The D _van model associated with microbial susceptibility, VAN PK, and dosing parameters was established. VAN population PK parameters derived from patients with hematological malignancies, microbial susceptibility derived from the Antimicrobial Testing Leadership and Surveillance (ATLAS) database and emulation dosing parameters derived from medication practice, were incorporated as the variables into the D _van model to estimate the D _van based on using MCSs. D _van achieving 90% of probability of target attainment (PTA) for bacterial isolate or cumulative fractions of response (CFR) for the bacterial population at an AUC₂₄/MIC ratio of 400–600 was considered sufficient to treat infection occurring in the target patients. On the basis of the predicted D _van, the physiological states of patients, and the pathogenic variables of infection, a VAN-dose-graphical tool for the target patients and a programming process for VAN dynamic dosage adjustment were constructed.

In the 2020 VAN therapeutic guideline (Rybak et al., 2020b), when VAN is used to treat bacterial infection, an AUC₂₄/MIC ratio of 400–600 (assuming an MIC of 1 mg/L determined by broth microdilution) as the primary PK/PD “efficacy” target is recommended considering the balance of nephrotoxicity and efficacy of VAN, and trough-only monitoring, with a target of 15–20 mg/L, is no longer recommended. Thus, an AUC₂₄/MIC ratio of 400–600 was used as the optimal VAN PK/PD “efficacy” target in this study. Of note, the AUC₂₄/MIC ratio of 400–600 refers to the total AUC₂₄/MIC values unless the ratio is designated as fAUC₂₄/MIC (f is the fraction of the unbound drug) since the total and free AUC₂₄/MIC (i.e., 50% protein binding × AUC₂₄/MIC) for VAN have been interchangeably reported (Rybak et al., 2009). In the administration mode of using intermittent infusion, the calculation model of the AUC₂₄/MIC ratio at a steady state is derived from deduction (see Supplementary Appendix S1: Derivation of AUC₂₄/MIC) as follows: A U C 24 / M I C = 24 v τ ⋅ ( e C L v a n / V d ⋅ τ − e C L v a n / V d ⋅ t inf ) [ t inf ( e C L v a n / V d ⋅ τ − 1 ) C L v a n − ( e C L v a n / V d ⋅ t inf − 1 ) 2 V d ] M I C , (1) where AUC₂₄ (mgh/L) is daily area under the curve, MIC (mg/L) is minimum inhibitory concentration, CL _van (L/h) is VAN clearance, V _d (L) is distribution volume, t _inf (h) is infusion time, τ (h) is dosing interval, v (mg/h) is the zero-order infusion rate, calculated as each dose divided by infusion time [i.e., D _van/(24/τ)/t _inf], and e is the natural constant.

Since the AUC₂₄/MIC value, designated as 400–600, is a constant reflecting PK/PD “efficacy,” here we set it to “φ.” Then, φ = 24 v τ ⋅ ( e C L v a n / V d ⋅ τ − e C L v a n / V d ⋅ t inf ) [ t inf ( e C L v a n / V d ⋅ τ − 1 ) C L v a n − ( e C L v a n / V d ⋅ t inf − 1 ) 2 V d ] MIC . (2)

Due to the relationship of v = D _van /(24/τ)/t _inf, the relation of AUC₂₄/MIC (i.e., φ) and D _van is as follows: D v a n = φ ⋅ M I C ⋅ ( e C L v a n / V d ⋅ τ − e C L v a n / V d ⋅ t inf ) ( e C L v a n / V d ⋅ τ − 1 ) C L v a n − ( e C L v a n / V d ⋅ t inf − 1 ) 2 t inf ⋅ V d . (3)

According to Eq. 3, determination of the D _van value requires the determination of PK parameters (i.e., CL _van and V _d ). Ideally, the individualized PK parameters of the target patients should be used because they are the most representative ones, especially in individualized dosing. However, these data are difficult to be obtained. Thus, the population PK parameters documented (preferably from the target population) were used as surrogates in the present study. The VAN population PK parameters, i.e., CL _van (L/h) = 1.08 × [creatinine clearance (CL _{cr(Cockcroft and Gault)}, in L/h)] and V _d (L) = 0.98 × total body weight (TBW, in kg), which were constructed based on the patients with hematological malignancies by Buelga et al. (2005), were chosen for our analysis. Regarding the reasons for the choice of these data, since 1) the a priori performance of these models was evaluated in another 59 patients and clinical suitability was confirmed, 2) these models were accurate, with more than 33% of the measured concentrations being within ±20% of the predicted value, and 3) the therapeutic precision is two-fold higher than that of a non-customized population model (16.1%), the corresponding standardized prediction errors included zero and a standard deviation close to unity.

