, -3A4 but not the isoform CYP3A5. Midazolam is used as a probe substrate for CYP3A4 inhibition and induction assays. Positive controls were used for demonstrating the validity and reproducibility of the methods. For CYP3A4-mediated competitive and time-dependent inhibition and induction, these are ketoconazole, verapamil, and rifampicin, respectively. Inhibition constant (*K*_{i}) values were obtained from measured half-maximal inhibitory concentration, IC_{50} values using the Cheng-Prusoff equation (Cheng and Prusoff, 1973), assuming competitive inhibition. Induction parameters were normalized with rifampicin data generated in-house. Plasma drug concentrations were analyzed using liquid chromatography-tandem mass spectrometry. In vitro parameters that were used input in Simcyp and static models for substrates and inhibitors are listed in Tables 2 and 3, respectively. For AZ4, the measured *K*_{i} is >35 μM. In this case, estimation of DDIs was performed using 35 μM.

#### DDI Predictions with Simcyp.

Simcyp Population-based Simulator V11 was used in DDI evaluations. As described previously (Tucker et al., 2001; Yang et al., 2005; Jamei et al., 2009), competitive inhibition, induction, and mechanism-based inactivation can be investigated using this software. Reference substrates and inhibitors used in the clinical studies were all available in the Simcyp compound library. No changes were made in the PK models or data provided by Simcyp for these compounds, except in the case of ketoconazole, for which dose dependence of clearance was taken into consideration for the 400-mg dose (Huang et al., 1986). In vitro intrinsic clearance (CL_{int}) from recombinant P450s, *K*_{i}, fraction unbound in plasma *(f*_{up}), Caco-2 permeability, and physicochemical data such as molecular weight, calculated log*P*, p*K _{a}*, and blood/plasma ratio (

*R*) were used as input in Simcyp. p

*K*values were obtained using the ACD/p

_{a}*K*algorithm p

_{a}*K*Predictor 30 (2011; Advanced Chemistry Development Inc., Toronto, ON, Canada). When a measured value of

_{a}*R*was not available, it was assumed to be 0.55 for acids and 1 for bases and neutral compounds. A first-order absorption model was used along with Caco-2 or MDCK permeability. A minimal physiologically based pharmacokinetic model was chosen for distribution. User-input values of steady-state volume of distribution (

*V*

_{ss}) derived from a single ascending dose or other phase I studies were used. Renal and metabolic clearances used as inputs in Simcyp were also obtained from clinical studies. All physicochemical data and PK parameters that were used in the evaluation are presented in Table 4. Because the clearance of a victim drug will influence the extent of interaction during hepatic first pass, Simcyp's retrograde calculator was used to compute CL

_{int}in microliters per minute per picomole of enzyme using the clinically observed metabolic clearance as well as the percentage contribution from each of the P450s obtained from the in vitro P450 reaction phenotyping assay. For CYP3A substrates, the CYP3A4 isoform is assumed to be the only isoform involved in their metabolism. Simcyp predictions were done using trial designs consistent with the clinical interaction studies with respect to healthy volunteers, size of population and proportion of females, doses of victims and perpetrators, and fasted/fed condition of subjects. The number of trials was kept at 10 instead of the single trial in the clinic to ensure reliability of Simcyp's variability prediction. The fraction of victim drug unbound in the gut (

*f*

_{u, g}) was set to unity, because this was shown to give the best predictions (Yang et al., 2007). No user input values were provided for blood flow to gut (

*Q*

_{gut}). The fraction unbound in microsome incubation (

*f*

_{u, mic}) was calculated (Austin et al., 2002) and used to correct in vitro parameters derived from microsomes. Apart from the time-based AUC ratios, Simcyp also provides an estimate of the AUC ratio with mechanistic static equations,

*R*

_{ss}, for which either the hepatic inlet or outlet (systemic) inhibitor concentration can be chosen. The hepatic outlet inhibitor concentration, which is the default option, was used for our analysis to enable comparison with the spreadsheet-based static equations described below.

#### DDI Predictions with Static Equations.

AUC ratio estimates from the mechanistic static equations in this section differ from static estimates from Simcyp, which are specifically referred to as *R*_{ss}. Henceforth, any reference to AUC ratios from static equations refers only to results from using the equations in this section. The following static equations were used in the prediction of AUC ratios for reversible inhibition, time-dependent inhibition (TDI) (Obach, 2009), and enzyme induction (Almond et al., 2009).

