What are the optimal pharmacokinetic/pharmacodynamic targets for β-lactamase inhibitors? A systematic review

Abstract Background Pharmacokinetic/pharmacodynamic (PK/PD) indices are widely used for the selection of optimum antibiotic doses. For β-lactam antibiotics, fT>MIC, best relates antibiotic exposure to efficacy and is widely used to guide the dosing of β-lactam/β-lactamase inhibitor (BLI) combinations, often without considering any PK/PD exposure requirements for BLIs. Objectives This systematic review aimed to describe the PK/PD exposure requirements of BLIs for optimal microbiological efficacy when used in combination with β-lactam antibiotics. Methods Literature was searched online through PubMed, Embase, Web of Science, Scopus and Cochrane Library databases up to 5 June 2023. Studies that report the PK/PD index and threshold concentration of BLIs approved for clinical use were included. Narrative data synthesis was carried out to assimilate the available evidence. Results Twenty-three studies were included. The PK/PD index that described the efficacy of BLIs was fT>CT for tazobactam, avibactam and clavulanic acid and fAUC0–24/MIC for relebactam and vaborbactam. The optimal magnitude of the PK/PD index is variable for each BLI based on the companion β-lactam antibiotics, type of bacteria and β-lactamase enzyme gene transcription levels. Conclusions The PK/PD index that describes the efficacy of BLIs and the exposure measure required for their efficacy is variable among inhibitors; as a result, it is difficult to make clear inference on what the optimum index is. Further PK/PD profiling of BLI, using preclinical infection models that simulate the anticipated mode(s) of clinical use, is warranted to streamline the exposure targets for use in the optimization of dosing regimens.


Introduction
β-Lactam (BL) antibiotics are one of the widely used classes of antimicrobials to battle the war against bacterial infections.Even though these antibiotics have been very effective in saving millions of lives, soon after their introduction into clinical practice, their effectiveness progressively reduced due to the development of resistance, mainly mediated by β-lactamase enzymes produced by Gram-negative bacteria. 1,2[5] A widely used strategy to circumvent resistance due to β-lactamase enzyme expression is combining BL antibiotics with β-lactamase inhibitors (BLIs), which bind to the enzymes to thwart the hydrolysis of BL antibiotics by the enzymes. 6,7LIs are classified into first-generation BLIs (clavulanic acid, sulbactam and tazobactam), which inactivate Class A and some Class C serine β-lactamases, and second-generation BLIs (avibactam, relebactam and vaborbactam), which inhibit Class A, Class C and some Class D serine β-lactamases.7,8 The use of these inhibitors with BL antibiotics allows the restoration of the therapeutic efficacy against MDR bacteria and their use has become a trend in drug discovery.In addition to combinations of amoxicillin/clavulanic acid, ampicillin/sulbactam and piperacillin/tazobactam, which have been in use for decades, recently ceftazidime/avibactam, meropenem/vaborbactam, imipenem/ cilastatin/relebactam and ceftolozane/tazobactam have been approved for clinical use.[9][10][11][12] A number of other combinations of novel BLIs with existing BL antibiotics are currently undergoing development.[13][14][15][16][17] The effectiveness of the combination depends on the inherent stability of the stand-alone BL against β-lactamase enzymes, the potency of the BLI and the adequacy of the BL/BLI amounts contained in the combination.18,19 The selection of optimal antibiotic dose is guided by doseexposure-response analysis, in which exposure is often described by pharmacokinetic/pharmacodynamic (PK/PD) parameters.[20][21][22][23][24][25] PK/PD parameters are usually determined by either in vivo or in vitro preclinical infection model studies.26 These models use dose-ranging and dose-fractionation experiments to determine the PK/PD index that correlates exposure to the efficacy of the antibiotic. In ilico methods may also be applied to predict PK/PD exposure metrics using advanced mathematical models built from in vitro or animal model experimental data.27,28 The three most common PK/PD exposure metrics include: the ratio of the area under the free drug concentration-time curve at 24 h to MIC (fAUC 0-24 /MIC); the ratio of the maximum free drug concentration to MIC (fC max /MIC); and the fraction of dosing interval that the free drug concentration remains above MIC (fT >MIC ).29,30 For BL antibiotics, fT >MIC best relates antibiotic exposure to efficacy, whereby a magnitude of 40%-70% fT >MIC is required to produce a bactericidal effect.31,32 This time-dependent PK/PD parameter for BLs is traditionally determined in a fixed ratio combination with BLIs, optimized using simpler static experiments, and is used to guide the dosing of BL/BLI combinations, often without considering any PK/PD exposure requirements for the BLIs.Most BLIs lack sufficient intrinsic antibacterial activity and delineating the PK/PD index that describes the efficacy of these agents is relatively complex.The PK/PD index of BL/BLI combinations should ideally consider the contribution of the inhibitor in the combination and be able to specify the magnitude of the exposure measure necessary for the efficacy of the BLI.However, identifying a single PK/PD index that describes the efficacy of both the BL antibiotic and the BLI is challenging.33 One strategy to tackle this problem might be optimizing the exposure of BLIs using a separate PK/PD exposure metric required to protect the combined BL.However, data on the optimal PK/PD targets of BLIs are limited.Therefore, this systematic review aims to assess existing literature and assimilate data on the PK/PD targets of clinically approved BLIs.