Due to the relationship established previously, it is understandable that CL _cr and TBW can be used as surrogates for CL _van and V _d to be simulated and may be more popular since these data are more accessible. Therefore, a modified final D _van model can be expressed as follows: D v a n = φ ⋅ M I C ⋅ ( e 1.08 ⋅ C L c r 0.98 ⋅ T B W ⋅ τ − e 1.08 ⋅ C L c r 0.98 ⋅ T B W ⋅ t inf ) ( e 1.08 ⋅ C L c r 0.98 ⋅ T B W ⋅ τ − 1 ) 1.08 ⋅ C L c r − ( e 1.08 ⋅ C L c r 0.98 ⋅ T B W ⋅ t inf − 1 ) 2 t inf ⋅ 0.98 ⋅ T B W . (4)

According to Eq. 4, determination of the D _van value requires the determination of CL _cr, TBW, and pathogen MIC. Various stages of CL _cr ranging from 10–150 ml/min (with a 30 mL/min increment) and TBW ranging from 40–150 kg (with a 10 kg increment) were simulated. The potential pathogens selected for our analysis were Staphylococcus spp.: Staphylococcus aureus (SA) as well as coagulase-negative Staphylococcus (CNS), Staphylococcus epidermidis (SE), and Staphylococcus haemolyticus (SH). The MIC frequency distributions of these pathogens, included in Table 1, were derived from the Antimicrobial Testing Leadership and Surveillance (ATLAS) database in 2020 (The Micron Group, 2022). The 2020 VAN therapeutic guideline emphasizes that under most circumstances of empiric dosing, the VAN MIC should be assumed to be 1 mg/L, and it does not recommend decreasing the dose to achieve the desired AUC₂₄ exposure for an MIC of even <1 mg/L (Rybak et al., 2020b). These statements imply that for MICs of even <1 mg/L, they should be identified as 1 mg/L and a VAN dosage with at least conventional levels for such MICs should be administered. An MIC of ≤1 mg/L (calculated as 1 mg/L), 2 mg/L, and 4 mg/L for the isolates and a pooled MIC for the populations were simulated, and D _van at any one of the physiology-infection states consisting of TBW–CL _cr –MIC or pathogen species, described in Figure 1, was estimated.

According to Eq. 4, determination of the D _van value also requires the determination of infusion parameters (i.e., τ and t _inf). In the administration mode of using intermittent infusion, dosing for every 8–12 h is recommended in the 2020 VAN therapeutic guideline (Rybak et al., 2020b). Considering the dose-dependent nephrotoxicity of VAN, in general, per dose of ≤2,000 mg and a daily dose of ≤4,000 mg are recommended when VAN is used in adults (Lodise et al., 2008; Filippone et al., 2017; Rybak et al., 2020a; U.S. Pharmacopeia). Moreover, VAN should be diluted for ≤5 mg/mL and infused over ≥1 h or at a rate of 10–15 mg/min (≥1 h per 1,000 mg) to minimize infusion-related adverse events (Rybak et al., 2020b). Due to the limit of ≤2,000 mg per dose and of ≥1 h infusion per 1,000 mg, it is understandable that VAN with 2–3 h infusion is the most frequent, especially at a conventional dose. Therefore, infusion parameters, i.e., τ of 8 h or 12 h and t _inf of 2–3 h, were simulated in the current study.