Reversible inhibition (eq. 1):
AUC is the area under the concentration-time curve of a victim drug in the absence of inhibitor, AUC_{i} is the area under the curve of a victim drug when an inhibitor is present, *f*_{gut}^{i}, is the fraction escaping gut metabolism in the presence of a perpetrator, *f*_{gut} is the fraction escaping gut metabolism in the absence of a perpetrator, *f*_{m} is the fraction of total clearance due to hepatic metabolism, *f*_{m, CYP} is the fraction of total hepatic metabolism due to the inhibited P450 enzyme, *K*_{iu} is the inhibition constant after correction for microsomal binding, and *I*_{u} is the unbound inhibitor concentration with *I* representing either *I*_{sys} (eq. 2), *I*_{max} (eq. 3), or *I*_{inlet} (eq. 4) (Kanamitsu et al., 2000b).
*F* is the clinically observed oral bioavailability of the inhibitor, τ is the inhibitor dosing interval, CL is the clinically observed total clearance of the inhibitor, *k* is the elimination rate constant obtained from CL and *V*_{ss}, *k*_{a} is the absorption rate constant, adopted from Simcyp V11 for reference compounds and for AZ compounds, *f*_{abs} is the fraction absorbed assumed as 1 (a valid assumption based on the physicochemical characteristics of the compounds), and *Q*_{pv} is the blood flow rate in the hepatic portal vein, whose value (19% of cardiac output) is adopted from Simcyp V11 for consistency. In the absence of intravenous PK data, per oral clearance, CL_{p.o.} is used directly in eq. 2 for CL/*F*.

Time-dependent inhibition (eq. 5):
*k*_{inact} is the maximal enzyme inactivation rate constant, *K*_{I, u} is the unbound inhibitor concentration at 50% *k*_{inact}, and *k*_{deg} is the endogenous degradation rate constant of enzyme. *k*_{deg} for CYP3A4 is 0.0193 h^{−1}, a value adopted from Simcyp V11 for consistency.

In eqs. 1 and 5, *f*_{gut}^{i} was set to 1, a reasonable assumption considering the high inhibitor concentrations that are likely in the gut. The use of maximal inhibition of intestinal CYP3A4 has been suggested as a pragmatic indicator of the intestinal contribution to the drug-drug interactions for CYP3A4-cleared drugs (Galetin et al., 2007). *f*_{gut} can be estimated from hepatic extraction and systemic bioavailability, assuming that fraction absorbed is 1. The bioavailability of an orally administered drug is the product of fraction absorbed, *f*_{gut}, and hepatic bioavailability (which is given by 1 − hepatic extraction). Dose linearity was ensured (Table 2) in deriving *f*_{gut} from clinical data. In the absence of sufficient information to estimate *f*_{gut}, it is assumed to be 0.5 for CYP3A substrates. Apart from being a central value, nearly one-third of the 25 compounds with known *f*_{gut} estimates have a value of approximately 0.5 (in the range of 0.4 to 0.6) (Gertz et al., 2010). Because the extent of CYP3A4 interaction in the gut can be extensive, a good estimate of *f*_{gut} can be crucial in obtaining a realistic estimate of interaction risk.

Induction (eqs. 6a–6c):
where
and
*E*_{max} and EC_{50} are the calibrated maximum fold induction over vehicle and the calibrated inducer concentration at 50% *E*_{max}, respectively. Equation 6b was described previously in the literature (Wang et al., 2004). No “d” correction as suggested by Fahmi et al. (2009) was applied for induction. However, to maintain consistency with the input provided for Simcyp, induction parameters were normalized with a positive control. *E*_{g} is the basal gut wall extraction, and *f*_{mg} is the fraction of gut metabolism mediated by the induced enzyme and is taken as 1 for compounds in this study, because the only known gut enzyme mediating gut metabolism for the victim compounds is CYP3A4. The inhibitor concentration in the small intestine, *I*_{gut}, is calculated using eq. 6 (Obach et al., 2007). *N* is the number of oral doses per day. *k*_{a} is the first-order absorption rate constant, *f*_{abs} is the fraction of dose absorbed, and *Q*_{villi} is the blood flow rate to the villi and is adopted from Simcyp V11 (6% of cardiac output) for consistency. The fraction of CYP3A4-mediated intestinal metabolism was assumed to be 0.57 and 0.66 for midazolam and simvastatin, respectively, as reported previously (Obach et al., 2007).

