Volume of Distribution is Unaffected by Metabolic Drug–Drug Interactions

Abstract

Introduction

It has been recognized that significant transporter interactions result in volume of distribution changes in addition to potential changes in clearance. For drugs that are not clinically significant transporter substrates, it is expected that drug–drug interactions would not result in any changes in volume of distribution.

Methods

An evaluation of this hypothesis proceeded via an extensive analysis of published intravenous metabolic drug–drug interactions, based on clinically recommended index substrates and inhibitors of major cytochrome P450 (CYP) isoforms.

Results

Seventy-two metabolic drug interaction studies were identified where volume of distribution at steady-state (V_ss) values were available for the CYP index substrates caffeine (CYP1A2), metoprolol (CYP2D6), midazolam (CYP3A4), theophylline (CYP1A2), and tolbutamide (CYP2C9). Changes in exposure (area under the curve) up to 5.1-fold were observed; however, ratios of V_ss changes have a range of 0.70–1.26, with one outlier displaying a V_ss ratio of 0.57.

Discussion

These results support the widely held founding tenant of pharmacokinetics that clearance and V_ss are independent parameters. Knowledge that V_ss is unchanged in metabolic drug–drug interactions can be helpful in discriminating changes in clearance from changes in bioavailability (F) when only oral dosing data are available, as we have recently demonstrated. As V_ss remains unchanged for intravenous metabolic drug–drug interactions, following oral dosing changes in V_ss/F will reflect changes in F alone. This estimation of F change can subsequently be utilized to assess changes in clearance alone from calculations of apparent clearance. Utilization of this simple methodology for orally dosed drugs will have a significant impact on how drug–drug interactions are interpreted from drug development and regulatory perspectives.

Key Points

While it is expected that significant xenobiotic transporter interactions will result in volume of distribution changes of a victim drug, metabolic drug interactions should not result in any volume of distribution changes.

Evaluation of exemplary metabolic drug–drug interactions with clinically recommended index substrates and inhibitors indicates that volume of distribution is largely unchanged in metabolic interactions, highlighting that volume and clearance are indeed independent parameters.

Understanding that metabolic interactions do not result in volume changes can allow for estimation of bioavailability changes in oral drug–drug interactions. Examination of the extent of change in the apparent volume of distribution will reflect changes in bioavailability alone due to the unchanged volume of distribution.

Estimates of changes in bioavailability can subsequently be utilized to differentiate changes in clearance alone from measures of apparent clearance following oral dosing, as we have recently demonstrated [3].

Introduction

Volume of distribution in pharmacokinetics is the theoretical volume in which a drug must distribute to relate the observed systemic drug concentrations to the amount of drug present in the body. It is a non-physiologic volume that reflects the degree of tissue distribution of a drug. It has been recognized that xenobiotic transporters can influence volume of distribution of drugs by allowing or restricting drug access to various tissues throughout the body [1], and therefore significant transporter drug interactions may result in changes in volume of distribution in addition to potential changes in clearance (CL) [2]. For drugs that are not clinically significant transporter substrates, it is expected that drug–drug interactions (DDIs) would not result in any changes in the steady-state volume of distribution (V_ss). As our laboratory has recently demonstrated, knowledge that V_ss is unchanged in metabolic DDIs can be helpful in implicating transporter involvement in complex DDIs as well as in facilitating the discrimination of changes in CL from changes in bioavailability (F) when only oral dosing data are available [3]. Here, we present a comprehensive evaluation of the hypothesis that V_ss remains unchanged in metabolic drug interaction studies.

Methods

Literature Search Strategy and Inclusion/Exclusion Criteria

Based on a recent compilation of recommended clinical index substrates of major drug-metabolizing enzymes and cytochrome P450 (CYP) isoforms [4], a comprehensive literature search identified caffeine (CYP1A2), metoprolol (CYP2D6), midazolam (CYP3A4), theophylline (CYP1A2), and tolbutamide (CYP2C9) as index substrates for which intravenous (IV) dosing drug interaction data were available. Oral drug interaction studies of these index substrates were excluded from the analysis to avoid the confounding impact that changes in F would have on apparent volume of distribution (V_ss/F). Owing to the large number of IV interaction studies for the probe substrate midazolam, the scope of the analysis was further refined to primarily include DDIs involving index inhibitors with known clinical inhibitory specificities against the various CYP isoforms and xenobiotic transporters, again based on the recent recommendations of Tornio et al. [4]. If additional victim-perpetrator combinations were investigated in these studies, these interaction data were also included in the analysis and information regarding the in-vivo substrate or inhibitory specificities of these drugs was referenced from the literature [5–11]. As V_ss is not often reported by clinical investigators, estimation of this parameter often proceeded via digitization and non-compartmental analysis of published PK profiles. If V_ss was not reported, studies were excluded if (1) PK profiles were not reported and/or were difficult to reliably digitize or if (2) resulting estimates of area under the curve (AUC) were greater than 25% different from reported values. The latter aspect is further discussed in the next section.

This analysis focuses on DDI studies conducted with the same subjects in the control and treatment arms, and as such, four midazolam studies with a parallel study design were excluded. However, some studies included in this analysis conducted the DDI investigation (within the same person) in multiple populations, for example, with respect to pharmacogenomic variance of drug-metabolizing enzymes or in healthy vs disease-state subjects. Thus, we also analyze changes in V_ss of the victim drug only between these populations to investigate the inherent potential of V_ss to change between different individuals.

The specificities of all substrates and inhibitors are summarized, and in addition, the Biopharmaceutics Drug Disposition Classification System is listed. This simple system classifies drugs based on solubility and permeability and can anticipate when metabolism vs transporter-mediated processes (such as renal and biliary elimination) are the major route of drug elimination [12].

Data Analyses

Thirty published DDI studies were examined and changes in exposure (AUC), CL, V_ss, mean residence time (MRT), and terminal half-life (t_1/2,z) were calculated and reported as ratios of interaction/control. When individual PK data were reported, the ratios of the parameters of interest were calculated for each individual and the average of this ratio for all subjects was reported (and indicated in the tables with a footnote). Although the initial volume of distribution in the central compartment and the terminal volume of distribution (V_z) are commonly reported in clinical PK studies, our primary analysis was based on changes in V_ss as it is a non-compartmental parameter that represents the whole-body volume of distribution, theoretically is independent of elimination measures [13], and is not associated with a particular compartment or phase of the PK curve (as is the case for volume of distribution in the central compartment and V_z for drugs that display multi-compartment kinetics). Methods of each paper were carefully reviewed to ensure reported V_ss was appropriately calculated. For investigations in which V_ss could not be determined, data for V_z were reported with the understanding that V_z changes will only reflect the same degree of change as V_ss if the victim drug follows a one-compartment model or if the distribution phase minimally affects measures of both AUC and area under the moment curve (AUMC).