The MCS method has been commonly used in antimicrobial PD studies to determine the appropriate dosage regimens for further clinical development, to help the selection of clinically relevant susceptibility breakpoints, to ascertain the effect of changing administration techniques (such as altering infusion duration) on an agent’s PD parameter of interest, or to even compare different antibiotics against selected populations of bacteria (Ambrose and Grasela, 2000; Drusano et al., 2001; Ambrose et al., 2003; Mouton et al., 2004). Regarding the principles, software application and specific implementation of the MCS method, they have been well described elsewhere (Moine et al., 2016; Song and Long, 2018; Song et al., 2021). Briefly, it is to integrate the simulated variables to estimate the predictive variable. Oracle Crystal Ball software (version 11.1.2; Decisioneering, Inc., Denver, CO, United states) was used to perform MCSs, and the physiology parameters (i.e., CL _cr and TBW), infusion parameters (i.e., τ and t _inf), and PD parameters (i.e., MIC and AUC₂₄) as the simulated variables were incorporated into the final D _van model to estimate the D _van value. Since the MCS method simulates thousands of patients at given simulated parameters, it is important to acknowledge assumptions made regarding the variability in these parameter estimates. Based on the characteristics of the simulated variables, custom distributions for τ and MIC and uniform distributions for CL _cr , TBW, φ, and t _inf were assumed in the present study. In our analysis, a 5,000-subject MCS was performed, and the confidence interval was set to 95%.

The results of MCSs are most commonly reported as: 1) the likelihood of a dosage regimen obtaining the targeted exposure for bacterial isolate with a specific MIC, referred to as the PTA or 2) the overall probability of a dosage regimen obtaining the targeted target for a bacterial population with pooled MICs, referred to as the CFR (Mouton et al., 2005). Regimen with the highest PTA or CFR would be optimal, as they would provide the highest likelihood of obtaining the targeted exposure for bacterial isolate or population. In antibiotic treatment, CFR and PTA are often used to measure the clinical acceptability of a dosage regimen. A 90% of PTA or CFR was assumed acceptable in clinic. With MCSs, a PTA-D _van (for bacterial isolate or a determinate MIC) or CFR-D _van (for bacterial population or pooled MICs) diagram, with D _van as the abscissa and PTA or CFR as the ordinate, was obtained. The desired D _van at the designated PTA or CFR target was acquired by assigning the PTA or CFR as the designated target value. D _van that maximized the PTA or CFR of simulated patients to 90% was defined as sufficient and acceptable.

According to the predicted D _van, a VAN-dose-graphical tool with CL _cr as the abscissa, TBW as the main ordinate, and MIC or pathogen population as the secondary ordinate can be drawn. According to the predicted D _van and τ, the predicted VAN dosage regimens can be determined and expressed in the form of “D _van (mg/day) divided every τ hours (i.e., D _van/(24/τ), q τh).”

On the basis of the dynamic monitoring of physiological variables of the target patients (e.g., CL _cr and TBW) and pathogenic variables (e.g., pathogen MIC) and the established VAN-dose-graphical tool, a programming process of VAN dosage dynamic adjustment can be formulated.

Daily doses divided every 8 h or 12 h at various MICs are displayed in Figure 2. At an AUC₂₄/MIC target of 400–600 and with a PTA of 90% as the clinical acceptability, VAN with approximately 270 mg/day for isolate with an MIC of 1 mg/L, 530 mg/day for isolate with an MIC of 2 mg/L, and 1,060 mg/day for isolate with an MIC of 4 mg/L in patients with CL _cr of 10–30 ml/min should be needed when administered every 8 h, regardless of TBW. However, approximately 740 mg/day for isolate with an MIC of 1 mg/L, 1,500 mg/day for isolate with an MIC of 2 mg/L, and 3,000 mg/day for isolate with an MIC of 4 mg/L may be requisite in patients with CL _cr of 31–60 ml/min. With an increase of CL _cr to 61–90 ml/min, VAN with approximately 1,400 mg/day for isolate with an MIC of 1 mg/L, 2,800 mg/day for isolate with an MIC of 2 mg/L, and 5,600 mg/day for isolate with an MIC of 4 mg/L should be administered. As the CL _cr continues to increase, however, >2,000 mg/day for isolate with an MIC of 1 mg/L, >4,000 mg/day for isolate with an MIC of 2 g/day and >8,000 mg/day for isolate with an MIC of 4 mg/L may be necessary. Unexpectedly, compared with the dosage regimen administered every 8 h, when VAN was administered every 12 h, approximately 12%–18% of these daily doses should be given additionally to obtain the desired AUC₂₄/MIC and PTA targets.