#### Proposed Multiplier to Account for Contribution to AUC Ratio from Hepatic First Pass.

For an orally administered inhibitor, the concentration at the enterocytes during its absorption phase is likely to be much higher than its concentration in the liver during hepatic first pass, which in turn is likely to be higher than its systemic concentration at steady state. Equations 1 and 5 account for contributions to DDI from gut and after steady state is attained, but ignore the contribution to DDI from hepatic first pass, if *I*_{sys} is used. To mitigate the risk for underestimation of DDI due to the neglect of the hepatic first-pass effect for orally coadministered inhibitor and victim, an additional multiplier term that accounts for the contribution to DDI from hepatic first pass (AUC*R*_{hfp}) was introduced into eqs. 1 and 5, such that the overall AUC ratio is a product of contributions to AUC ratio from gut (AUC*R*_{gut}), hepatic first-pass, and systemic (AUC*R*_{systemic}) inhibition of the affected enzyme. Thus,
The contribution to DDI during hepatic first pass of an orally administered inhibitor, AUC*R*_{hfp}, can be given by eq. 7, similar to gut contribution during intestinal first pass:
where *f*_{h} and *f*_{h}^{i} are the fractions of the victim drug escaping hepatic first-pass metabolism in the absence and presence of inhibitor, respectively. *Q*_{LI} is the hepatic blood flow rate and CL_{substrate} is the plasma clearance of the substrate compound in the absence of the inhibitor, estimated from clinical PK data as described before. In the absence of intravenous PK, CL_{substrate} is obtained from the best estimate of bioavailability and CL_{p.o}. CL_{i, substrate} is the plasma clearance of the substrate when coadministered with an inhibitor given by eqs. 8 and 9 for the reversible and time-dependent inhibition, respectively.

The mechanistic, static models (eqs. 1, 5, and 6a and incorporating eq. 7 into eqs. 1 and 5) were all compiled in a spreadsheet to enable easy calculation of AUC ratios. Using this spreadsheet, AUC ratios can be calculated for different types of inhibitor concentrations (*I*_{sys}, *I*_{max}, and *I*_{inlet}).

#### Data Analysis.

The 90% confidence interval (CI) was chosen as measure of variability because it was the statistical parameter used to describe the clinical data. For both AUC and maximum concentration (*C*_{max}) ratios 90% confidence intervals were computed using the output data generated in Simcyp. If *N* is the size of the population, df, the number of degrees of freedom, is *N* − 1. The upper and lower limits of confidence interval are then given by eq. 10:
where *t*_df is the *t* distribution corresponding to df and S D is the standard deviation. A similar equation was used to describe confidence intervals for the *C*_{max} ratio.

Prediction performance of Simcyp (time-based and *R*_{ss}) as well as that of static equations outlined in this section was judged by the percentage of compounds that were predicted within 2-fold of the observed clinical interaction parameters. When predictions indicate no DDI, contrary to clinical observation, it is considered to be an underprediction, even if the observed AUC ratio is less than 2. Prediction precision was assessed with root mean square error (RMSE) (eq. 11):
To assess Simcyp's estimate of variability associated with DDI predictions, the ratio of variance (square of SD) of estimated to clinically observed was calculated (eq. 12):
Variance ratio was also plotted against the geometric mean (GM) of the geometric means of the estimated and clinically observed interaction ratios, which is given by eq. 13:
A plot of variance ratio versus GM (Simcyp, observed) should reveal any systematic dependencies of estimated variability on DDI magnitude.

## Results

The 19 DDI clinical trials from the 11 AstraZeneca compounds were subdivided into three categories:

AstraZeneca compounds that are perpetrators of reversible or irreversible P450 inhibition

AstraZeneca compounds that are victims of reversible or irreversible P450 inhibition

AstraZeneca compounds that are victims or perpetrators of P450 induction

Table 5 summarizes the clinically observed interaction parameters as well as predicted values using Simcyp and mechanistic static equations for all the 19 interactions falling into the three categories.