For investigations that did not explicitly report all parameters of interest, the parameter was either (1) back calculated from reported data or (2) estimated by digitization of reported plasma concentration–time profiles. Clearance and AUC could be calculated from one another if only one of the two parameters were reported by using a known dose and the equation: CL = dose/AUC. Similarly, CL can be used to calculate either V_ss or MRT (if one of the two parameters were reported) using Eq. (1) [13]:

$$V_{\text{ss}}=\text{CL}·\text{MRT}.$$ 1

If MRT values were not reported, MRT was calculated via non-compartmental methods by Eq. (2):

$$\text{MRT}=\frac{\text{AUMC}}{\text{AUC}}-\text{MIT},$$ 2

where MIT is the mean input time. For IV bolus doses, MIT is zero. For IV infusions, MIT is defined as half of the length of the dosing interval ($\tau$), i.e., MIT = $\tau$/2. For investigations that did not report V_ss (or any of the other PK parameters of interest), plasma concentration–time profiles were digitized using WebPlotDigitizer Version 4.2 (Ankit Rohatgi, San Francisco, CA, USA) and analyzed by a non-compartmental analysis with WinNonlin Professional Edition Version 2.1 (Pharsight, Mountain View, CA, USA). Digitized AUC values were compared to reported AUC values and studies were excluded if reported average AUC values were greater than 25% different from digitized values. All PK ratios calculated from digitization of published concentration–time profiles are specifically indicated in the data tables with a footnote. Published values of PK parameters were reported in priority, with digitization/reanalysis of reported average concentration–time profiles utilized only to supplement unreported data. Each value in the data tables is annotated based on calculation methods (published vs digitized, individual vs average PK data used for ratios, equations used, or assumptions made).

The average absolute differences in AUC and V_ss were compared to one another for all 72 DDIs, as well as the subset of DDIs with a greater than 30% AUC change (i.e., ratios outside of the range of 0.77 and 1.30, n = 49), which could be considered a potentially clinically significant interaction. To account for interactions resulting in a decrease in AUC, such as potential enzyme induction, the inverse for all ratios less than unity was utilized in calculation of average absolute AUC and V_ss changes. Box plot representations of the data were generated to allow visual depiction of any differences in the degree of change in these two parameters, which indicate the median and 25th and 75th percentiles, range from minimum to maximum values, and depict each individual point. To investigate if the classic trend of CL changes being equal (but opposite in magnitude) to half-life and MRT changes in these metabolic DDIs, the relationship between changes in half-life and MRT were compared to the inverse of the change in CL.

Results

Relevant information on the specificity of all substrates analyzed are outlined in Table 1 and the inhibitory specificities of the perpetrator drugs included in this analysis are listed in Table 2. The comprehensive literature search identified DDI studies for the following index substrates where V_ss measurements were available: caffeine [14], metoprolol [15], midazolam [16–25], theophylline [26–38], and tolbutamide [39] (Table 3). Any additional victim-perpetrator combinations (with non-index substrates) investigated in these studies where V_ss measurements were available were also analyzed, including alfentanil [20], antipyrine [27], and lidocaine [19] (Table 4). When only V_z values were available, these studies are summarized in Table 5 and include the victim drugs antipyrine [40], desipramine [41], imipramine [41], and theophylline [40, 42–44].

Table 1.

Enzyme specificities of clinical index substrates and additional victim drugs

Substrate	BDDCS class	Enzyme	Other relevant enzymes/transporters	Refs.
Antipyrine	1	CYP1A2 CYP2C9 CYP3A	Multiple CYPs (2A6, 2B6, 2C, 2E1)	[7]
Alfentanil	1	CYP3A	–	[5]
Caffeine	1	CYP1A2	Xanthine oxidase N-Acetyl transferase	[4]
Desipramine	1	CYP2D6	CYP3A	[4]
Imipramine	1	CYP2C19	CYP2D6	[5]
Lidocaine	1	CYP3A	CYP1A2	[7]
Metoprolol	1	CYP2D6	CYP3A	[4]
Midazolam	1	CYP3A	–	[4]
Theophylline	1	CYP1A2	CYP2E1 CYP3A	[4]
Tolbutamide	2	CYP2C9	OAT2	[4, 10]

BDDCS Biopharmaceutics Drug Disposition Classification System, CYP cytochrome P450, OAT organic anion transporter, Refs references

Table 2.

Inhibitory specificities of clinical index inhibitors and additional perpetrator drugs

Index inhibitor	BDDCS class	Enzyme	Other relevant enzymes/transporters	Refs.
Cimetidine	3	OCT2 CYP2C19 CYP3A	MATE1 CYP1A2 CYP2C9 CYP2D6	[5]
Ciprofloxacin	4	CYP1A2	CYP3A4	[4]
Clarithromycin	3	CYP3A4	CYP2C19 P-gp	[4]
Diltiazem	1	CYP3A4	CYP1A2 CYP2D6 P-gp	[5]
Disulfiram	2	CYP2E1	CYP1A2 CYP2C9 CYP2D6	[5]
Enoxacin	4	CYP1A2		[4]
Erythromycin	4	CYP3A4	P-gp	[4]
Famotidine	3	Unknown
Fluconazole	3	CYP2C9 CYP2C19	CYP3A4	[4]
Itraconazole	2	CYP3A4	CYP2J2 P-gp	[4]
Ketoconazole	2	CYP3A4	CYP2C19 P-gp	[4]
Lidocaine	1	CYP3A4	CYP1A2	[7]
Nalidixic acid	2	Unknown
Nelfinavir	2	CYP3A4	CYP2D6	[8]
Norfloxacin	4	CYP1A2		[9]
Ofloxacin	3	Unknown
Olanzapine	2	Unknown
Ondansetron	1	Unknown
Primaquine	1	Unknown
Quinidine	1	CYP2D6	P-gp	[4]
Ranitidine	3	OCT2 CYP3A	CYP2C9 CYP2D6	[5]
Rifampin (single dose)	2	OATPs	CYP3A4	[6, 11]
Rifampin (multiple dose)	2	(Inducer) CYP3A CYP2C9 P-gp	(Inducer) CYP1A CYP2B6 CYP2C8 CYP2C19	[6]
Ritonavir (single dose)	2	CYP3A4	P-gp	[4]
Ritonavir (multiple dose)	2	CYP induction		[4]
Sulfaphenazole	1	CYP2C9		[8]
Terbinafine	2	CYP2D6	CYP1A2	[4]
Verapamil	1	CYP3A4	P-gp	[4]

BDDCS Biopharmaceutics Drug Disposition Classification System, CYP cytochrome P450, MATE Multidrug and Toxic Extrusion, OCT organic cation transporter, P-gp P-glycoprotein, Refs references

Table 3.