Study protocol
This systematic review was conducted following the Preferred Reporting Items for Systematic Review and Meta-analysis (PRISMA) guidelines. 34he protocol for this review was registered at the international prospective register of systematic reviews (PROSPERO) with registration number CRD42023440787 (https://www.crd.york.ac.uk/prospero/display_ record.php?ID=CRD42023440787).

Data sources and search strategy
Literature was searched online through PubMed, Embase, Web of Science, Scopus and Cochrane Library databases up to 5 June 2023.The search strategy was designed based on two concepts: (i) BLI: clavulanic acid, sulbactam, tazobactam, avibactam, relebactam and vaborbactam; and (ii) target exposure: target concentration, threshold concentration, PK/PD index, PK/PD target, PK/PD ratio, pharmacodynamics, IC 50 , effective concentration, critical concentration and PD index.Appropriate indexing terms, truncations and Boolean operators were used to make the search exhaustive.In addition, relevant articles were searched from reference lists of retrieved articles.The search was limited to the English language.The detailed search terms used for each database are presented in Table S1 (available as Supplementary data at JAC Online).

Inclusion and exclusion criteria
Inclusion criteria were: for BLIs, those approved for clinical use before 5 June 2023; for study design, preclinical (in vitro, in vivo, in silico) and clinical studies that reported the PK/PD index and/or concentration of BLI that protected the companion BL antibiotic; for outcome, the exposure measure (PK/PD index) associated with the efficacy of BLI and the magnitudes of the exposure measures (PK/PD target) necessary for the efficacy of BLI; and for language, articles published in the English language.
Exclusion criteria were: studies that had not determined the threshold concentration or PK/PD exposure target of BLIs; and reviews, guidelines, protocols, brief communications, books, letters to the editor, errata and conference abstracts.

Study selection
The citations retrieved from various databases were imported to Covidence software (www.covidence.org).The software identified, recorded and removed duplicates, and careful visual assessment was undertaken to remove duplicates that were not detected by the software.Two authors (G.M.A. and S.A.M.) independently assessed the titles, abstracts and full documents of each record using the predefined selection criteria.Disagreements between the two authors during the screening process were solved through discussion.

Quality assessment tool
][37] The tool consisted of 15 items to assess the quality of in vitro and in vivo studies (Table S2) and 13 items to assess the quality of in silico studies (Table S3).The quality of the included papers was assessed by G.M.A. and S.A.M. and discrepancies were solved by discussion.

Data extraction
The data extraction form was prepared in Microsoft Excel and data were extracted from the included studies' texts, tables and graphs.The data extracted included name of the author, year of publication, methods used, BLI studied, companion BL, species and strain of the bacteria, β-lactamase enzyme expressed, initial concentration of the bacteria, duration of the experiment, PK/PD index that described the BLI efficacy and the magnitudes of the exposure measures necessary for net bacterial stasis, 1 log and 2 log kills.

