PK/PD) Index Map for Selecting an Optimal PK/PD Index from Conventional Indices

Drug Metab. Pharmacokinet. 29 (6): 455–462 (2014). Copyright © 2014 by the Japanese Society for the Study of Xenobiotics (JSSX) Regular Article A Proposal of a Pharmacokinetic/pharmacodynamic (PK/PD) Index Map for Selecting an Optimal PK/PD Index from Conventional Indices

(AUC/MIC, Cmax/MIC, and TAM) for Antibiotics

Yoshiaki KITAMURA1,*,KentaYOSHIDA2,MakikoKUSAMA2 and Yuichi SUGIYAMA3 1Discovery Research Laboratories, Kyorin Pharmaceutical Co., Ltd., Tochigi, Japan 2Graduate School of Pharmaceutical Sciences, The University of Tokyo, Tokyo, Japan 3Sugiyama Laboratory, RIKEN Innovation Center, RIKEN Research Cluster for Innovation, Yokohama, Japan

Full text and Supplementary materials of this paper are available at http://www.jstage.jst.go.jp/browse/dmpk

Summary: A pharmacokinetic/pharmacodynamic (PK/PD) analysis is important in antibiotic chemotherapy. Basically, the in vivo efﬁcacy of antibiotics that exert concentration-dependent effects can be predicted using conventional PK/PD indices such as theratiooftheareaunderthecurvetotheminimum

inhibitory concentration (AUC/MIC) and/or the ratio of the maximum plasma concentration to MIC (Cmax/ MIC), whereas that of antibiotics with time-dependent effects can be determined using the period of time for which the drug concentration exceeds the MIC (time above MIC [TAM]). However, an optimal PK/PD index remains to be established for some antibiotics. Thus, a PK/PD model which describes the PK profile and effect of an antibiotic was developed, and the results obtained from this model were interpreted to form a PK/ PD index map to assess the optimal PK/PD index for the antibiotic. The findings from the map were generally consistent with clinical outcomes even for the antibiotics which proved to be exceptions to the conventional classification. For example, AUC/MIC was an optimal index for azithromycin despite its time-dependent

bactericidal activity, and Cmax/MIC was a poor index for arbekacin despite its concentration-dependent proﬁle.Thus,themapwouldbeusefulforselectingtheappropriatePK/PDindexforanantibiotic.

Keywords: pharmacokinetics and pharmacodynamics; antibiotics; AUC/MIC; Cmax/MIC; time above MIC

bactericidal activity. These classifications evolved into the follow- Introduction ing three PK/PD indices: the in vivo effect of concentration- For decades, the importance of pharmacokinetic/pharmaco- dependent drugs is associated with the ratio of the area under the dynamic (PK/PD) analysis has been increasing in antibiotic curve (AUC) to MIC (AUC/MIC) and/or the ratio of the maximum chemotherapy. Understanding the PK/PD relationship, an estimate plasma concentration (Cmax) to MIC (Cmax/MIC), whereas the of in vivo efficacy on the basis of plasma concentration, is essential in vivo effect of time-dependent drugs is associated with the time for determining the dosing regimen in clinical use. Historically, the above MIC (TAM).2) Antibiotics have been conventionally clas- minimum inhibitory concentration (MIC) was considered the prin- sified into these three categories, usually according to their class. cipal PD parameter to determine in vivo efficacy. However, since However, for some antibiotics, the correlation between the antibiotics with the same MIC value can have different bactericidal identified PK/PD index and the actual clinical efficacy is contro- characteristics,1) MIC alone cannot predict in vivo efficacy. versial. For example, for arbekacin, a concentration-dependent Antibiotics are generally classified into two groups according to aminoglycoside, AUC/MIC data were considered a good predic- 2–4) the shape of the time–kill curve. Concentration-dependent drugs tor, whereas Cmax/MIC was concluded to be the best index in exhibit a linear relationship between drug concentration and the some studies.5,6) For vancomycin, a time-dependent drug, both killing rate after the administration of a clinically approved dose. concentration and the TAM were regarded as predictive indices;7) Time-dependent drugs have a low maximum killing rate, and the conversely, Moise-Broder et al. showed that AUC/MIC was the bactericidal activity is independent of drug concentration above most predictive index.8) These discrepancies cannot be resolved the MIC; rather, the exposure time predominantly determines the easily because they necessitate extensive clinical studies.