Intravenous drug–drug interaction (DDI) studies of cytochrome P450 (CYP) index substrates

Victim	Perpetrator	Victim enzymes or transporters	Perpetrator enzymes or transporters	Population	N	$\frac{{\text{AUC}}^{\text{DDI}}}{{\text{AUC}}^{\text{Con}}}$	$\frac{{\text{CL}}^{\text{DDI}}}{{\text{CL}}^{\text{Con}}}$	$\frac{V_{\text{ss}}^{\text{DDI}}}{V_{\text{ss}}^{\text{Con}}}$	$\frac{{\text{MRT}}^{\text{DDI}}}{{\text{MRT}}^{\text{Con}}}$	$\frac{t_{1/2,z}^{\text{DDI}}}{t_{1/2,z}^{\text{Con}}}$	Percent AUC extrapolation	Refs.
Caffeine	Ketoconazole (400 mg; single dose)	CYP1A2 NAT XO	CYP3A4 CYP2C19 P-gp	Healthy subjects	8	1.17b	0.88b	0.97a	1.14a	1.18b	36%/30%a	[14]
Caffeine	Terbinafine (500 mg; single dose)	CYP1A2 NAT XO	CYP2D6 CYP1A2	Healthy subjects	8	1.31b	0.81b	1.05a	1.48a	1.35b	45%/30%a	[14]
Metoprolol	Quinidine (50 mg; single dose)	CYP2D6 CYP3A4	CYP2D6 P-gp	Healthy subjects; male, white, CYP2D6 extensive metabolizers	3	2.43d	0.44b	0.87b	2.06f	1.56a	29%/15%a	[15]
Metoprolol	Quinidine (250 mg BID; 3 days)	CYP2D6 CYP3A4	CYP2D6 P-gp	Healthy subjects; male, white, CYP2D6 extensive metabolizers	4	3.08d	0.36b	0.70b	1.99f	2.36a	44%/15%a	[15]
Metoprolol	Quinidine (50 mg; single dose)	CYP2D6 CYP3A4	CYP2D6 P-gp	Healthy subjects; male, white, CYP2D6 poor metabolizers	3	1.12d	0.98b	1.18b	1.30f	1.09a	35%/34%a	[15]
Metoprolol	Quinidine (250 mg BID; 3 days)	CYP2D6 CYP3A4	CYP2D6 P-gp	Healthy subjects; male, white, CYP2D6 poor metabolizers	3	1.26d	0.88b	1.26b	1.39f	1.32a	43%/34%a	[15]
Midazolam	Clarithromycin (500 mg BID; 7 days)	CYP3A4	CYP3A4 CYP2C19 P-gp	Healthy subjects	16	2.66	0.37	1.05a	2.79a	2.66	38%/12%a	[16]
Midazolam	Clarithromycin (500 mg BID; 7 days)	CYP3A4	CYP3A4 CYP2C19 P-gp	Healthy subjects; elderly	16	3.2	0.35	1.16a	2.24a	4.06	44%/20%a	[17]
Midazolam	Erythromycin (500 mg TID; 7 days)	CYP3A4	CYP3A4 P-gp	Healthy subjects	6	2.17c	0.46	1.40	3.03e	1.77	NR	[18]
Midazolam	Erythromycin (500 mg QID; 5 days)	CYP3A4	CYP3A4 P-gp	Healthy subjects	8	1.60d	0.71b	0.93a	1.31a	1.50b	19%/13%a	[19]
	+ Lidocaine (1 mg/kg; 2 days)		CYP3A4 CYP1A2
Midazolam	Fluconazole (100 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	1.3	0.78	1.01a	1.28a	1.16	10%/7%	[20]
Midazolam	Fluconazole (200 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	1.4	0.68	1.10a	1.68a	1.20	11%/7%	[20]
Midazolam	Fluconazole (400 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	2.0	0.54	0.93a	1.73a	1.56	17%/7%	[20]
Midazolam	Fluconazole (400 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects; African American CYP3A5*1/*1	6	1.62b	0.64b	0.81a	1.15a	1.35b	17%/14%a	[21]
Midazolam	Fluconazole (400 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects; African American CYP3A5*1/*X	7	1.67b	0.60b	0.99a	1.70a	1.43b	17%/8%a	[21]
Midazolam	Fluconazole (400 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects; African American CYP3A5*X/*X	6	1.97b	0.51b	0.79a	1.61a	1.44b	16%/8%a	[21]
Midazolam	Fluconazole (400 mg, 1 day; 200 mg QD, 5 days)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	2.02c	0.49	0.92	1.85e	1.52	1%/1%a	[22]
Midazolam	Itraconazole (200 mg QD; 6 days)	CYP3A4	CYP3A4 CYP2J2 P-gp	Healthy subjects	12	3.22c	0.31	1.08	3.49e	2.41	16%/1%a	[22]
Midazolam	Ketoconazole (200 mg BID; 2 days)	CYP3A4	CYP3A4 CYP2C19 P-gp	Healthy subjects; white	9	5.1	0.21	1.20a	5.97a	4.12	22%/6%a	[23]
Midazolam	Ketoconazole (400 mg QD; 4 days)	CYP3A4	CYP3A4 CYP2C19 P-gp	Healthy subjects; female, Korean	12	4.61c	0.22	0.57b	4.61b	1.98	2%/2%b	[24]
Midazolami	Nelfinavir (1250 mg BID; 14 days)	CYP3A4	CYP3A4 inhibition and induction	Healthy subjects	16	1.83	0.57	0.79a	1.22a	1.41	2%/3%a	[25]
Midazolam	Rifampin [induction] (600 mg QD; 10 days)	CYP3A4	CYP3A4 inhibition and induction	Healthy subjects; female, Korean	12	0.48c	2.07	1.01b	0.50b	0.74	2%/2%b	[24]
Midazolami	Rifampin [induction] (600 mg QD; 14 days)	CYP3A4	CYP3A4 inhibition and induction	Healthy subjects	16	0.44	2.16	1.19a	0.54a	0.61	4%/3%a	[25]
Midazolami	Ritonavir (600 mg TID; 1 day; 300 mg BID; 6 days; 400 mg BID; 7 days)	CYP3A4	CYP3A4 inhibition and induction	Healthy subjects	16	3.31	0.29	1.04a	3.22a	2.85	21%/3%a	[25]
Theophylline	Cimetidine (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects; male, young	8	1.31c	0.77	1.10	1.44e	1.41	NR	[26]
Theophylline	Cimetidine (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects; female, young	8	1.42c	0.71	1.05	1.48e	1.43	NR	[26]
Theophylline	Cimetidine (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy; male, elderly	8	1.36c	0.73	0.98	1.34e	1.31	NR	[26]
Theophylline	Cimetidine (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy; female, elderly	8	1.33c	0.75	1.08	1.43e	1.36	NR	[26]
Theophylline	Cimetidine (1000 mg QD; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects	7	1.56d	0.66b	1.02b	1.58f	1.84b	NR	[27]
Theophylline	Cimetidine (1000 mg QD; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects	9	1.33c	0.75	1.13g	1.83g	1.24	19%/5%g	[28]
Theophylline	Cimetidine (1000 mg QD; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Patients with liver cirrhosis	9	1.22c	0.82	0.97g	1.36g	1.66	15%/9%g	[28]
Theophylline	Cimetidine (300 mg QID; 2.75 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects; male	5	1.69d	0.61	1.11h	1.90h	1.73	32%/13%h	[29]