Outcome measurement
The primary outcome of this systematic review was the PK/PD index associated with the efficacy of the BLI and the magnitude of this exposure necessary for the efficacy of the BLI.

Search findings
A total of 3737 studies were retrieved from databases and citation searching, from which 1712 duplicates were removed.Of Systematic review 2025 studies that underwent title and abstract screening, 264 passed for full document review.Finally, 23 studies were included in the systematic review.The whole study selection process is presented in the PRISMA flow diagram (Figure 1).

Quality assessment results
From 23 preclinical studies, 10 studies reported all quality assessment items.The least reported items of the quality assessment tool for the in vitro and in vivo studies were appropriate methodology for dose-fractionation/ranging studies, and magnitude of exposure measure associated with the efficacy of BLI, which were not reported by 6 and 7 studies, respectively, as shown in Table S4.Additionally, in the case of in silico studies, two out of the three studies did not carry out prospective validation of their in silico predictions, as shown in Table S5.
46 Consistent with this, Louie et al 47 demonstrated that fT >CT adequately describes the exposureresponse relationship for avibactam. The PD portn of the PK/PD index of these BLIs, due to lack of intrinsic antibacterial activity, is usually represented by a C T for inhibition instead of MIC. 33 Th C T is the lowest concentration of BLI that must be maintained to achieve sufficient β-lactamase inhibition to protect the hydrolysis of the companion BL. 61 The PK/PD index that described the efficacy of relebactam 42,49,59 and vaborbactam 45 was fAUC 0-24 /MIC at the MIC of imipenem and meropenem potentiated with each BLI, respectively, as depicted in Table 2.

Clavulanic acid
The combination of clavulanic acid with ceftibuten is in development for the treatment of complicated urinary tract infection (cUTI) caused by ESBL-producing Enterobacterales.The PD of this combination was evaluated using in vitro onecompartment 46 and in vivo murine thigh infection models, 38 against different strains of K. pneumoniae and E. coli that express different β-lactamase enzymes.The PK/PD index that best described the efficacy of clavulanate when combined with ceftibuten was fT >CT in both models.The C T required for the efficacy of clavulanate when combined with ceftibuten was 0.5 mg/L in a murine thigh infection model, 38 and ranged from 0.006 to 1 mg/L in an in vitro infection model, depending on the bacterial strain. 46he magnitude of fT >CT required to achieve net bacterial stasis and 1 log 10 kill were 21% and 92%, respectively, in an in vivo study, 38 but varied according to the test strain in an in vitro study (31% and 48% for E. coli; and 52% and 92% for K. pneumoniae for net stasis and 1 log 10 kill, respectively). 46

Sulbactam
Unlike other BLIs, sulbactam has inherent antibacterial activity against Acinetobacter baumannii strains.Even though the PK/PD index that described the efficacy of sulbactam with a companion BL is not clearly reported, the PK/PD of sulbactam alone against A. baumannii was evaluated by Yokoyama et al. using in vivo murine thigh and lung infection models. 60In both models, the relationship between the efficacy of sulbactam against A. baumannii ATCC 19606 and the common PK/PD indices (fT >MIC , fAUC 0-24 /MIC and fC max /MIC) was evaluated.The antibacterial activity of sulbactam was best correlated with fT >MIC with R 2 values of 0. 95 and 0.96 in the thigh and lung infection models, respectively.The fT >MIC required for net stasis, 1 and 2 log 10 cfu reductions were 21%, 33% and 44% in the thigh infection model and 20%, 25% and 29% in the lung infection model, respectively.They also reported sulbactam was sufficiently bactericidal when an fT >MIC of >60% and >40% is achieved in the thigh and lung infection models, respectively.However, the PK/PD index associated with sulbactam's efficacy when combined with BLs is not clearly stated.For instance, studies done by Alexov et al., 62 and Lister et al. 63 reported that the efficacy of the combination is maintained when the concentration of the sulbactam is above the enzyme inhibitory concentration.According to these studies, the enzyme inhibition efficacy of sulbactam can be maximized by prolonging fT >CT ; however, they didn't report the specific C T required for its action.