Table 6 lists the RMSEs for all static and dynamic predictions of DDIs. The use of unbound *I*_{sys} in static equations (eqs. 1 and 5) is associated with the lowest RMSE. This finding is also evident from Fig. 2, which shows a comparison of AUC ratios from static equations using the three different types of inhibitor concentrations: *I*_{sys}, *I*_{inlet}, and *I*_{max} for the inhibition-based interactions. *I*_{inlet} and *I*_{max} tend to overpredict the interaction risk. Therefore, *I*_{sys} was used in all evaluations with the static equations for comparison with the time-based Simcyp predictions. With the inclusion of hepatic first-pass correction (eq. 7) into mechanistic static eqs. 1 and 5, systemic inhibition with *I*_{sys}, hepatic first-pass inhibition with *I*_{inlet}, and gut enzyme inhibition with the *f*_{gut} would be considered. However, inclusion of AUC*R*_{hfp} tends to overpredict the DDI risk. The overall accuracy decreased (see RMSE in Table 6).

Clinically observed interactions for the 11 compounds were moderate (AUC ratio ≤5) for category A compounds and moderate to strong (strong being AUC ratio >5 for inhibition and <0.2 for induction) for the category B and C compounds. No clinical AUC ratios were >10-fold. This is also evident in Fig. 3, in which time-based AUC ratios and *R*_{ss} from Simcyp are plotted against the clinically observed AUC ratios for all three categories of compounds. Whereas the clinical AUC ratios of the interactions studied range between 0.1 and 10, Simcyp-predicted ratios (both time-based and *R*_{ss}) exceed this range, especially for larger AUC ratios. Because the hepatic outlet (or systemic) inhibitor concentration was used in the estimation of *R*_{ss}, it should be comparable to results from static models with unbound *I*_{sys}, presented in the last column of Table 5. However, *R*_{ss} consistently overpredicts DDIs compared with AUC ratios from eqs.1 to 3, possibly because of differences in the estimation of gut contributions to DDIs. This is especially true for CYP3A4-mediated interactions. Therefore, only time-based predictions from Simcyp have been used for the comparative analysis with static equations. Figure 4 shows the predicted and observed AUC ratios for the three categories of compounds. Prediction performance of Simcyp V11 and that of the best of the static equations (*I*_{sys} with and without hepatic first-pass correction) are shown in Table 7.

Among the 19 interactions studied, the AZ5-metoprolol interaction is the only non-CYP3A4 interaction for which the predicted AUC ratio is >1 and for which the AUC ratios from both Simcyp and mechanistic static models match. Because the gut contribution to DDI is irrelevant for CYP2D6-mediated interactions, the static and Simcyp predictions for these interactions can be expected to be similar, suggesting that differences in *f*_{gut} between the two methods may be the reason for differences in their prediction of AUC ratios. A comparison of *f*_{gut} used in static equations with those estimated in Simcyp for the eight victim compounds in this study show no correlation between the two (Fig. 5). If *f*_{gut} predicted by Simcyp is low, as in the case of simvastatin and AZ7 (Table 2), then DDIs mediated by the inhibition of gut enzymes will be overpredicted by Simcyp, leading to a large AUC ratio.

For category A, two of the six interactions are mediated by CYP2D6 and the remaining by CYP3A4. The overprediction of the AZ1-simvastatin interaction by Simcyp is probably due to the low gut bioavailability (0.09) predicted by Simcyp for the victim compound, simvastatin, as explained above. For the AZ4-metoprolol interaction, both Simcyp and static models predict no AUC change, whereas a less than 2-fold AUC change is observed clinically. Obviously, in this case, the measured in vitro *K*_{i} (*K*_{i} >35 μM) did not capture the observed interaction, which is probably mediated by TDI or by an inhibitory metabolite in vivo. This interaction has been included in the analysis only to illustrate that a negative in vitro result need not necessarily hold in vivo. AZ5 being lipophilic, the predicted *f*_{u, mic} is very low. Any error in this prediction could lead to substantial changes in the estimated AUC ratio. A sensitivity analysis was therefore performed (Supplemental Fig. 1). The AUC ratio goes from approximately 1.3 to 1 in the full range of *f*_{u, mic}. In the case of AZ5, an imprecise prediction of *f*_{u, mic} had little effect on the overall result.