Received January 28, 2014; Accepted June 26, 2014 J-STAGE Advance Published Date: July 8, 2014, doi:10.2133/dmpk.DMPK-14-RG-013 *To whom correspondence should be addressed: Yoshiaki KITAMURA, Ph.D., Discovery Research Laboratories, Kyorin Pharmaceutical Co., Ltd., 2399-1, Nogi, Nogi-machi, Shimotsuga-gun, Tochigi 329-0114, Japan. Tel. ©81-280-56-2201, Fax. ©81-280-57-1293, E-mail: yoshiaki. [email protected]

455 456 Yoshiaki KITAMURA, et al.

To describe and predict the in vivo antibacterial activity more 1 accurately than the conventional approach, the concept of model- MIC ¼ EC50 ð5Þ " based PK/PD analysis has been proposed, in which the time course 3,4) of the plasma concentration is considered. According to this where ka is the absorption rate constant from the gut compartment approach, in addition to MIC, in vitro parameters that are neces- to the central compartment, ke is the elimination rate constant from sary to distinguish between concentration-dependent and time- the central compartment, X1 is the amount of drug in the gut com- dependent drugs are incorporated to describe the bactericidal char- partment, X2 is the amount of drug in the central compartment, Vd acteristics more precisely. Although the predictability of this model is the distribution volume, fp is the free fraction in plasma, Cfree is is assumed superior to that of the conventional approach, this model the plasma concentration of free drug, N is the number of bacteria, requires modeling and simulation capabilities that may preclude is the growth rate of bacteria without drug, ¾ is the maximum kill it from general use. Thus, the goal of this study was to develop a rate constant, £ is the Hill coefficient, EC50 is the concentration of method for this model-based analysis without the use of advanced drug at which 50% of the maximum effect is obtained, and MIC is PK/PD modeling and computer simulation. Here, the PK/PD index the minimum inhibitory concentration, which is equal to Cfree when map was presented to assess the predictability of conventional PK/ dN/dt = 0. PD indices by using the model-based analysis. The PK/PD index PK/PD simulation under steady state after repeated dosing: map enables the selection of the optimal PK/PD index, requiring The PK profile of an antibiotic in vivo and the number of bacteria only a few parameters, such as the elimination rate constant (ke) were calculated at steady state from 0 to 24 h in 4 different dosing and in vitro bactericidal characteristics (¾, £, and ). The dosing schedules—once-daily dosing at time 0, twice-daily dosing at schedule map was also developed to determine whether once-daily times 0 and 12 h, 4 times daily dosing every 6 h, and 8 times daily dosing is more effective than divided dosing. These maps were dosing every 3 h—by numerical integration using the ode23s developed with regard to efficacy only; the occurrence of adverse function of MATLAB (The MathWorks Inc., Natick, MA), which events and the emergence of resistant strains were not considered. is based on a modified Rosenbrock formula of order 2.9) Initial conditions for the numerical integration were given as follows Methods (Supplemental material 1): PK/PD modeling: The PK/PD model consists of 2 units 1 (Fig. 1). The pharmacokinetic unit is a typical 1-compartment X1ð0Þ¼F D ð6Þ 1 expðk Þ model with a gut compartment. The bacterial unit—the time profile a exp exp — F D ka ðke Þ ðka Þ of the number of bacteria at the infection site is essentially iden- 2ð0Þ¼ ð 6¼ Þ X 1 exp 1 exp ka ke tical to the “enhanced-death constant-replication” model described ka ke ðke Þ ðka Þ by Czock et al.3) These units are related to each other under the (7–1) assumption that the free plasma concentration at a certain point in expðkÞ X2ð0Þ¼F D k ðka ¼ ke ¼ kÞ (7–2) time determines the kill rate of bacteria at the same time. f1 expðkÞg2 dX1 0 ¼k X1 ð1Þ Nð Þ¼N0 (8) dt a ¸ dX2 where F is the oral bioavailability, D is the oral dose, is the dosing ¼ k X1 k X2 ð2Þ dt a e interval, and N0 is the number of bacteria at 0 h. X1(0) and X2(0) represent steady-state trough concentrations in the gut compart- f pX2 Cfree ¼ ð3Þ ment and the central compartment, respectively. In most cases, Vd X2(0) was calculated using Eq. (7–1). However, when ka is equal dN " Cfree 4 – ¼ N ð Þ to ke, the denominator of Eq. (7 1) becomes 0, which means that dt Cfree þ EC50 X2(0) cannot be calculated. In such cases, Eq. (7–2) was used instead. PK/PD index mapping: The dose at which the number of bacteria at 24 h is equal to that at 0 h was determined using the fminbnd function of MATLAB, which is based on golden section search and parabolic interpolation. This dose was defined as the static dose (Dosestatic,n), where n is the daily dosing frequency. For each static dose (Dosestatic,1, Dosestatic,2, Dosestatic,4, and Dosestatic,8), AUC/MIC was calculated using fixed parameters F, Vd,fp,ka,ke, ¾, £, , and EC50. Then, AUC/MIC values corresponding to each of the four different dosing schedules were obtained. The ratio of the Fig. 1. Schematic illustration of pharmacokinetic/pharmacodynamic (PK/ fi PD) model maximum to minimum among the four values was de ned as the The PK/PD model comprises 2 units: the PK profile of an antibiotic in the index ratio (AUC/MIC) for the parameters F, Vd,fp,ka,ke, ¾, £, , human body and the time profile of the number of bacteria at the infection site. and EC50. The same calculation was used to determine the index These units are related under the assumption that the free plasma concentration at a certain point in time determines the kill rate of bacteria at the same time. ratios for Cmax/MIC and TAM. ka, the absorption rate constant from the gut compartment to the central Index ratio ðAUC=MICÞ compartment; ke, the elimination rate constant from the central compartment; maximum AUC=MIC among the four dosing schedules , the growth rate of bacteria without drug; ¾, the maximum kill rate constant; ¼ = £, the Hill coefficient; X1, the amount of drug in the gut compartment; X2, the minimum AUC MIC among the four dosing schedules amount of drug in the central compartment; N, the number of bacteria at the (9–1) infection site.