Figure 2 shows the VAN-dose-graphical tool for pathogen isolate with a definite MIC. It showed the potential VAN dosage regimens at different CL _cr, TBW, and pathogen MIC.

Daily doses divided every 8 or 12 h at pooled MICs are presented in Figure 3. At an AUC₂₄/MIC target of 400–600 and with a CFR of 90% as the clinical acceptability, VAN with approximately 250 mg/day for current SA, CNS, and SH populations and 360 mg/day for current SE populations may be adequate in patients with CL _cr of 10–30 ml/min when administered every 8 h, regardless of TBW. However, approximately 670, 600, 900, and 640 mg/day for current SA, CNS, SE, and SH populations, respectively, in patients with CL _cr of 31–60 ml/min, and 1,300, 1,000, 1,600, and 1,200 mg/day for these populations in patients with CL _cr of 61–90 ml/min should be administered to reach the desired AUC₂₄/MIC and CFR targets. As the CL _cr increases to 91–120 ml/min, approximately 2,000, 1,400, 2,400, and 1,700 mg/day for current SA, CNS, SE, and SH populations, respectively, may be requisite for attaining the desired AUC₂₄/MIC and CFR targets. However, approximately 2,000 mg/day for SH and CNS populations, 3,100 mg/day for SE populations, and 2,600 mg/day for SA populations may be necessary for these targets when patients have CL _cr of 121–150 ml/min. Interestingly, compared with the dosage regimen administered every 8 h, when VAN was administered every 12 h, approximately 7%–20% of these daily doses should be given additionally to obtain the desired AUC₂₄/MIC and CFR targets. The appearance of subparallel shape for D _van versus TBW and of stepped shape for D _van versus CL _cr , shown in Figure 4, implies that not TBW but CL _cr appears to have a significant association with D _van , regardless of whether VAN is administered every 8 or 12 h.

Figure 3 shows the VAN-dose-graphical tool for pathogen populations or species with pooled MICs. It showed potential VAN dosing regimens at different CL _cr , TBW, and pathogen species.

The formulation process of VAN dosage dynamic adjustment is shown in Figure 5. Four steps are included as follows: 1) estimating the renal function of the patient via laboratory tests; 2) obtaining dynamic serum creatinine levels and pathogen MIC or species; 3) calculating dynamic CL _cr levels by the Cockcroft–Gault method (Cockcroft and Gault, 1976); and 4) obtaining dynamic D _van in Figure 2 (for isolate with a definite MIC) or Figure 3 (for pathogen populations) to develop dynamic VAN dosing regimens. For details of formulation process of VAN dosage dynamic adjustment, see Supplementary Appendix S2: A short case report.

Many studies (Moise et al., 2000; Jeffres et al., 2006; Neuner et al., 2010; Kullar et al., 2011; Holmes et al., 2013) that advocate a target VAN AUC for the AUC₂₄/MIC ratio of 400 predict the AUC using a model established on CL _van and CL _cr , i.e., AUC₂₄ = dose per 24 h/[CL _cr × 0.79 + 15.4]×16 (also AUC₂₄ = D _van /CL _van ), which was derived from previous studies (Rodvold et al., 1988; Moise-Broder et al., 2004). In the estimation of VAN response, this application is also a consistent practice in most current studies (Moise-Broder et al., 2004; Jeffres et al., 2006; Holmes et al., 2013; Lewis, 2018). However, this simplified model for determining the AUC may cause deflected estimation, since 1) in this model, the impact of infusion time and rate on AUC₂₄, which is quite important in the administration mode of using prolonged infusion, was not well considered. Of interest, VAN is just such an antibiotic that requires prolonged infusion. Understandably, ignoring the effect of these factors on AUC may result in an inaccurate AUC assessment; 2) this model is derived from the administration mode of using intravenous bolus and is therefore not well appropriate for antibiotics requiring prolonged infusion, such as VAN; and 3) the AUC₂₄ determined by this model is measured based on a single dose and is referred to the total exposure from 0 h to infinity (i.e., AUC_∞) (Rosenbaum, 2011; Drennan et al., 2019), in spite of a dose per 24 h used in this model. Understandably, this model is not well suitable for the situation of using multi-dose and intermittent administration. Thus, we derived the modified AUC₂₄ model based on the classical PK formulas derived from the administration mode of using intravenous infusion and further obtained the D _van model. Conceivably, these models improve the predictability of outcomes.