For category B, AZ compounds were victims of CYP3A4 inhibition. The product *f*_{m} × *f*_{m, CYP} is nearly 1 for all except for AZ9. The AZ6-ketoconazole interaction is the only one for which the ketoconazole dose was 400 mg. Ketoconazole exhibits dose-dependent PK (Huang et al., 1986), possibly due to autoinhibition. A lower oral clearance of 7.4 l/h (Huang et al., 1986) at 400 mg was used both in Simcyp and in static equations. The AUC ratio predicted by static equations improves slightly from 6.4 to 8.1 with the use of lower hepatic clearance. The interaction of AZ7 with ketoconazole is overpredicted by Simcyp. *f*_{gut} estimated by Simcyp was 0.08 compared with 0.43 (see Table 2) used in static equations. AZ7 is a highly bound (*f*_{up} = 0.001) compound, and, in this case, fixing *f*_{u, g} = 1 may not be valid. The sensitivity of *f*_{gut}, CL_{p.o.}, and mean AUC ratio to *f*_{u, g} for the AZ7-ketoconazole interaction is presented in Supplemental Fig. 2. Fixing *f*_{u, g} closer to the *f*_{up} of AZ7 gave a more accurate AUC ratio of 4 for the AZ7-ketoconazole interaction (communications with staff at Simcyp Ltd). For the AZ7-diltiazem interaction, the additional contribution to CYP3A4 inhibition from the metabolite of diltiazem (Rowland Yeo et al., 2010) is built into Simcyp. Likewise, for the AZ9-itraconazole interaction, inhibition by the metabolite of itraconazole is considered in Simcyp. These were not considered in static equations. AZ9 is not a very sensitive substrate because it has a low *f*_{m} × *f*_{m, CYP} (∼0.4) and low clearance. Thus, although the metabolites are known to be more potent in vitro than the parent and account for ∼50% of the overall CYP3A inhibition in vivo (Templeton et al., 2008; Guest et al., 2011), their impact on the AZ9-itraconazole interaction is low. The interactions of AZ8 with ketoconazole are underpredicted only by Simcyp. As highlighted earlier, gut-mediated DDIs are likely to be different in the two approaches because of differences in *f*_{gut}. The *f*_{gut} estimated by Simcyp for AZ8 was 0.86 compared with 0.23 (see Table 2) used in static equations, which might explain the differences in the AUC ratio. The difference in estimated AUC ratios between static and dynamic models for the AZ10-ketoconazole interaction is probably attributable to differences in the treatment of intestinal and hepatic first pass in the two models. Because AZ10 has a very high CL_{p.o.}, the difference between the 2 approaches is also large. Unlike Simcyp, the mechanistic static models do not consider interaction during hepatic first pass. The inclusion of AUC*R*_{hfp} in the static DDI estimation should provide a value closer to that from Simcyp. Simcyp reports an estimated systemic clearance of 33 l/h from CL_{p.o.} and *f*_{gut} (0.5) provided as input, whereas the static equation uses 13.6 l/h, a low value arising from the low bioavailability of AZ10. Therefore, the estimated AUC*R*_{hfp} correction is low (1.12). With use of a clearance value of 33 l/h, the AUC*R*_{hfp} correction is 1.4 and the AUC ratio using the static model becomes 5.6.

It is worthwhile to note that for 15 of the 16 interactions for which *C*_{max} ratios were available, the DDI risk indicated by clinical *C*_{max} ratios was less than or comparable to (AZ8-ketoconazole interaction) that corresponding to AUC ratios. This finding is in keeping with the smaller range of *C*_{max} ratios compared with AUC ratios reported for 54 clinical DDIs involving mechanism-based CYP3A inhibitors (Wang, 2010). Assuming that *C*_{max} is affected by first pass, this reflects a reduced importance of first pass (hepatic, intestinal, or both) in DDIs. One explanation could be that whereas the magnitude of the AUC ratio depends only on the extent of intestinal and/or hepatic extraction, the magnitude of the *C*_{max} ratio would, in addition to these, depend on the region of the gastrointestinal tract where maximum absorption of substrates occurs. Substrates of an inhibited intestinal enzyme that has high permeability are more likely to have *C*_{max} ratios that are comparable to their AUC ratios, if, like CYP3A4, the inhibited enzyme is expressed mainly in the small intestine (Paine et al., 2006). The AZ6-ketoconazole interaction has a relatively large deviation of the *C*_{max} ratio from its AUC ratio. If this interaction is compared with the AZ8-ketoconazole interaction, we note that the victim drugs in both interactions have similar clearance. However, the permeability of AZ8 is much higher than that of AZ6, which supports the hypothesis that maximum absorption in the jejunal region where CYP3A4 expression is maximum would result in AZ8 having a *C*_{max} ratio comparable to its AUC ratio.