Index ratio ðCmax=MICÞ Pharma, Co., Ltd.; 2011; Package insert of Vancomycin 12th ed.

maximum Cmax=MIC among the four dosing schedules Osaka, Japan, Shionogi & Co., Ltd.; 2009; Package insert of ¼ Zithromacμ Tablets 18th ed. Tokyo, Japan, Pfizer Japan Inc.; minimum Cmax=MIC among the four dosing schedules 2013). The elimination rate constant (k ) was obtained by fitting (9–2) e the plasma concentration to a 1-compartment model (weight: Index ratio ðTAMÞ 1/conc2). Parameter optimization was performed using the com- maximum TAM among the four dosing schedules puter program WinNonlin (version 6.3; Certara, Saint Louis, MO). ¼ minimum TAM among the four dosing schedules In the case of azithromycin, only the data up to 24 h were used (9–3) because the plasma concentrations up to 72 h did not align well with a 1-compartment model. When the index ratio of a PK/PD index approximates 1, the PK/PD In vitro antibiotic parameters for arbekacin, cefditoren, index can be regarded as robust, regardless of the dosing schedule. levofloxacin, tebipenem, and vancomycin were obtained from the The PK/PD index map was developed by determining the index literature.10) For azithromycin, the killing profile derived by Den ratios after varying two selected parameters as described below. Hollander et al.11) was converted to a time–kill curve. The number Effect of varying ka and ke of bacteria was transformed to its natural logarithm, and the initial PK/PD index maps were generated by varying ka (from 0.1 to slope of the time–kill curve was plotted against the drug con- ¹1 ¹1 ¹1 6h ) and ke (from 0.05 to 1 h ) at 4 different ¾–£ pairs (¾ = 3h , centration (C). The growth rate of bacteria () was determined from £ = 1; ¾ = 3h¹1, £ = 3; ¾ = 10 h¹1, £ = 1; and ¾ = 10 h¹1, £ = 3). the slope in the absence of drug. Other in vitro antibiotic param- Other parameters were fixed at the following values: F = 1, eters (¾, £, and EC50) were determined by fitting these plots to the ¹1 Vd = 1 L/kg, fp = 1, = 1h , and EC50 = 1 µg/mL. following equation. Effect of varying ¾ and £ " C PK/PD index maps were generated by varying ¾ (from 1.5 to slope ¼ (10) C þ EC50 ¹1 15 h ) and £ (from 0.5 to 10) at 4 different ke values (0.1, 0.2, 0.5, and 1 h¹1). Other parameters were fixed at the following values: ¹1 ¹1 Results F = 1, Vd = 1 L/kg, fp = 1, = 1h ,ka = 1h , and EC50 = 1 µg/mL. PK/PD index mapping: Dosing schedule mapping: For the static doses of once-daily Effect of varying of ka and ke on the index ratio (Dosestatic,1) and 4 times daily dosing (Dosestatic,4), the total daily The PK/PD index map is shown in Figure 2. According to the dose amounts required to achieve the same antibacterial outcome flip-flop phenomenon in pharmacokinetics, the ka and the ke are were calculated, and their ratio (1 © Dosestatic,1/4 © Dosestatic,4) was essentially interchangeable in this pharmacokinetic model analysis. defined as the dose ratio. When the dose ratio is <1, once-daily The analysis regarding the case of ka < ke (shown in gray triangles dosing requires a smaller amount of antibiotic than 4 times daily in Fig. 2) can be substituted for the equivalent case by alternating dosing to exert the same antibacterial effect, suggesting that a ka and ke to one another. For each ¾–£ pair, ke had a