Theophylline	Cimetidine (300 mg QID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects	10	1.46d	0.74b	1.12a	1.53a	1.38b	30%/17%a	[30]
Theophylline	Cimetidine (400 mg TID; 9 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects; male	7j	1.42	0.73	1.02a	1.30a	1.38	13%/8%a	[31]
Theophylline	Cimetidinek (800 mg BID; 9.5 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Patients with chronic obstructive pulmonary disease	15	1.35d	0.77b	1.10b	1.47b	1.45b	13%/6%a	[32]
Theophylline	Cimetidine (600 mg QID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects	8	1.63	0.60	1.07	2.01	1.80	NR	[33]
Theophylline	Ciprofloxacin (500 mg BID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects	8	1.43	0.69	1.04	1.70	1.51	NR	[33]
Theophylline	Ciprofloxacin (500 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male	8	1.34d	0.76b	1.02	1.36e	1.43b	21%/12%a	[34]
Theophylline	Ciprofloxacin (500 mg BID; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male, young	8	1.49c	0.67	1.02	1.52e	1.51	NR	[26]
Theophylline	Ciprofloxacin (500 mg BID; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; female, young	8	1.50c	0.67	1.02	1.53e	1.48	NR	[26]
Theophylline	Ciprofloxacin (500 mg BID; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male, elderly	8	1.42c	0.71	1.04	1.47e	1.40	NR	[26]
Theophylline	Ciprofloxacin (500 mg BID; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; female, elderly	8	1.40c	0.71	1.08	1.51e	1.45	NR	[26]
Theophylline	Ciprofloxacin (500 mg BID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects	8	1.80	0.55	1.11	2.26	2.03	NR	[33]
	+ Cimetidine (600 mg QID; 6 days)		CYP enzymes OCT2 MATE1
Theophylline	Ciprofloxacin (500 mg BID; 15 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male, young	8	1.64c	0.61	1.08	1.78e	1.73	NR	[26]
	+ Cimetidine (400 mg BID; 8 days)		CYP enzymes OCT2 MATE1
Theophylline	Ciprofloxacin (500 mg BID; 15 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; female, young	8	1.79c	0.56	1.02	1.84e	1.75	NR	[26]
	+ Cimetidine (400 mg BID; 8 days)		CYP enzymes OCT2 MATE1
Theophylline	Ciprofloxacin (500 mg BID; 15 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male, elderly	8	1.64c	0.61	1.00	1.64e	1.64	NR	[26]
	+ Cimetidine (400 mg BID; 8 days)		CYP enzymes OCT2 MATE1
Theophylline	Ciprofloxacin (500 mg BID; 15 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; female, elderly	8	1.60c	0.63	1.08	1.72e	1.68	NR	[26]
	+ Cimetidine (400 mg BID; 8 days)		CYP enzymes OCT2 MATE1
Theophylline	Diltiazem (120 mg TID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 CYP1A2 CYP2D6 P-gp	Healthy subjects	10	1.02c	0.98	1.11g	1.01g	1.06	9%/9%g	[35]
Theophylline	Enoxacin (200 mg TID; 3 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2	Healthy subjects	5	2.00c	0.50	1.09a	2.35a	2.12	33%/7%a	[36]
Theophylline	Famotidine (40 mg BID; 6 days)	CYP1A2 CYP3A4 CYP2E1	Unknown	Healthy subjects	10	0.95d	1.07b	1.12a	1.06a	1.08b	17%/16%a	[30]
Theophylline	Famotidinek (40 mg BID; 9.5 days)	CYP1A2 CYP3A4 CYP2E1	Unknown	Patients with chronic obstructive pulmonary disease	15	0.99d	1.02b	1.03b	1.02b	1.02b	6%/6%a	[32]
Theophylline	Nalidixic acid (500 mg QID; 7 days)	CYP1A2 CYP3A4 CYP2E1	Unknown	Healthy subjects; male	8	0.99d	1.04b	1.04	1.02e	1.12b	NR	[34]
Theophylline	Norfloxacin (200 mg TID; 3 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2	Healthy subjects	5	1.08c	0.93	1.11a	1.29a	1.17	13%/7%a	[36]
Theophylline	Norfloxacin (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2	Healthy subjects; male	8	1.17d	0.86b	1.02	1.19e	1.24b	18%/12%a	[34]
Theophylline	Ofloxacin (200 mg TID; 3 days)	CYP1A2 CYP3A4 CYP2E1	Unknown	Healthy subjects	5	1.00c	1.00	1.08a	1.11a	1.06	10%/7%a	[36]
Theophylline	Olanzapine (5 mg; 1 day; 7.5 mg; 1 day; 10 mg QD; 7 days)	CYP1A2 CYP3A4 CYP2E1	Unknown	Healthy subjects; male	12	0.94	1.04	1.08a	1.01a	1.02	7%/7%a	[31]
Theophylline	Ranitidine (150 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A CYP2C9 CYP2D6 OCT2	Healthy subjects	7	1.21d	0.92b	0.97b	1.16f	1.28b	NR	[27]
Theophylline	Verapamil (40 mg TID; 4 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects; male, white	12	1.13	0.92	0.98	1.06e	1.11	15%/11%a	[37]
Theophylline	Verapamil (80 mg TID; 4 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects; male, white	12	1.19	0.86	0.95	1.11e	1.11	16%/11%a	[37]
Theophylline	Verapamil (120 mg TID; 4 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects; male, white	12	1.28	0.82	0.90	1.10e	1.25	18%/11%a	[37]
Theophylline	Verapamil (120 mg TID; 8 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects	7	1.25d	0.81b	0.97b	1.21f	1.22b	45%/37%g	[38]
Theophylline	Verapamil (120 mg QID; 6 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects	10	1.29c	0.77	0.98 g	1.31g	1.33	6%/3%g	[35]
Tolbutamide	Cimetidine (1000 mg QD, 4 days; 600 mg, 1 day)	CYP2C9	CYP enzymes OCT2 MATE1	Healthy subjects	6	1.15c	0.87	1.01a	1.19a	1.13	4%/2%a	[39]
Tolbutamide	Cimetidine (400 mg QID; 4.5 days)	CYP2C9	CYP enzymes OCT2 MATE1	Healthy subjects	6	1.53c	0.65	0.96a	1.46a	1.46	5%/2%a	[39]
Tolbutamide	Primaquine (45 mg; single dose)	CYP2C9	Unknown	Healthy subjects	6	1.04c	0.96	0.82a	0.89a	0.90	2%/4%a	[39]
Tolbutamide	Sulfaphenazole (500 mg BID; 3.5 days)	CYP2C9	CYP2C9	Healthy subjects	7	3.10c	0.32	0.86a	3.21a	3.07	26%/4%a	[39]