Category C represents induction-mediated interactions. Static equation calculations have been done using *I*_{sys} with and without the gut contributions to DDIs. Inclusion of gut interaction seems to overestimate the risk, especially for interactions with rifampicin. For carbamazepine, Simcyp uses the calibrated slope of the fold induction versus concentration plot in the linear range of concentrations, Ind_{slope}. For carbamazepine the value of Ind_{slope} used in Simcyp is 0.16. Static equations used *E*_{max} and EC_{50} values (7.7-fold and 40 μM, respectively) from the literature (McGinnity et al., 2009). It is clear from Table 5 that predictions of AUC ratios from Simcyp and static equations are comparable. Many previous evaluations (Einolf, 2007; Youdim et al., 2008; Fahmi et al., 2009; Perdaems et al., 2010) have shown similar prediction success with Simcyp.

Geometric means, 90% confidence intervals, and variances for the 19 interactions are shown in Table 5. Figure 6, A and B, shows that the variances in the AUC ratio and *C*_{max} ratio are not independent of their corresponding geometric means. The greater the deviation of the AUC ratio from 1, the greater is the variance, which is to be expected. This finding is also evident from Fig. 4, in which the absolute extent of variability is seen to be proportional to the mean values of AUC and *C*_{max} ratios. Figure 4 also shows that the clinical variability in terms of 90% confidence interval ranges roughly between 10 and 40% of observed AUC ratios, whereas estimated variability covers a broader range. Figure 6C shows the variance ratio (Simcyp, observed) plotted against the GM (Simcyp, observed). This ratio should be 1 for all interactions, if the estimated variability matches the observed. If arbitrary acceptance limits of 2-fold of observed (shown by dotted lines in Fig. 6C) are set, it can be seen that Simcyp tends to over- or underestimate the variability for a considerable number of interactions, depending on the mean values. In addition to this, overprediction of mean AUC ratio by Simcyp, as in the case of the AZ1-simvastatin or AZ7-ketoconazole interaction, can further exaggerate its variability estimation.

Clinical and Simcyp-predicted PK parameters for all AZ compounds are provided in Supplemental Tables 1 and 2.

## Discussion

Static equations using the unbound average steady-state systemic inhibitor concentration (*I*_{sys}) have been shown to perform better with respect to accuracy than Simcyp V11 for the 19 interactions studied in this report (84 and 58% of the interactions predicted within 2-fold, respectively). Other retrospective validations (Wang, 2010; Guest et al., 2011; Shardlow et al., 2011) indicate comparable predictions. Guest et al. (2011) reported that Simcyp and static models predicted 71 and 77%, respectively, of the DDIs within 2-fold. The authors attributed the comparability to high potency and large dosing of the inhibitors in their study. The higher prediction accuracy of Simcyp reported by Guest et al. (2011) could also have occurred because the validation compounds in their study were all well characterized azole inhibitors and benzodiazepine substrates.