significant single dose is better than multiple dosing; a ratio >1 suggests that effect on the index ratio, whereas ka had a marginal influence on 4 times daily dosing is better. The dosing schedule map was the index ratio when ka > ke. developed by calculating the dose ratios after varying ¾ (from 1.5 Effect of varying ¾ and £ on the index ratio ¹1 to 15 h ) and £ (from 0.5 to 10) at 4 different ke values (0.1, 0.2, The PK/PD index value is dependent on ¾/, not their absolute 0.5, and 1 h¹1). Other parameters were fixed at the following values (Supplemental material 2). Small ¾/ corresponds to drugs ¹1 ¹1 values: F = 1, Vd = 1 L/kg, fp = 1, = 1h ,ka = 1h , and that demonstrated time-dependent antibacterial activity, where EC50 = 1 µg/mL. saturation of the killing rate occurred at low multiples of the Effect of MIC on the calculation of TAM: The static dose MIC—usually around four to five times the MIC.12) Concentrations of each dosing schedule was calculated at 4 different ke values above these values did not kill the organisms any faster. Large (0.1, 0.2, 0.5, and 1 h¹1) under the following conditions: F = 1, ¾/ corresponds to those drugs that demonstrated concentration- ¹1 ¹1 ¹1 Vd = 1 L/kg, fp = 1, ka = 1h , ¾ = 3h , £ = 1, = 1h , and dependent characteristics, where bactericidal activity increased EC50 = 1 µg/mL. MIC was theoretically determined to be 0.5 with increased concentrations of the antibiotic, across a wide range µg/mL from the given parameters by using Eq. (5). To investigate of concentrations. The PK/PD index can be regarded as a good the impact of the accuracy of MIC on the calculation of TAM, predictor when the index ratio approximates 1 (shown in red), and TAM values at the static doses were calculated using 2 different a poor predictor when its index ratio is large (shown in pale blue) MIC values around the theoretical value (0.4 and 0.6 µg/mL). (Fig. 3). The map suggests that the best PK/PD index is dependent Actual data collection: The plasma concentration of 6 on both ¾/ and £. The map appeared different with different antibiotics on the market (arbekacin, cefditoren, levofloxacin, ke values, showing that ke is another important factor. This is tebipenem, vancomycin, and azithromycin) belonging to different consistent with the observation from the ka–ke maps in Figure 2. classes (aminoglycoside, cephem, fluoroquinolone, carbapenem, For time-dependent drugs (i.e., small ¾/), TAM was always a good glycopeptide, and macrolide, respectively) were obtained from the predictor, regardless of £ and ke;ifke was low, AUC/MIC was also package inserts (Package insert of Habekacinμ Injections 7th ed. a good predictor. For concentration-dependent drugs (i.e., large Tokyo, Japan, Meiji Seika Pharma, Co., Ltd.; 2011; Package insert ¾/), the predictability of AUC/MIC and Cmax/MIC was dependent μ of Meiact MS Tablets 5th ed. Tokyo, Japan, Meiji Seika Pharma, on £ and ke. Generally, AUC/MIC was a good predictor if £ was μ Co., Ltd.; 2011; Package insert of Cravit Tablets 7th ed. Tokyo, small; Cmax/MIC was a good predictor if £ was large. If ke was Japan, Daiichi Sankyo Company, Limited; 2011; Package insert large, both AUC/MIC and Cmax/MIC were poor predictors at of Orapenemμ Fine Granules 5th ed. Tokyo, Japan, Meiji Seika £ = 3–4.