Pharmacokinetic values reported in the table are based on published average values, unless otherwise noted

AUC area under the curve, BID twice daily, CL clearance, Con control, MATE1 Multidrug and Toxic Extrusion 1, MRT mean residence time, NAT N-acetyl transferase, NR not reported, OCT organic cation transporter, P-gp P-glycoprotein, QD once daily, QID four times a day, t_1/2,z terminal half-life, Refs reference, TID three times a day, V_ss volume of distribution at steady state, XO xanthine oxidase

^aRatios are calculated by digitization of published average plasma concentration–time profiles and performing a non-compartmental analysis

^bRatios are calculated for each individual using published individual pharmacokinetic data; the reported value reflects the average of each individual ratio

^cAUC was calculated with the equation AUC = dose/CL using known dose and reported average values of CL

^dAUC was calculated for each individual with the equation AUC = dose/CL using known dose and reported individual values of CL; the reported value reflects the average of each individual ratio

^eMRT was calculated with the equation V_ss = CL·MRT using reported average values of CL and V_ss

^fMRT was calculated for each individual with the equation V_ss = CL·MRT using reported individual values of CL and V_ss; the reported value reflects the average of each individual ratio

^gRatios are calculated by digitization of a published plasma concentration–time profile of a single representative subject, which may not be reflective of all subjects in the study

^hRatios are calculated by digitization of individual published plasma concentration–time profiles and performing a non-compartmental analysis; the reported value reflects the average of each individual ratio

ⁱMidazolam was dosed intravenously at the same time as an oral probe cocktail of tolbutamide, dextromethorphan, and caffeine

^jInteraction arm included n = 7 subjects; however, the control arm is only n = 6 as one subject dropped out of the study

^kA list of additional drugs being taken by these subjects with chronic obstructive pulmonary disease can be found in the original article by Bachmann et al. [32]

Table 4.

Intravenous drug–drug interaction (DDI) studies with additional substrates (not cytochrome P450 [CYP] index substrates)

Victim	Perpetrator	Victim enzymes or transporters	Perpetrator enzymes or transporters	Population	N	$\frac{{\text{AUC}}^{\text{DDI}}}{{\text{AUC}}^{\text{Con}}}$	$\frac{{\text{CL}}^{\text{DDI}}}{{\text{CL}}^{\text{Con}}}$	$\frac{V_{\text{ss}}^{\text{DDI}}}{V_{\text{ss}}^{\text{Con}}}$	$\frac{{\text{MRT}}^{\text{DDI}}}{{\text{MRT}}^{\text{Con}}}$	$\frac{t_{1/2,z}^{\text{DDI}}}{t_{1/2,z}^{\text{Con}}}$	Percent AUC extrapolation	Refs.
Alfentanil	Fluconazole (100 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	1.2	0.84	0.93a	1.18a	1.18	2%/1%	[20]
	+ Ondansetron (4 mg; single dose)		Unknown
	+ Midazolam (1 mg; single dose)		Unknown
Alfentanil	Fluconazole (200 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	1.6	0.62	0.89a	1.45a	1.36	3%/1%	[20]
	+ Ondansetron (4 mg; single dose)		Unknown
	+ Midazolam (1 mg; single dose)		Unknown
Alfentanil	Fluconazole (400 mg; single dose)	CYP3A4	CYP3A4 CYP2C9 CYP2C19	Healthy subjects	12	2.2	0.46	0.90a	1.92a	1.73	5%/1%	[20]
	+ Ondansetron (4 mg; single dose)		Unknown
	+ Midazolam (1 mg; single dose)		Unknown
Antipyrine	Cimetidine (1000 mg BID; 7 days)	CYP enzymes	CYP enzymes OCT2 MATE1	Healthy subjects	7	1.33d	0.76b	1.05b	1.40f	1.30b	NR	[27]
Antipyrine	Ranitidine (150 mg BID; 7 days)	CYP enzymes	CYP3A CYP2C9 CYP2D6 OCT2	Healthy subjects	7	1.08d	0.93b	1.02b	1.09f	1.06b	NR	[27]
Lidocaine	Erythromycin (500 mg QID; 5 days)	CYP3A4 CYP1A2	CYP3A4 P-gp	Healthy subjects	8	1.19d	0.96b	1.14a	1.19a	1.37b	28%/23%a	[19]
	+ Midazolam (0.075 mg/kg; single dose)		Unknown

Pharmacokinetic values reported in the table are based on published average values, unless otherwise noted

AUC area under the curve, BID twice daily, CL clearance, Con control, MATE1 Multidrug and Toxic Extrusion 1, MRT mean residence time, NR, not reported, OCT organic cation transporter, P-gp P-glycoprotein, QID four times a day, Refs reference, t_1/2,z terminal half-life, V_ss volume of distribution at steady state

^aRatios are calculated by digitization of published average plasma concentration–time profiles and performing a non-compartmental analysis

^bRatios are calculated for each individual using published individual pharmacokinetic data; the reported value reflects the average of each individual ratio

^dAUC was calculated for each individual with the equation AUC = dose/CL using known dose and reported individual values of CL; the reported value reflects the average of each individual ratio

^fMRT was calculated for each individual with the equation V_ss = CL·MRT using reported individual values of CL and V_ss; the reported value reflects the average of each individual ratio

Table 5.