Tazobactam
Tazobactam is one of the most studied BLIs.3][56][57][58] Piperacillin/tazobactam The PK/PD of tazobactam, combined with piperacillin, was evaluated by one in vivo and two in vitro studies.Nicasio et al. 52 used an in vitro infection model and isogenic CTX-M-15-producing E. coli that transcribed different levels of bla CTX-M-15 to describe the PK/PD index associated with tazobactam efficacy when combined with piperacillin.Data from dose-ranging and dose-fractionation studies showed that fT >CT is the PK/PD index that best correlates with the enzyme inhibitory efficacy of tazobactam when combined with piperacillin, irrespective of the transcription level of the enzyme (r 2 = 0.839), but the C T varies from 0.25 to 2 mg/L based on the transcription level of the enzyme, as shown in Table 2.The magnitude of fT >CT (at C T from 0.25 to 2 mg/L) required for tazobactam for bacterial Systematic review stasis and a 1 and 2 log 10 bacterial kill were 45%, 63% and 85%, respectively. 52 study by Rodriguez et al. used a neutropenic murine thigh infection model to assess the efficacy of the piperacillin/tazobactam combination on two isogenic strains of E. coli that express TEM-1 differentially.fT >CT is the PK/PD index that best described the efficacy of tazobactam with C T values of 0.5 and 2 mg/L for the two strains of E. coli that express TEM-1 differently.The mean fT >CT required for net bacterial stasis and 1 log 10 kill was 42% and 56%, respectively. 53other study identified piperacillin MIC reduction with an increased concentration of tazobactam.This study showed that the clinical regimen of piperacillin/tazobactam (4 g/0.5 g q8h) was unable to suppress the bacterial load of the four tested strains using a hollow-fibre infection model (HFIM).However, increasing the dose of tazobactam to 1 and 1.5 g suppressed the growth of SHV-12-producing E. coli and CTX-M-15-producing K. pneumoniae strains, respectively.The parameter fT >MICi , where MICi represents the impact of varying concentrations of the BLI on the MIC of the companion BL antibiotic, serves as a modified  PK/PD index for BL/BLI combinations.This index measures the exposure of the BL, piperacillin, at variable concentrations of the inhibitor, tazobactam.For the CTX-M-15-producing K. pneumoniae strain (using 1.5 g of tazobactam), a 55% fT >MICi of piperacillin (4 g) was associated with stasis, while for the SHV-12-producing E. coli strain (with 1 g of tazobactam), the corresponding value was 60%.However, increasing the tazobactam dose up to 4 g did not result in effective bacterial suppression for the other two CTX-M-15-producing K. pneumoniae strains. 39ftolozane/tazobactam The study by VanScoy et al. 57 used a one-compartment in vitro infection model to evaluate the PK/PD of ceftolozane/tazobactam against an isogenic E. coli strain that produces bla CTX-M-15 .This study evaluated the effect of administering tazobactam at different dosing intervals (6, 8, 12 and 24 h) with similar total daily doses and the more frequent administrations of tazobactam (q6h and q8h) were shown to enable reduction of the bacterial load by more than 2 log 10 cfu/mL at 24 h regardless of the β-lactamase enzyme construct. 57The relationship between the different PK/PD parameters and change in log 10 cfu at 24 h was evaluated and fT >CT was identified as the exposure measure that best predicted the efficacy of tazobactam (r 2 = 0.938) with a C T of 0.05 mg/L for the low and moderate (r 2 = 0.975 and 0.972, respectively) and 0.25 mg/L (r 2 = 0.914) for the high β-lactamase gene transcription levels.The fT >CT of 0.05 mg/L (for low and moderate β-lactamase expression) and 0.25 mg/L (for high β-lactamase expression) necessary for net bacterial stasis, 1 and 2 log cfu reduction at 24 h was 35%, 50% and 70% of the dosing interval, respectively. 57s shown by VanScoy et al., 57 in the study described above, the C T of tazobactam was variable for a single isolate that expressed β-lactamase enzyme at different levels.To further understand this concept, the same group of researchers evaluated the relationship between tazobactam enzyme inhibition efficacy and fT >CT using four different E. coli isolates. 56This study observed that the relationship between fT >CT and change in log 10 cfu from baseline at 24 h was well described by a sigmoid function (r 2 = 0.90-0.99)and the estimated C T for each isolate ranged from 0.5 to 4 mg/L.Moreover, they pooled the C T of each E. coli isolate together and showed that the efficacy of tazobactam is expressed by the MIC of ceftolozane/tazobactam for each isolate multiplied by 0.5 (fT >0.5 × MIC ), which also performs well for the extended datasets that include four E. coli and three K. pneumoniae isolates.The tazobactam fT >CT at 0.5 × MIC of ceftolozane/tazobactam required for net bacterial stasis, 1 log cfu/mL kill and 2 log 10 cfu/mL kill at 24 h were 66%, 77% and 90% of the dosing interval. 56he PD of tazobactam in combination with ceftolozane was further evaluated by an in vivo study using a neutropenic mouse thigh infection model. 50This study also identified fT >CT as the PK/PD index that best predicted the efficacy of tazobactam when combined with ceftolozane, and the C T required for efficacy ranged from 0.5 to 2 mg/L, depending on the strain.The mean fT >CT at a C T of 0.5 mg/L tazobactam responsible for net bacterial stasis and a 1 log kill were 28.2% and 44.4%, respectively, for all tested strains. 50fepime/tazobactam Two studies evaluated the PK/PD of cefepime/tazobactam combinations. 51,58The study conducted  51 In the other study done by VanScoy et al., 58 they developed a translational relationship with the MIC characterizing the PK/PD index of tazobactam when combined with cefepime against