Fig. 2. Pharmacokinetic/pharmacodynamic (PK/PD) index map (ka–ke plot) ¹1 ¹1 The PK/PD index maps with regard to AUC/MIC, Cmax/MIC, and TAM are depicted, varying ka (from 0.1 to 6 h ) and ke (from 0.05 to 1 h ) at 4 different ¾–£ pairs ¹1 ¹1 ¹1 ¹1 (¾ = 3h , £ = 1; ¾ = 3h , £ = 3; ¾ = 10 h , £ = 1; and ¾ = 10 h , £ = 3). Other parameters were fixed at the following values: F = 1, Vd = 1 L/kg, fp = 1, ¹1 = 1h , and EC50 = 1 µg/mL. According to the flip-flop phenomenon of pharmacokinetics, ka and ke are essentially interchangeable in this pharmacokinetic model analysis. The analysis regarding the case of ka < ke (shown by the gray triangles) can be substituted for the equivalent case, replacing ka and ke with one another.

Fig. 3. Pharmacokinetic/pharmacodynamic (PK/PD) index map (¾/–£ plot) ¹1 The PK/PD index maps with regard to AUC/MIC, Cmax/MIC, and TAM are depicted, varying ¾ (from 1.5 to 15 h ) and £ (from 0.5 to 10) at 4 different ke values (0.1, ¹1 ¹1 ¹1 0.2, 0.5, and 1 h ). Other parameters were ﬁxed at following values: F = 1, Vd = 1 L/kg, fp = 1, = 1h ,ka = 1h , and EC50 = 1 µg/mL. The parameters of actual antibiotic drugs are from Tables 1 and 2. TAM is not suitable for practical use for a drug with low ke (surrounded by the gray rectangle).

Fig. 4. Dosing schedule map (¾/–£ plot) Static daily dose was determined for once-daily and 4 times daily dosing; the ratio was deﬁned as dose ratio. The dose ratios were plotted, varying ¾ (from 1.5 to 15 h¹1) ¹1 and £ (from 0.5 to 10) at 4 different ke values (0.1, 0.2, 0.5, and 1 h ) to generate the dosing schedule map. Other parameters were ﬁxed at following values: F = 1, ¹1 ¹1 Vd = 1 L/kg, fp = 1, = 1h ,ka = 1h , and EC50 = 1 µg/mL. The parameters of actual antibiotic drugs are from Tables 1 and 2.

Fig. 5. Effect of minimum inhibitory concentration (MIC) on the time above MIC (TAM) To investigate the effect of varying MIC, TAM values were calculated assuming 3 different MIC values (0.4, 0.5, and 0.6 µg/mL). TAM is very sensitive to MIC when ke is small and dosing is frequent.