The application of our results to clinical practice would consist of using Figures 2, 3 as nomograms to obtain, depending on the patient’s TBW and CL _cr, the optimal VAN daily dosage for the treatment of infection due to the simulated Staphylococcus spp. These nomograms provide us with very useful directions on estimated VAN dosage regimens, regardless of whether VAN is used in empirical or follow-up therapy.

In empirical therapy, due to the unavailability of the pathogen species and susceptibility before VAN therapy, one useful approach for formulating VAN dosage regimens in MCSs could be to use the cumulative probability of achieving the target exposure against a causative pathogen population to screen the regimens. The nomograms inform us that at a CFR of 90% as the clinical acceptability, a standard VAN dosage of 2,000 mg/day is often sufficient for SH and CNS populations even in infected patients with CL _cr of up to 121–150 ml/min. This is also the case for the SA population, but for these patients, approximately 2,500–3,000 mg/day should be requisite if VAN is used to resist the SA population. However, for the SE population, the dosage of 2,000 mg/day is adequate only for patients with CL _cr of ≤90 ml/min. Understandably, this standard schedule seems preferable for the treatment of Staphylococcus spp. infection occurring in patients with CL _cr of ≤90 ml/min, implying that it should be questioned when used in those with CL _cr of >90 ml/min. Consistently, del Mar Ferna′ndez de Gatta et al. (2009) also questioned this standard schedule since very low CFRs were observed in patients with CL _cr of even >60 ml/min when this dosage was simulated against Staphylococcus spp. (a CFR of <60% for SA population, <40% for CNS population and SH population, and <30% for SE population).

In follow-up therapy, with availability of the bacterial culture and susceptibility test, one useful approach for formulating VAN dosage regimens in MCSs could be to use the PTA of achieving the target exposure against a causative isolate or a definite MIC. From these nomograms, it can be seen that at a PTA of 90% as the clinical acceptability, when VAN is used to resist Staphylococcus spp. isolates with an MIC of 1 mg/L and administered every 8 h, a dosage of approximately 270, 740, 1,400, 2,100, and 2,800 mg/day for patients with CL _cr of 10–30, 31–60, 61–90, 91–120, and 121–150 ml/min, respectively, may be required, regardless of the patient’s TBW. Interestingly, when VAN is used to resist Staphylococcus spp. isolates with an MIC of 2 and 4 mg/L, approximately twice and four times the aforementioned dosage, respectively, may be needed. Speculatively, a VAN dosage of standard 2,000 mg/day might be more suitable for the treatment of Staphylococcus spp. infection due to isolates with MICs of ≤1 mg/L and for patients with CL _cr of ≤90 ml/min, and a dosage of tolerable 4,000 mg/day might be more suitable for the treatment of Staphylococcus spp. infection due to isolates with MICs of ≤2 mg/L and for patients with CL _cr of ≤90 ml/min. Thus, a VAN dosage of 2,000 mg/day as a standard regimen for isolates with MICs of >1 mg/L might be questioned although part of these isolates, such as those with MICs of 1–4 mg/L, are currently considered susceptible to VAN.