Avibactam
The PK/PD of avibactam (formerly known as NXL104 and AVE1330A) is the most studied among the second-generation BLIs.The clinical use of avibactam in combination with ceftazidime is FDA-approved, while its combination with aztreonam is currently under development. 9,13ftazidime/avibactam The PK/PD of avibactam in combination with ceftazidime was studied using in vivo, 40 in vitro 43,44,48 and in silico methods. 55he in vivo method used murine thigh and lung infection models inoculated with different strains of P. aeruginosa to study the PK/PD index that described the efficacy of avibactam when combined with ceftazidime.After the dose-fractionation study, both the thigh and lung infection models identified fT >CT as the PK/ PD index that best described the efficacy of avibactam when combined with ceftazidime, with a C T of 1 mg/L.The magnitude of fT >CT at a C T of 1 mg/L required to achieve net bacterial stasis and 1 log 10 kill is higher in the thigh infection model (31% and 46.9%, respectively) than the lung infection model (13.6% and 14.3%, respectively), even though the two models were inoculated with a similar number of bacteria. 40oleman et al. 43 and Drusano et al. 44 used an HFIM to study the PD of ceftazidime and avibactam.The study by Coleman et al. used different bacterial species of Enterobacterales (K.pneumoniae, Enterobacter cloacae and Citrobacter freundii) at a low inoculum concentration (10 5 cfu/mL) and Drusano et al. used two strains of K. pneumoniae at higher inoculum concentrations (>10 8 cfu/mL).Drusano et al. identified fT >CT as the PK/PD index that described the efficacy of avibactam when combined with ceftazidime.The C T required for the efficacy of avibactam was identified to be 4 mg/L by Drusano et al.; 44 however, it was not identified by Coleman et al. (suggested to be less than 0.3 mg/L). 43The fT >CT required to achieve net bacterial stasis, 1 or 2 log kill was not determined by either study.
An in vitro infection model was used by MacGown et al. to study the PD of avibactam in combination with ceftazidime and ceftaroline.The study applied a series of dose-fractionation experiments to identify the PK/PD index that described avibactam efficacy when combined with ceftazidime and ceftaroline against CTX-M-producing E. coli, AmpC-hyperproducing E. cloacae and KPC-producing K. pneumoniae.Unlike other studies discussed above, AUC 0-24 and C max adequately described the efficacy of avibactam when combined with ceftazidime and ceftaroline across the three strains and the researchers recommended to use AUC 0-24 , which could be better estimated in patients as the exposure measure to describe the efficacy of avibactam. 48y et al. 55 used a semi-mechanistic mathematical model analysis to determine the PK/PD indices of avibactam when combined with ceftazidime against P. aeruginosa.They replicated the thigh and lung infection model in neutropenic mice, 40 presented above, to simulate the relationship between bacterial load and the drug concentrations in the plasma and epithelium of the alveoli following various dose-fractionation studies.The analysis showed that the more frequent dosing regimens of avibactam had a larger killing effect for the same total daily dose, suggesting time-dependent activity, and fT >CT was most strongly correlated with a change in bacterial load (R 2 = 0.9), with a C T of 1 mg/L. 55ftaroline/avibactam Louie et al. 47 used an HFIM to evaluate the PD of avibactam in combination with ceftaroline against K. pneumoniae, which expresses different β-lactamase enzymes.The dose-ranging studies in this experiment identified that 8 mg/L avibactam administered in combination with ceftaroline (600 mg q8h) consistently succeeded in killing the K. pneumoniae.The dose-fractionation study identified fT >CT as the PK/PD index linked to the efficacy of avibactam when combined with ceftaroline.However, the study by MacGown et al., 48 presented above, reported that the efficacy of avibactam when combined with ceftaroline was best described by AUC 0-24 and C max .