Dosing schedule mapping: The dosing schedule map was Table 1. In vitro antibiotic parameters developed by plotting the dose ratio. According to the dosing Class Bacterial species ¾/£ schedule map, the dose regimen was very important for antibiotics Arbekacin aminoglycoside MRSA 2.4–65 0.47–1.14 with large ke (Fig. 4). For time-dependent drugs, divided dosing Cefditoren cephem S. pneumoniae 2.2, 2.3 2.31, 10.4 was strongly recommended. For concentration-dependent drugs, Levofloxacin fluoroquinolone S. pneumoniae 3.1, 3.1 2.61, 2.63 single dosing was preferred if £ was large. In contrast, for anti- Tebipenem carbapenem S. pneumoniae 2.5, 3.0 2.13, 3.27 – – biotics with small k , the selection of the dose regimen exerted only Vancomycin glycopeptide MRSA 1.3 1.6 0.37 14.0 e Azithromycin macrolide S. pneumoniae 2.58 2.08 a slight influence on the treatment effectiveness. Effect of MIC on the calculation of PK/PD indices: Small MRSA: methicillin-resistant Staphyloccocus aureus. Parameters were obtained from the literature10) or calculated from the con- differences in MIC strongly affected the calculated TAM values centration–killing curve.11) is the growth rate of bacteria without drug, ¾ is the £ fi – when ke was low and the compound was administered multiple maximum kill rate constant, and is the Hill coef cient of the concentration kill ¹1 rate curve. times per day (Fig. 5). For example, if ke = 0.1 h , the theoretical TAM value (MIC = 0.5 µg/mL) at the static dose for a drug administered 4 times daily (Dosestatic,4) was 54%; the calculated TAM Table 2. In vivo pharmacokinetic parameters in humans values at Dosestatic,4 was 100% and 0% with MIC values of 0.4 and ¹1 ¹1 0.6 µg/mL, respectively. However, if ke = 1h and the drug was Dosing amount and route ke (h ) administered 4 times daily, the theoretical TAM value (MIC = 0.5 Arbekacin 200 mg, iv infusion (1 h) 0.30 « 0.03 Cefditoren 200 mg, po 0.56 « 0.23 µg/mL) at Dosestatic,4 was 50%, and the calculated TAM values Levofloxacin 500 mg, po 0.12 « 0.02 were 58% and 46% with MIC values of 0.4 and 0.6 µg/mL, Tebipenem 250 mg, po 0.89 « 0.10 respectively. Conversely, variability in AUC/MIC and Cmax/MIC Vancomycin 500 mg, iv infusion (1 h) 0.16 « 0.04 was always inversely proportional to the variability in MIC. Azithromycin 500 mg, po 0.094 « 0.033 Comparison between prediction and actual data: Actual The plasma concentration was obtained from package inserts (Package insert of antibiotic and pharmacokinetic parameters of 6 antibiotics from Habekacinμ Injections 7th ed. Tokyo, Japan, Meiji Seika Pharma, Co., Ltd.; μ different classes are summarized in Tables 1 and 2, and plotted on 2011; Package insert of Meiact MS Tablets 5th ed. Tokyo, Japan, Meiji Seika Pharma, Co., Ltd.; 2011; Package insert of Cravitμ Tablets 7th ed. Tokyo, the PK/PD index maps and the dosing schedule maps. Because Japan, Daiichi Sankyo Company, Limited; 2011; Package insert of Orapenemμ ¹1 maps are provided only for ke = 0.1, 0.2, 0.5, and 1 h , each drug Fine Granules 5th ed. Tokyo, Japan, Meiji Seika Pharma, Co., Ltd.; 2011; was plotted on the map with the k that was closest to the actual Package insert of Vancomycin 12th ed. Osaka, Japan, Shionogi & Co., Ltd.; e μ fi value (Figs. 3 and 4). The PK/PD index map shows that the in vivo 2009; Package insert of Zithromac Tablets 18th ed. Tokyo, Japan, P zer Japan Inc.; 2013). The elimination rate constant (ke) was obtained by fitting the plasma effects of cefditoren and tebipenem are associated with TAM, concentration to a 1-compartment model using WinNonlin. For azithromycin, because these compounds lie in the area of good predictor (red plasma concentrations up to 24 h were used for the calculation. color) on the TAM map, and in the area of a poor predictor (blue pale color) on the AUC/MIC and the Cmax/MIC maps (Fig. 3). Similarly, the in vivo effects of arbekacin, levofloxacin, and Discussion azithromycin are associated with AUC/MIC. According to the dosing schedule map, divided dosing was better than once daily A PK/PD index map was devised to assess the optimal PK/PD dosing for cefditoren, tebipenem, and vancomycin (Fig. 4). For index for a given antibiotic with the use of a model-based PK/PD arbekacin, the dosing schedule map predicts that divided dosing analysis. The map suggests that the elimination rate constant (ke)is might have a slightly better outcome. Conversely, administration an important in vivo PK parameter for selecting the relevant PK/ frequency has only limited influence on the in vivo effectiveness of PD index; the absorption rate constant (ka) plays a marginal role. levofloxacin and azithromycin. Selection of the optimal PK/PD index was also dependent on