Drug–drug interaction (DDI) studies that only report terminal volume of distribution (V_z)

Victim	Perpetrator	Victim enzymes or transporters	Perpetrator enzymes or transporters	Population	N	$\frac{{\text{AUC}}^{\text{DDI}}}{{\text{AUC}}^{\text{Con}}}$	$\frac{{\text{CL}}^{\text{DDI}}}{{\text{CL}}^{\text{Con}}}$	$\frac{V_z^{\text{DDI}}}{V_z^{\text{Con}}}$	$\frac{{\text{MRT}}^{\text{DDI}}}{{\text{MRT}}^{\text{Con}}}$	$\frac{t_{1/2,z}^{\text{DDI}}}{t_{1/2,z}^{\text{Con}}}$	Percent AUC extrapolation	Refs.
Antipyrine	Cimetidine (1000 QD; 10 days)	CYP1A2 CYP2C9 CYP3A4	CYP enzymes OCT2 MATE1	Healthy subjects	7	1.41	0.79	1.24	NR	1.59	NR	[40]
Desipramine	Disulfiram (500 mg QD; 31 days)	CYP2D6 CYP3A4	CYP2E1 CYP1A2 CYP2C9 CYP2D6	Healthy subject; male	1	1.32	0.76	0.93	NR	1.20	NR	[41]
Imipramine	Disulfiram (500 mg QD; 14 days)	CYP2C19 CYP2D6	CYP2E1 CYP1A2 CYP2C9 CYP2D6	Healthy subjects; male	2	1.30b	0.77b	0.89b	NR	1.16b	NR	[41]
Theophylline	Cimetidine (300 mg PO QID; 1.5 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT2 MATE1	Healthy subjects; male	10	1.27c	0.79	1.00	NR	1.24	NR	[42]
Theophylline	Cimetidine (300 mg IV infusion QID; 1.5 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT MATE1	Healthy subjects; male	10	1.21c	0.83	1.02	NR	1.20	NR	[42]
Theophylline	Cimetidine (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT MATE1	Healthy subjects; male	6	1.34c	0.74	1.04	NR	1.42	NR	[43]
Theophylline	Cimetidine (1000 QD; 10 days)	CYP1A2 CYP3A4 CYP2E1	CYP enzymes OCT MATE1	Healthy subjects	7	1.10	0.90	1.04	NR	1.15	NR	[40]
Theophylline	Ciprofloxacin (500 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male	6	1.48c	0.68	1.00	NR	1.47	NR	[43]
Theophylline	Ciprofloxacin (400 mg BID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP1A2 CYP3A4	Healthy subjects; male	6	1.70c	0.59	1.00	NR	1.78	NR	[43]
	+ Cimetidine (500 mg BID; 7 days)		CYP enzymes OCT2 MATE1
Theophylline	Erythromycin (250 mg QID; 7 days)	CYP1A2 CYP3A4 CYP2E1	CYP3A4 P-gp	Healthy subjects; male	8	1.38c	0.74b	0.92b	NR	1.27b	NR	[44]

Pharmacokinetic values reported in the table are based on published average values, unless otherwise noted

AUC area under the curve, BID twice daily, CL clearance, Con control, CYP cytochrome P450, IV intravenous, MATE1 Multidrug and Toxic Extrusion 1, MRT mean residence time, NR not reported, OCT organic cation transporter, PO oral, QD once daily, QID four times a day, Refs reference, t_1/2,z terminal half-life

^bRatios are calculated for each individual using published individual pharmacokinetic data; the reported value reflects the average of each individual ratio

^cAUC was calculated with the equation AUC = dose/CL using known dose and reported average values of CL

The changes in PK parameters (AUC, CL, V_ss, MRT, and t_1/2,z) of clinically recommended index substrates are listed in Table 3 and additional victim drugs in Table 4, totaling 72 DDI studies. For these primarily metabolized drugs, the AUC ratio range was 0.44–5.1 while the V_ss range was 0.57–1.40. The average absolute difference in AUC ratios for these 72 DDI studies averaged 1.69 ± 0.78, while the average absolute difference in V_ss averaged 1.10 ± 0.12. For the 49 interactions with at least a 30% change, i.e., those interactions that could potentially be clinically significant, the absolute AUC changes averaged 1.95 ± 0.83, while V_ss averaged 1.11 ± 0.13. Figure 1 depicts box plot representations of these values. Of the 72 DDI studies examined, only three (4.2%) resulted in a greater than 30% change in V_ss (i.e., ratios outside of the range of 0.77–1.30) with ratios of 0.70 [15], 1.40 [18], and 0.57 [24].

Fig. 1.

Box plot depictions of the absolute magnitude of change in victim drug exposure (area under the curve [AUC]) and volume of distribution at steady state (V_ss) expressed as ratios of interaction to control for a all drug–drug interactions (n = 72) and b the subset of these interactions that are potentially clinically significant (with absolute AUC ratios > 1.3; n = 49). The box indicates the median and 25th and 75th percentiles, the whiskers range from minimum to maximum values, and each individual data point is also depicted

An additional ten DDI studies were identified from five studies for which only V_z was reported and V_ss could not be determined (due to a lack of published PK profiles) (Table 5). Changes in AUC had a range of 1.10–1.70, but V_z had only a range of 0.89–1.24.

While the inclusion criteria of this analysis focused on studies that include the same patients in the control and interaction phases, three DDI studies investigated here performed the same drug interaction study in multiple groups, either with respect to pharmacogenomic variance of the metabolizing enzyme [15, 21] or disease state [28]. To investigate the impact of inter-individual variability on V_ss, the control phase (victim drug only) between each group were compared to one another (Table 6). When comparing the pharmacokinetics of the index substrate alone between groups, V_ss for the victim drug was observed to change with ratios of 0.51 (metoprolol with CYP2D6 pharmacogenomics), 0.72 and 0.79 (midazolam with CYP3A5 pharmacogenomics), and 0.70 (healthy patients vs patients with liver cirrhosis), while AUC was observed to change 0.98- to 2.56-fold in these studies. In the same studies, however, minimal change in V_ss was observed in the same individual between the drug interaction and control phases, with a ratio range of 0.70–1.13 (Table 3).

Table 6.