Aztreonam/avibactam
The PK/PD of avibactam in combination with aztreonam was evaluated using an HFIM, and a murine thigh infection model was used to validate the C T of avibactam determined from the HFIM.The efficacy of the combination was assessed against different strains of E. coli and K. pneumoniae.The HFIM predicted fT >CT to be the PK/PD index that best described the efficacy of avibactam when combined with aztreonam, and the C T required for the efficacy of avibactam ranged from 2 to 2.5 mg/L, depending on the type of strain used in both models.The range of fT >CT required for net bacterial stasis and 1 log 10 kill was different for the two models (34%-56.4% and 37.7%-58.2%for stasis and 1 log 10 kill in the HFIM, and 23%-25% and 35%-40% for stasis and 1 log 10 kill in the murine thigh infection model). 54

Relebactam
The PK/PD relationship of relebactam (formerly known as MK-7655) in combination with imipenem was explored by using an HFIM and a murine thigh infection model.These studies identified that fAUC 0-24 /MIC best described the efficacy of relebactam at the relebactam-potentiated MIC of imipenem. 49,59Mavridou et al. 49 reported that the fAUC 0-24 /MIC required for stasis effect of relebactam was approximately 5.2, and Wu et al. 59 reported that the fAUC 0-24 /MIC (at the MIC of the imipenem/relebactam combination) required for bacterial net stasis, 1 and 2 log 10 cfu reduction was 8.2, 12 and 18, respectively.
Bhagunde et al. used an in silico method based on data from the HFIM to determine the PK/PD index of relebactam.The first model relates the PK/PD of imipenem/relebactam to fT >MICi at various concentrations of relebactam and >69% fT >MICi of the combination is required to suppress microbial growth. 41The other model explored fAUC 0-24 /MIC (at the MIC of imipenem/ relebactam) as a PK/PD index that correlates with the efficacy of relebactam and the magnitude of fAUC 0-24 /MIC required for net bacterial stasis, 1 and 2 log kill was 2.5, 4.7 and 7.5, respectively. 42

Vaborbactam
The PK/PD of meropenem and vaborbactam was evaluated by Griffith et al., using an HFIM and mouse thigh infection model against different strains of E. coli, K. pneumoniae and E. cloacae.In both investigations, the PK/PD index that best described the efficacy of vaborbactam was fAUC 0-24 /MIC (at the vaborbactampotentiated meropenem MIC) and the magnitudes of the exposure for net bacterial stasis, 1 and 2 log kill were 12, 18 and 25, respectively, in the HFIM and 9, 38 and 220, respectively, in the mouse thigh infection model. 45