Copyright © 2014 by the Japanese Society for the Study of Xenobiotics (JSSX) 460 Yoshiaki KITAMURA, et al. in vitro characteristics, including the ratio of the maximum kill obvious concentration-dependent antibiotic profile (large ¾). How- rate constant to the growth rate of bacteria without drug (¾/) and ever, this is inconsistent with many clinical studies in which in vivo the Hill coefficient (£) of the concentration–kill rate curve. The antibacterial effects were similar regardless of the dosing frequency 13–15) PK/PD classifications by the map were mostly in agreement with within the same total daily dose, suggesting that the Cmax/MIC convention; TAM is a good index for the in vivo effects of time- is a poor index for aminoglycosides. The PK/PD index map dependent drugs, and Cmax/MIC and AUC/MIC are good indices (Fig. 3) indicates that the Cmax/MIC is a poor index for arbekacin, 2) for concentration-dependent drugs. The selection of Cmax/MIC an aminoglycoside, despite its concentration-dependent character- versus AUC/MIC was predominantly dependent on £. istic. For azithromycin, a time-dependent drug, convention dictates Our results suggest that indices incorporating MIC must con- that the in vivo efficacy is dependent on TAM; however the clinical sider the error in the measured value inherent in the method used observation shows that the AUC/MIC is a good index.16) Generally to derive it, i.e. 2-fold dilution concentration series.4) Errors in this inconsistency has been attributed to factors like post antibiotic 17) AUC/MIC and Cmax/MIC are always inversely proportional to the effect (PAE) or sub-MIC effect (SME). However, the PK/PD error in MIC, irrespective of ke. Conversely, small errors in MIC index map would suggest that AUC/MIC is a good index for a are amplified in the calculation of TAM when ke is low (Fig. 5). time-dependent drug such as azithromycin, without employing For example, the calculated AUC/MIC and Cmax/MIC always additional factors. These observations suggest that the PK/PD decrease by 33% when the MIC changed from 0.4 to 0.6 µg/mL, index map can be a better predictor of the antibacterial effect than irrespective of the dosing frequency and ke. Our simulation demon- the conventional classification. Regarding vancomycin, although strated that the calculated TAM values at Dosestatic,4 for a drug with AUC/MIC and TAM have been identified as predictive indices, the ¹1 small ke (0.1 h ) decreased dramatically from 100% to 0% when PK/PD index map showed that none of the conventional PK/PD ¹1 the MIC changed from 0.4 to 0.6 µg/mL, whereas the reduction indices seemed to be useful. Since the ke is 0.16 h , the TAM ¹1 was only 12% (from 58% to 46%) for a drug with large ke (1 h ). cannot be appropriate for practical use as mentioned above. The Thus, our results suggest that TAM should not be used for a drug Cmax/MIC appeared to be a poor index and the AUC/MIC would ¹1 with a ke less than 0.2 h , even if the drug belongs to the time- be of only limited use. Thus, the PK/PD index map deduced that dependent category. none of conventional PK/PD indices is predictable and the clinical The PK/PD index map suggests that the in vivo effects of regimen should be decided by a model-based PK/PD analysis on a cefditoren and tebipenem are related more closely with TAM, case-by-case basis. whereas those of arbekacin, levofloxacin, and azithromycin are The PK/PD index map shows that the selection of the PK/PD associated with AUC/MIC (Fig. 3). These predictions by the index is dependent on the ke of antibiotics. It is known that map are largely in good agreement with the clinical results,2–4,7) pharmacokinetic parameters show inter-individual variability in suggesting that the map is fairly reliable (Table 3). Regarding humans for various reasons. Drug-drug interactions can also change ¹1 azithromycin, the ke estimated using WinNonlin (0.094 h ) was the pharmacokinetics of antibiotics; for example, concomitant quite different from that calculated from the half-life on the package probenecid administration decreases the ke of some cephalosporin insert (0.011 h¹1). This difference can be explained by the different antibiotics, primarily