Of interest, these nomograms also informed us that to achieve the desired AUC₂₄/MIC and PTA or CFR targets, the D _van at the regimen of dosing every 12 h appeared to be significantly higher than that at the regimen of dosing every 8 h, regardless of the patient’s TBW and CL _cr . It suggested that at the same VAN daily dose, the administration mode using multiple dosing may be more competitive. Furthermore, to achieve the desired AUC₂₄/MIC target, the VAN dosage must vary with CL _cr . This is very important for patients with acute renal impairment or recovery since fluctuant renal function, which is reflected by changed CL _cr , will cause altered VAN exposure and resultant efficacy or nephrotoxicity. Fortunately, these charts provide useful directions on VAN dosage used at different renal function stages. In addition, for any one of the physiology-infection states consisting of TBW–CL _cr –MIC or pathogen species, the nomograms afford the estimated VAN dosage. Combined with the formulation process of VAN dosage dynamic adjustment described in Figure 5, clinicians can easily formulate an optimal VAN dosage regimen for the target patients based on these factors, regardless of whether VAN is used in empirical or follow-up therapy.

Another interesting phenomenon is that a subparallel shape of D _van vs. TBW and a stepped shape of D _van vs. CL _cr were observed, as shown in Figure 4. It suggested that not TBW but CL _cr creates significant influence on the determination of D _van , thus implying that a “one dose fits all TBW” approach seems feasible in the patients with hematological malignancies when they have relatively stable renal function. However, this dosing approach is inconsistent with the TBW-based dosing approach recommended in the 2020 VAN therapeutic guideline (Rybak et al., 2020b). However, this guideline does not offer specific dosage regimens or recommendations about VAN used in cancer patients (Rybak et al., 2020b).

From these PK/PD analyses, the need for dosage, tailored according to population kinetics (mainly CL _cr ), pathogen susceptibility (mainly MIC), and dosing strategy (mainly τ), seems evident. These considerations make it clear that the traditional “one dose fits all cases” approach to VAN, although logistically attractive, is grossly flawed. However, these optimal regimens based on the PK/PD strategy cannot replace a clinical study, and the possibility of VAN nephrotoxicity, especially at a high estimated dosage, is another important issue that should be noted before its use in the clinical setting (Jeffres et al., 2007; Ingram et al., 2008; Lodise et al., 2008). Therefore, we suggest the use of these initial regimens but followed by therapeutic drug monitoring, which is cost-effective in this population (de Gatta et al., 1996). Also, it could be useful to investigate nephrotoxicity associated with a higher VAN dosage.

As a tool to assist prescribers in constructing dosing regimens, the MCS method has been widely used in optimized antibiotic therapy. MCS-based feasibility for optimizing exposure to improve antimicrobial effectiveness has been expounded and applied in OPTAMA studies (Kuti and Nicolau, 2005), and MCS-indicated theoretical efficacy has been demonstrated by Eguchi et al. (2010) in an in vitro PD model study on meropenem against P. aeruginosa, in which in vitro viable cell counts of P. aeruginosa strain was used as a measure for in vitro bactericidal activity of meropenem. Thus, we believe that our approach is appropriate since VAN population PK models used were derived from the patients with hematological malignancies (Buelga et al., 2005), and PK variability was taken into account; the PD target was adopted from the 2020 VAN therapeutic guideline (Rybak et al., 2020b); the MIC values correspond to those reported in the ATLAS database (The Micron Group, 2022); and the emulation infusion parameters were derived from medication practice. Therefore, the results on VAN dosage could be applied if the patient and pathogen populations match those considered here. If this was not the case, the same methodological procedure could be followed, but the actual PK (relationship between CL _van and CL _cr and V _d and TBW due to patient variables) and PD modeling (MIC distribution) would have to be used. It should be pointed out that other factors in addition to the AUC₂₄/MIC ratio have been reported as variables affecting the clinical outcome of patients treated with VAN, such as immunocompetence, which may even demand higher PK/PD targets (Schentag, 2001). Of note, this factor should be attached more importance in cancer patients because these populations often have altered immunocompetence due to their chemotherapy or biotherapy. Also, if clinical trials could define the targets for such patients, our methodological approach would still be valid. Also, local resistance data would improve the reliability of the predictions. Although this model analysis lacks sufficient power to detect clinical outcomes to some extent, our results provide further justification for prospective clinical trials aimed at evaluating the potential influence of a pharmacodynamically targeted VAN dosing schedule on the clinical outcomes of this population.