Discussion
This systematic review assimilated data on the PK/PD exposure requirements of BLIs when used in combination with BL antibiotics.The major findings of this review are, firstly, the fT >CT is the most frequent PK/PD index identified to best describe the efficacy of clavulanic acid, tazobactam and avibactam in terms of enabling sufficient inhibition of β-lactamase enzymes to protect the companion BL antibiotic and thereby achieve either net bacterial stasis or 1 to 2 log kill.For relebactam and vaborbactam, fAUC 0-24 /MIC (MIC of the companion BL) is the PK/PD index frequently reported to describe their efficacy.Secondly, the target C T is highly variable from isolate to isolate, depending on the level of β-lactamase enzyme expression and degree of stability of the BL antibiotic against β-lactamase-mediated degradation.The variability and distribution of C T appears to be somehow analogous to the MIC variability and distribution.Thirdly, the proposed magnitude of exposure for the BLI, fT >CT and fAUC 0-24 /MIC, are not consistent between studies such that existing data appear inadequate to define a generalized target exposure that could be used to guide dosing.
The difference in the PK/PD index identified for BLIs, fT >CT for tazobactam, [50][51][52][53][56][57][58] clavulanic acid 38,46 and avibactam, 40,43,44,47,54,55 and fAUC 0-24 /MIC for relebactam 42,49,59 and vaborbactam, 45 may be related to differences in target binding rate and disassociation kinetics. For istance, tazobactam exhibits relatively slow but irreversible binding, 64 such that the duration of exposure is important to allow sufficient inhibition; hence the time-dependent PK/PD index, fT >CT , appears consistent with its binding characteristics. On the other hand, the apid but slowly reversible target-binding characteristics of vaborbactam 65,66 mean that the magnitude of exposure over time would facilitate enzyme binding and thus is consistent with the observation of fAUC 0-24 /MIC as the PK/PD index related to its efficacy.
The exposure of BLIs required for effective protection is variable among companion BL antibiotics, 25,32,67 which is in part related to differences in the inherent stability of each BL antibiotic against β-lactamase degradation.Melchers et al. determined the C T for tazobactam when combined with two different cephalosporins and found different values: 0.5 mg/L when combined with ceftolozane 50 and 0.25 mg/L when combined with cefepime. 51urthermore, the magnitude of fT >CT required for tazobactam to achieve net bacterial stasis was ≥42%, ≥28% and ≥22% when combined with piperacillin, ceftolozane and cefepime, respectively.This might be related to the relative stability of cefepime against β-lactamase degradation, rapid cell wall penetration and faster bactericidal effect; 68 as a result, it may need relatively less tazobactam for protection. 33,69In another study, Ambrose et al. 70 compared the amount of the BLI CB-618 required to protect the hydrolysis of meropenem and cephalosporins (cefepime, ceftazidime and ceftolozane) against a wide range of β-lactamase enzymes, including OXA-48-like carbapenemase.Exposure-response analysis indicated that a higher CB-618 exposure (fAUC 0-24 /MIC) was needed for meropenem relative to that estimated for the cephalosporins as a group from pooled data.This might have been influenced in part by the difference in intrinsic stability of meropenem and cephalosporins against different β-lactamase enzymes such as OXA-48 carbapenemase. 71he other factors affecting the magnitude of BLI exposure to protect the companion BL are the β-lactamase enzyme transcription levels and bacterial species.Bacterial strains of the same species, which express a β-lactamase enzyme at different levels (low-, moderate-or high-level expression), require different amounts of BLIs commensurate with the level of expression. 25,52,53,57In addition, the exposures of BLIs required to protect the BL against different bacterial species such as P. aeruginosa, K. pneumoniae and E. coli are also different, 46,50,54 which further implies that the exposure to the BLIs needs to either cover all expected pathogens or be tailored for each isolate.
The high variability in PK/PD exposure requirements of BLIs means that it is challenging to determine a single PK/PD target for multiple bacteria across a wide MIC range.Furthermore, the effects of dynamic BLI concentration on the susceptibility of bacteria to the BL antibiotic has been difficult to integrate into the PK/PD exposure measure.3][74] To address this concern, a modified PK/PD index, fT >MICi has been proposed for BL/BLI combinations, which reflects the effect of different BLI concentrations on the susceptibility of the bacteria and on how each β-lactamase-producing isolate interacts with the inhibitor. 39,41,74However, this target measure remains to be validated against multiple species of bacteria.An alternative approach proposed by other researchers to account for variability is to define C T in fT >CT as the product of the individual isolates' BL/BLI MIC value and a multiplier, which can be easily determined from in vitro studies. 56,58Nevertheless, the applicability of this approach to various BL/BLI combinations against different bacterial species remains to be validated.
The main purpose of establishing quantifiable PK/PD targets is to use them as a guide for the development and optimization of dosage regimens.However, the PTA for the BLI has rarely been considered in the past, either during drug development or postmarketing optimization, with most studies assessing the PTA for the BL only without considering the PTA for the BLI.6][77][78][79] However, tazobactam was unable to attain these PK/PD targets in epithelial lining fluid during dialysis days, 77 and in CSF, even with the 1.5 g q8h dosage regimen. 80This indicates Systematic review the PK/PD targets of tazobactam might not be achieved in some groups of patients and needs reconsideration.][83][84][85][86][87] Similarly, for therapeutic drug monitoring-guided dose optimization of BL/BLI combinations, PK/PD targets for BLIs are usually not considered for dose optimization.Given that all BL/BLI products are available as fixed-dose combinations, adjusting the dose of either the BL or the BLI independently is practically difficult, if not impossible.A potential solution for this clinical challenge may be the use of stand-alone BLIs, simultaneously administered with the BL antibiotic of interest; this will allow greater flexibility to independently tailor the dosage of the BL and the BLI as appropriate for the therapeutic context. 33here are some limitations in the studies included in this systematic review.The duration of the experiment for most studies was 24 h, which is insufficient to evaluate the ability of the exposure studied to suppress the regrowth of pre-existing resistant subpopulations, which often emerge during prolonged exposure.In addition, most of the experiments evaluated the magnitudes of the exposure measures at lower bacterial inoculum, which might underestimate the amount of BLI required in severe infections with higher bacterial loads.Testing high inoculums is also advantageous to reveal resistance and study exposures that are likely to suppress regrowth of resistant subpopulations.Additional studies utilizing preclinical infection models (i.e.HFIM) in which the BL/BLI is administered to mimic the anticipated mode(s) of clinical use, 25 with higher inoculum concentration, are needed to address these limitations.