by reducing their renal clearance.18) Renal data used to estimate the parameter. The index ratio of AUC/MIC impairment also accounts for the decreased renal clearance of 19) always decreases with a decreasing ke when the values of ¾/ and £ antibiotics such as ciprofloxacin and levofloxacin. Single nucleo- are fixed (Fig. 2). According to the PK/PD index map of ke = tide polymorphisms on the genes encoding metabolic enzymes and 0.1 h¹1, AUC/MIC is a good predictor for azithromycin (Fig. 3), transporters20–22) may affect the metabolism and excretion of some ¹1 because the ke of azithromycin is smaller than 0.1 h in either case. antibiotics. Pediatric patients may exhibit different pharmacokinetic There has been some difference between the clinically observed properties compared to adults.23) In such cases, a different PK/PD effect and the conventional classification of the antibacterial effect. index might have a better correlation with the therapeutic efficacy For example, aminoglycosides have generally been classified in the due to an individual difference in the ke. Since the ke can also 2,4) Cmax/MIC or the AUC/MIC category because they exhibit an have some species differences between experimental animals and humans,24) a PK/PD index identified in an animal study would not be always applicable to the clinical prediction. In addition to the PK/PD index map, the dosing schedule map Table 3. Comparison of antibiotic selection: recommendation by pharmacokinetic/pharmacodynamic (PK/PD) index map vs. conventional classi- was developed to predict the relative effectiveness of once-daily fication versus divided dosing (Fig. 4). According to the dosing schedule map, the selection of the dosing regimen has little effect on the PK/PD index map Conventional classification clinical outcome for drugs with low ke, such as levofloxacin and Arbekacin AUC/MIC AUC/MIC, Cmax/MIC Cefditoren TAM TAM azithromycin. In contrast, for drugs with large ke, the dosing Levofloxacin AUC/MIC AUC/MIC, Cmax/MIC regimen exerts a greater influence. The map suggests that divided Tebipenem TAM TAM dosing is better for time-dependent drugs such as cefditoren, # Vancomycin no good index AUC/MIC, TAM tebipenem, and vancomycin. Contrary to convention, divided Azithromycin AUC/MIC AUC/MIC (PAE) dosing might be better for a concentration-dependent drug when it AUC: area under the curve, MIC: minimum inhibitory concentration, TAM: time has very low £ and high k . A comparison between the recom- above MIC. e #For vancomycin, model-based PK/PD analysis is necessary on a case-by-case mendation by the dosing schedule map and the clinical usage is basis. summarized in Table 4. Most of the clinical dosing regimens were 2–4,7) Conventional classification was quoted from the literature. For arbekacin, consistent with those suggested by the dosing schedule map, levofloxacin, and vancomycin, two indices have been identified, depending on the source. It is conventionally suggested that the post-antibiotic effect (PAE) is supporting the validity of the map. involved in the in vivo effect of azithromycin. One limitation of this study is that we only considered the

Table 4. Comparison of daily dosing regimen: recommendation by dosing in vivo PK (ke) parameters. Moreover, a dosing schedule map was schedule map vs. clinical regimen generated using this model-based analysis to predict whether once- Dosing schedule Clinical regimen Clinical regimen daily or divided dosing is more effective. The PK/PD index map map in Japan in the U.S. and the dosing schedule map are expected to be a practical guide ² Arbekacin divided once once (unapproved) for optimizing antibiotic therapy, by exploiting the advantages of Cefditoren divided º once 3 times twice Levofloxacin divided = once once once the model-based analysis without the need for advanced PK/PD Tebipenem divided º once twice (unapproved) modeling and computer simulation. Vancomycin divided º once 2–4 times 3–4 times Azithromycin divided = once once once References Clinical regimens in Japan and U.S. were quoted from documents (Package insert 1) Regoes, R. R., Wiuff, C., Zappala, R. M., Garner, K. 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