Differences in the prediction outcomes between static and dynamic models can be attributed to differences in the treatment of hepatic and intestinal first pass and to differences in inhibitor concentration. In addition, the neglect of metabolite inhibition and auto-inactivation of the affected enzyme by a time-dependent inhibitor in static models can lead to an underestimation of DDI risk. AUC ratios from Simcyp exceeding 10-fold should be treated with caution, because clinical interactions rarely exceed that limit (Brown et al., 2005). This study has identified a significant risk for overestimating DDI liability with Simcyp, largely attributable to uncertainty in CYP3A-mediated intestinal DDIs. This result is consistent with a recent report (Sinha et al., 2012). In the gut, CYP3A represents the principal drug-metabolizing P450 enzyme (Paine et al., 1997, 2006). The high gut concentrations of an orally administered inhibitor and the significant intestinal extraction of a substrate despite the low gut CYP3A4 content of just ∼1% of that found in liver (Paine et al., 1997) translate to a significant gut contribution to DDIs. In addition, although CYP3A4 (a low-affinity, high-capacity enzyme)-mediated DDIs could be limited by alternative metabolic/elimination pathways in the liver, intestinal CYP3A4-mediated DDIs could still be high, because CYP3A is almost the only P450 enzyme in the gut. Thus, difficulty in assessing *f*_{gut} of a substrate or inhibitor in Simcyp due to uncertainties in *f*_{u, g} and/or due to quality of in vitro data could result in a substantial deviation of predicted DDI from that observed. An underestimation of substrate *f*_{gut} would mean underestimation of DDI risk (due to underestimation of substrate gut metabolism), whereas underestimation of inhibitor *f*_{gut} would mean overestimation of DDI risk (due to higher inhibitor concentration resulting from neglect of gut extraction). Information on human-relevant gut metabolism is sparse in drug discovery. Even during clinical development, such information requires an additional intravenous clinical PK study to be done to be able to distinguish between gut and hepatic first pass. When multiple gut enzymes (e.g., CYP3A4 and UGT2B7) are involved, an assessment of the relative contribution to *f*_{gut} is an additional challenge. The use of an estimated *f*_{gut} value in static equations is therefore an attractive alternative to using the dynamic model for predicting the AUC ratio of CYP3A-mediated DDI. In the absence of an *f*_{gut} estimate in humans, an assumption of *f*_{gut} = 0.5 is suggested for CYP3A substrates (S. Peters, unpublished analysis). Because competition with permeability is likely to limit gut metabolism, compounds with fairly good permeability cannot have very high extraction in the gut. Thus, if the extent of gut metabolism is not capacity-limited, a central value of 0.5 can be rationalized. Interactions involving substrates with large deviations of *f*_{gut} from those used in static equations were either under- or overpredicted by Simcyp, which further lends support for an *f*_{gut} of 0.5.

Hepatic first-pass correction to overcome a possible underprediction of DDI with the use of *I*_{sys} in static equations, resulted in systematic overprediction of DDI risk. However, this may be a useful approach to estimate a maximum expected risk, especially for high-clearance drugs for which it can make a substantial difference. The importance of hepatic first pass may depend on the nature of the interacting compounds. *C*_{max} is seen as critical in summarizing the DDI risk. However, the clinical interaction data used in this study show that *C*_{max} ratios are generally less than the AUC ratios. Thus, AUC ratio prediction should provide an adequate estimate of the maximum DDI risk.

To further understand the basis for the differences in AUC ratios predicted by Simcyp (time-based), Simcyp *R*_{ss}, and the proposed static equations, we need to consider the differences in inhibitor concentrations in the three approaches. Because the aim of clinical DDI studies is to achieve a steady-state inhibitor concentration, before administration of the victim, differences in average inhibitor concentrations and therefore DDI can be expected to be minimal in the three approaches for inhibitors that are administered intravenously. However, for orally administered inhibitors that are not metabolized in the gut, the higher-than-systemic hepatic concentrations during the absorption phase implies that the use of a single uniform inhibitor concentration in static equations is likely to under- or overestimate DDI, depending on whether a systemic or hepatic inlet concentration is used, as in the estimation of *R*_{ss}. The proposed static equations using *I*_{sys} and incorporation of AUC*R*_{hfp} should be expected to perform better. In the case of time-based Simcyp, the high levels of inhibitor concentrations in the portal vein are valid only during the absorption phase, reflecting the reality. In our analysis, because *I*_{sys} has been chosen for *R*_{ss} estimation, we should expect Simcyp *R*_{ss} and static equations with *I*_{sys} to give similar results for non-CYP3A substrates. Finally, for orally administered inhibitors that are metabolized in the gut, high inhibitor concentrations in the gut need to be additionally considered. In the *R*_{ss} method, *I*_{gut} is a constant high value, explaining its tendency to overpredict the CYP3A-mediated interaction, whereas in the static equations proposed in this study, it is simply dependent on estimated *f*_{gut} and on the validity of assuming maximal inhibition of gut enzymes by the inhibitor. In Simcyp (time-based), the dynamically varying inhibitor concentration starts off at a high value but drops substantially over the absorption phase. Thus, differences in the inhibitor concentration ([I]) during hepatic and/or intestinal first pass make the three approaches different. Simcyp's dynamic treatment of [I] should be expected to provide a better prediction of DDIs under conditions when the inhibitor concentration is not at steady state (e.g., the intended human dose schedule is not long-term). However, uncertainties in the input used in the two models (Fig. 1) can dominate prediction performance and can offset any advantages of a dynamic approach. Simple models with fewer input data are therefore preferable for DDI predictions.