Intravenous pharmacogenomic interaction studies and disease state drug–drug interaction studies

Drug	Enzyme	Population	N	$\frac{{\text{AUC}}^{\text{Int}}}{{\text{AUC}}^{\text{Con}}}$	$\frac{{\text{CL}}^{\text{Int}}}{{\text{CL}}^{\text{Con}}}$	$\frac{V_{\text{ss}}^{\text{Int}}}{V_{\text{ss}}^{\text{Con}}}$	$\frac{{\text{MRT}}^{\text{Int}}}{{\text{MRT}}^{\text{Con}}}$	$\frac{t_{1/2,z}^{\text{Int}}}{t_{1/2,z}^{\text{Con}}}$	Percent AUC extrapolation	Refs.
Metoprolol	CYP2D6	Control: healthy subjects, white, male, CYP2D6 extensive metabolizers; 58–80 kg	3	2.56c	0.40	0.51	1.29e	1.81a	34%/15%a	[15]
		Phenotype: healthy subjects, white, male, CYP2D6 poor metabolizers; 65–86 kg	4
Midazolam	CYP3A	Control: healthy subjects, African American, CYP3A5*1/*1; 57–97 kg for all subjects	6	0.98	1.04	0.79a	0.70a	0.93	8%/14%a	[21]
		Phenotype: healthy subjects, African American, CYP3A5*1/*X; 57–97 kg for all subjects	7
Midazolam	CYP3A	Control: healthy subjects, African American, CYP3A5*1/*1; 57–97 kg for all subjects	6	1.05	0.99	0.72a	0.70a	0.96	8%/14%a	[21]
		Phenotype: healthy subjects, African American, CYP3A5*1/*X; 57–97 kg for all subjects	6
Theophylline	CYP1A2 CYP3A4 CYP2E1	Control: healthy subjects; average weight 80.7 kg	9	1.54c	0.65	0.70g	1.2g	1.76	8%/14%a	[28]
		Disease state: patients with liver cirrhosis; average weight 68.6 kg	9

Pharmacokinetic values reported in the table are based on published average values, unless otherwise noted

AUC area under the curve, CL clearance, Con control (indicating the wild-type pharmacogenomic phenotype or healthy subject group), CYP cytochrome P450, Int interaction (indicating the reduced function pharmacogenomic phenotype or disease state group); MRT mean residence time, Refs reference, t_1/2,z terminal half-life, V_ss, volume of distribution at steady state

^aRatios are calculated by digitization of published average plasma concentration–time profiles and performing a non-compartmental analysis

^cAUC was calculated with the equation AUC = dose/CL using known dose and reported average values of CL

^eMRT was calculated with the equation V_ss = CL·MRT using reported average values of CL and V_ss

^gRatios are calculated by digitization of a published plasma concentration–time profile of a single representative subject (one healthy subject and one patient with liver cirrhosis), which may not be reflective of all subjects in the study

Discussion

For primarily metabolized drugs, IV drug interaction studies resulted in minimal changes to V_ss. Changes in drug exposure (AUC) up to 5.1-fold were observed; however, ratios of V_ss changes only had a range of 0.70–1.40, with one outlier displaying a 43% decrease in V_ss (ratio of 0.57) (Table 3) for a midazolam-ketoconazole interaction in healthy female Koreans where the AUC ratio was 4.61 [24]. In contrast, a second midazolam–ketoconazole interaction study in healthy white subjects with a similar AUC ratio of 5.1 only exhibited a V_ss ratio of 1.20 [23]. The trend of unchanged V_ss was observed for all index substrates and CYP isoforms investigated (caffeine and theophylline, CYP1A2; metoprolol, CYP2D6; tolbutamide, CYP2C9; midazolam, CYP3A4) [data not shown].

It should be noted that a listed high percent AUC extrapolation value does not necessarily indicate that AUCs (or PK parameters derived from AUCs) are unreliable if the slope of the elimination phase is adequately captured. Additionally, the PK parameters reported by the original authors were used in priority to calculate the ratios presented in this analysis, such as the frequently reported parameters AUC, CL, and t_1/2,z. Estimation of less frequently reported parameters, such as V_ss and MRT, proceeded via digitization of the average concentration–time profiles reported by the original authors, and it should be noted that these average profiles may not accurately represent changes within any one particular individual in the DDI study.

When V_ss was not reported (and could not be calculated because of the lack of published PK curves), changes in V_z were examined (Table 5). Changes in V_z were minimal (0.89–1.24). Examination of theophylline PK curves from the other studies in this analysis indicate that the distribution phase of theophylline is very short, and therefore V_z changes would likely be similar to V_ss changes. No such conclusions related to the potential similarity between V_z and V_ss could be made for the antipyrine, desipramine, or imipramine data because of the lack of published IV PK curves in the other studies examined here.

Of note, the clinical studies included in this analysis were all conducted with the same individuals in the control vs interaction arms, to minimize the confounding effects of inter-individual variability. Three of the studies examined here also conducted DDIs in multiple subject groups with respect to disease-state [28] or pharmacogenomic variance of drug-metabolizing enzymes [15, 21]. To examine the potential impact of inter-individual differences in V_ss, the PK parameters associated with the control arms (victim drug only) of each group were compared to one another, resulting in V_ss ratios of 0.51–0.79 associated with AUC changes of 0.98–2.56 (Table 6). In comparison to the earlier part of this analysis where changes in V_ss within the same individual (with and without addition of a perpetrator drug) were examined, these same studies displayed V_ss ratios of 0.70–1.26 associated with AUC increases of 1.12–3.08. Reported data related to the body weights of individuals in each arm are also noted in Table 5. However, accounting for average differences in body weight between the two groups does not necessarily result in V_ss ratios that are closer to unity. For instance, the reported differences in metoprolol V_ss between CYP2D6 poor metabolizers and extensive metabolizers resulted in a ratio of 0.51, and the reported values used to calculate this ratio were normalized by body weight of each individual by the original investigators. This indicates that volume of distribution differences in different individuals can be significant and do not only depend on total body weight differences. Further, the variability associated with V_ss values was much greater in extensive metabolizers than poor metabolizers, with CV values of 44% and 22%, respectively. The issue of variability between individuals is further compounded in pharmacogenomic studies where often only a very small number of individuals can be recruited for the less frequently occurring genotypes.

This highlights that for the same drug, V_ss may change significantly between subjects. These findings are in contradiction to the belief that all PK parameters are expected to be similar in homogenous populations, such as in healthy subjects, as the pharmacogenomic interactions studied here included healthy subjects in each arm. As a result, we suggest that it may not appropriate to assume that V_ss is unchanged across different subject populations and therefore, it is crucial to consider clinical study design (parallel vs crossover). Further, based on this observation, we emphasize that the examination of differences in pharmacokinetics in different pharmacogenomic variance or disease-state populations should be considered as a qualitative outcome. Although changes in AUC and CL can reasonably be compared between groups, as V_ss may inherently be different between individuals in each group, changes in terminal half-life should not be considered significant nor be utilized to suggest changes in the dosing regimen between the two populations studied. Further investigation into this finding is warranted, and is an area of high interest to our laboratory.