Conclusions
fT >CT and fAUC 0-24 /MIC are useful surrogate indicators of the BLI exposures required for optimal protection of BL antibiotics, ensuring desirable microbiological outcomes.However, the magnitude of exposure required for optimal microbiological outcomes is highly variable depending on the companion BL antibiotic, bacterial species and the level of transcription of genes that express β-lactamase enzyme in the target isolate.As a result, clear inference on what the optimum index is cannot be made.Further PK/PD profiling of BLIs, using dynamic preclinical PK/PD infection models that mimic the clinical dosing/exposure scenario, is therefore warranted to streamline the exposure requirements (targets) for use in optimization of dosing regimens.

Figure 1 .
Figure 1.PRISMA flow diagram showing the selection process of identified studies.This figure appears in colour in the online version of JAC and in black and white in the print version of JAC.

Table 1 .
Study characteristics

Table 2 .
The PK/PD index associated with efficacy and the magnitude of exposure for the efficacy of the BLIs -producing Enterobacterales of different MICs.They proposed fT >0.125 × MIC as the PK/PD index of tazobactam when combined with cefepime, with the MIC of cefepime/tazobactam measured by conventional methods.The magnitudes of fT >0.125 × MIC necessary for bacterial suppression and a 1 log 10 kill at 24 h were 22% and 53%, respectively. ESBL