The neglect of autoinhibition and auto-inactivation of the affected enzyme by AZ1 to AZ5 would lead to an underprediction of DDI risk, because it amounts to neglecting the prolonged high concentrations of the inhibitor. Simcyp accounts for the auto-inactivation by the mechanism-based inhibitors, AZ1 and AZ3, but, with the input provided, it cannot consider the autoinhibition by the reversible inhibitors, AZ2, AZ4, and AZ5. Static equations do not consider either of these. Because there is no information on the clinical relevance of autoinhibition, it is difficult to quantify its impact.

With the exception of the AZ10-carbamazepine interaction, all induction interactions were predicted well with static equations, if the gut contribution to DDI is ignored. Inclusion of the gut contribution results in an overestimation of DDI risk. A rationale for this result could be that an increase in gut enzymes due to induction may not really affect the extent of metabolism of the victim compound, because there is a competition between permeability and metabolism in the enterocytes. Therefore, enzyme capacity may have a lesser role than might be anticipated in the absence of a competition from permeability. Victim compounds of induction in this analysis have log*P* of at least 0.88 and good permeability. Because dynamic models can consider the effect of permeability on the rate and extent of gut metabolism, Simcyp's estimation of AUC ratios agree with clinically observed values.

This study demonstrated a tendency for Simcyp-estimated variability to be under- or overpredicted, depending on the mean value. Thus, when the mean AUC ratios are themselves overpredicted by Simcyp, the associated variability is likely to be exaggerated for extreme individuals in a population. Because the variability associated with clinical DDI parameters is generally <40% of the mean values, this study recommends a conservative estimate of 40% of predicted mean AUC ratio estimated by mechanistic static equations as a rule of thumb. This recommendation is consistent with the proposed coefficient of variation for CYP3A4 content of 41% (Cubitt et al., 2011) and 33% (Kato et al., 2010). A fixed variability that is slightly higher than the clinically observed margins will have the advantage of covering for any prediction uncertainty and/or higher clinical variability.

In conclusion, this analysis highlights the importance of characterizing the gut and hepatic metabolism of a substrate as well as its major elimination routes in human. This is possible only through having at least the intravenous clinical PK of the substrate. In the absence of relevant information, the use of unbound *I*_{sys}, *f*_{u, mic}, AUC*R*_{hfp}, and an estimated *f*_{gut} in mechanistic static equations with a neglect of gut interactions for induction-mediated DDI can provide reasonable predictions. Considering the possibility for large deviations of Simcyp-predicted AUC ratios from those observed, a fixed measure of variability around the mean static equations-predicted AUC ratios appears to be preferable over a population-based approach during early development phases for assessing the potential for individuals with extreme interactions to experience adverse events. However, during later clinical development, a population-based approach can be valuable in simulating the simultaneous impact of disease, ethnicity, age, and multiple inhibitors (including potent metabolites) as well as enzyme and transporter polymorphism on DDIs.

## Authorship Contributions

*Participated in research design:* Peters.

*Performed data analysis:* Peters, Schroeder, and Giri.

*Wrote or contributed to the writing of the manuscript:* Peters, Schroeder, and Dolgos.

## Acknowledgments

We acknowledge the extensive support received from Boel Löfberg, Camilla Berglund, Christine Pattison, Diansong Zhou, Dominic Surry, Helen Rollison, Maria Learoyd, Pawel Baranczewski, Sarah Kelly, and Timothy Schulz-Utermoehl in data collection. We are grateful to Anna-Lena Ungell, Pawel Baranczewski, Denis Projean, Ulf Eriksson, and François Guillou for their comments thank the staff at Simcyp for the fruitful discussions we have had with them. We also thank Brian J. Middleton for his help with statistical analysis.

## Footnotes

Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.

↵

^{}The online version of this article (available at http://dmd.aspetjournals.org) contains supplemental material.ABBREVIATIONS:

- DDI
- drug-drug interaction
- P450
- cytochrome P450
- AUC
- area under the concentration-time curve
- PK
- pharmacokinetic
- AZ
- AstraZeneca
- MDCK
- Madin-Darby canine kidney
- TDI
- time-dependent inhibition
- CI
- confidence interval
- RMSE
- root mean square error
- GM
- geometric mean.

- Received January 14, 2012.
- Accepted May 7, 2012.

- Copyright © 2012 by The American Society for Pharmacology and Experimental Therapeutics