It should be noted that perpetrator drugs have the potential to displace victim drug from plasma or tissue-binding sites, which may result in V_ss changes. From Eq. (1), changes in protein binding should result in comparable changes for CL and V_ss with no change in MRT or half-life. However, we find no examples of such an interaction in the same subjects within our dataset. Thus, the data presented here for IV metabolic drug interaction studies very strongly support our contention that V_ss does not change to any significant degree for metabolic DDIs.

The DDI studies evaluated here follow the classic PK trend of changes in CL resulting in an equal but opposite change in MRT, owing to the fact that V_ss remains unchanged for metabolic interactions (Eq. 1) [45]. These relationships are depicted in Fig. 2, where the inverse of ratios of CL changes are plotted against both MRT and t_1/2,z ratios. The results for each comparison fall very close to the line of unity, highlighting the intuitive trend that decreases in CL result in increases in MRT and t_1/2,z of approximately equal magnitude. In comparing the AUC–MRT relationship to the AUC–t_1/2,z relationship, as expected the MRT relationship falls closer to the line of unity than a few of the t_1/2,z points associated with larger 1/CL ratios, as t_1/2,z may change differently than MRT for drugs that display multi-compartment kinetics, and this difference is likely amplified in DDI studies of a larger magnitude. In general, Fig. 2 highlights that changes in CL are opposite in direction but similar in magnitude to MRT and t_1/2,z and this is in sharp contrast to significant transporter–drug interactions, where decreases in CL can often be associated with decreases in half-life and MRT, owing to changes in V_ss [2].

Fig. 2.

Ratios of change in a mean residence time (MRT) and b terminal half-life (t_1/2,z) compared with the inverse of change in clearance (CL). The red line indicates the line of unity

As our laboratory has recently presented, knowledge that V_ss remains unchanged in metabolic DDI studies can facilitate the estimation of changes in CL from changes in F following an oral dose [3]. In the Quinney et al. [17] study of the interaction of midazolam and clarithromycin in elderly subjects, the interaction was conducted following both orally and intravenously dosed midazolam. Thus, estimates of changes in CL vs F based on the oral interaction study can be confirmed by examining the observed changes resulting from the IV midazolam interaction study. Following oral dosing, an 8.2-fold increase in midazolam exposure was observed (compared with only a 3.2-fold increase in midazolam AUC in the IV drug interaction study) when clarithromycin was dosed 500 mg twice daily for 7 days (Table 7). Knowing that V_ss largely remains unchanged for IV metabolic DDIs (based on the analysis presented here) supports the assumption that changes in V_ss/F following an oral dose will reflect changes in F alone. This estimation of F change can subsequently be utilized to assess changes in CL alone from calculations of apparent CL [3]. Utilizing this methodology, the predicted increase in F was 2.84-fold and CL was predicted to decrease by 60% (ratio of 0.40), compared with the observed 2.12-fold increase in F and 65% reduction in CL (ratio of 0.35) (Table 7). Thus, recognition that V_ss remains unchanged in metabolic interactions allows the discrimination of two PK parameters thought to be indistinguishable from one another following oral dosing.

Table 7.

Utilization of the Sodhi and Benet methodology [3] to discriminate clearance (CL) from bioavailability (F) changes for orally dosed midazolam (victim) and clarithromycin (perpetrator) from the study of Quinney et al. [17]

Victim	Perpetrator	$\frac{{\text{AUC}}^{\text{DDI}}}{{\text{AUC}}^{\text{Control}}}$	Percent AUC extrapolation (DDI/control)	$\frac{V_{\text{ss}}/F^{\text{DDI}}}{V_{\text{ss}}/F^{\text{Control}}}$	$\frac{V_{\text{ss}}^{\text{DDI}}}{V_{\text{ss}}^{\text{Control}}}$	$\frac{F^{\text{DDI}}}{F^{\text{Control}}}$	$\frac{\text{CL}/F^{\text{DDI}}}{\text{CL}/F^{\text{Control}}}$	$\frac{{\text{CL}}^{\text{DDI}}}{{\text{CL}}^{\text{Control}}}$	Refs.
Midazolam (IV)	Clarithromycin (500 mg BID; 7 days)	Observed: 3.2	Observed: 44%/19%a	–	Observed: 1.16a	Observed: 2.12	–	Observed: 0.35	[17]
15N3-Midazolam (oral)	Clarithromycin (500 mg BID; 7 days)	Observed: 8.2	Observed: 33%/12%a	Observed: 0.35a	Assumed: 1	Estimated: 2.84b	Observed: 0.14	Estimated: 0.40b	[17]

Pharmacokinetic values reported in the table are based on published average values, unless otherwise noted

AUC area under the curve, BID twice daily, DDI drug–drug interaction, IV intravenous, Refs reference, V_ss volume of distribution at steady state

^aRatios are calculated by digitization of published average plasma concentration–time profiles and performing a non-compartmental analysis

^bRatios are calculated for each individual using published individual pharmacokinetic data; the reported value reflects the average of each individual ratio

Conclusions

Based on an extensive evaluation of 72 clinical DDI studies, V_ss remains unchanged for IV metabolic drug interactions as expected, with a small minority of outliers (only three) with ratios indicating a change, where for the largest V_ss change, a second study of the same interacting drugs in a different population did not show this marked V_ss change. These results uphold the widely held founding tenant of pharmacokinetics that CL and V_ss are independent parameters. Differences in victim drug V_ss can significantly vary throughout the population due to inter-individual variability that may not necessarily be accounted for by body weight. This highlights that differences in PK parameters observed between groups in pharmacogenomic and disease state studies (or any clinical trial with a parallel study design) should be accompanied with the understanding that V_ss could differ significantly between groups. Therefore, although changes in AUC and CL between groups indicate meaningful differences, terminal half-life differences should be considered qualitative due to their dependence on the inherently variable V_ss value between individuals. Further, following oral dosing the changes in V_ss/F will reflect only changes in F for metabolic interactions. Therefore, this estimation of F change can subsequently be utilized to assess changes in CL alone from calculations of apparent CL/F, two parameters that are considered indistinguishable from one another following oral dosing [3].

Declarations

Funding

This work was supported in part by a Mary Ann Koda-Kimble Seed Award for Innovation. Jasleen K. Sodhi was supported in part by an American Foundation for Pharmaceutical Education Predoctoral Fellowship, National Institute of General Medical Sciences Grant R25 GM56847, and a Louis Zeh Fellowship. Leslie Z. Benet is a member of the University of California, San Francisco Liver Center supported by a National Institutes of Health Grant P30 DK026743.

Conflict of interest

Jasleen K. Sodhi, Caroline H. Huang, and Leslie Z. Benet have no conflicts of interest that are directly relevant to the content of this study.

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.