Vancomycin is a tricycle glycopeptide antibiotic derived from Streptomyces orientalis, first used in 1958; by inhibiting the synthesis of the wall, it achieves a high bactericidal power against methicillin-resistant Staphylococcus aureus (MRSA), methicillin-susceptible Staphylococcus aureus (MSSA), streptococci, enterococci and Clostridium difficile. ^{1 , 2} Pharmacokinetic and pharmacodynamic studies of vancomycin suggest that prior trough monitoring is associated with increased nephrotoxicity, with rates between 5% and 43%, related to high doses or high levels of exposure, mainly in special populations such as elderly and critically ill patients. ^{3 , 4} Therefore, the current dosing and monitoring recommendations of the revised consensus guideline and review by ASHP/PIDS/SIDP/IDSA establish an AUC/MIC ratio of 400–600 h ⁻¹ (assuming a MIC of 1 mg/L) to achieve clinical efficacy and ensure safety for patients treated for serious MRSA infections. ⁵

Although therapeutic drug monitoring (TDM) for vancomycin remains controversial, it has been shown to significantly increase the rate of clinical efficacy and decrease the rate of nephrotoxicity. ⁵ TDM of Vancomycin is essential for the development of PopPK models by the use of Bayesian software for AUC estimation and model-informed precision dosing (MIPD), which has been improved outcomes in patients with culture-proven gram-positive infections just with a single concentration monitoring. ⁶ The PopPK modeling plays a crucial role in optimizing drug dosing regimens, particularly for drugs with a narrow therapeutic index (NTI). NTI drugs, where small changes in drug concentration can result in significant therapeutic consequences, require precise dosing to maximize efficacy and minimize toxicity. ⁷ PoPK models enable the integration of various physiological, biochemical, and drug-specific factors to predict drug behavior in different patient populations. By simulating a range of dosing scenarios, these models allow for the identification of optimal dosing strategies that balance therapeutic benefit with safety, ensuring that NTI drugs achieve their intended clinical outcomes while avoiding adverse effects. This modeling approach is essential for personalizing therapy, reducing the risk of underdosing or overdosing, and improving patient outcomes. ⁸

PopPK is an emerging discipline developed from the combination of classical pharmacokinetic compartment model and statistical principles, which helps to achieve the preliminary prediction of parameters. ⁹ Despite having been described more than 30 years ago, PopPK models are not widely used due to mathematical complexity, the variety of the study population and limited access to software. ¹⁰ This review aims to summarize the main models, software, parameters and covariates in non-critical adult patients that can be used in future applications for MIPD.

We developed and performed a scoping review of existing reports about PopPK models of vancomycin in adult population out of intensive care. The research protocol was reviewed and approved by the research subcommittee of School of Medicine of Universidad de La Sabana. The review follows the guidelines of Preferred Reporting Items for Systematic reviews and Meta-Analyses Extension for Scoping Reviews (PRISMA-ScR) and the Johanna Briggs Institute. ^{11 , 12} Reporting checklist extended data E1.

The primary review question was formulated using the population, concept, context framework, as “What are the published vancomycin population pharmacokinetic models with non-critically ill hospitalized adult patients?”. Search criteria were established to include studies with: (1) original vancomycin PopPK models, (2) adult patients, and (3) non-critical ill patients; articles were excluded if they: (1) are the wrong publication type, (2) patients are hospitalized in the intensive care or burn unit, (3) do not define equations or parameters, and (4) have a broad range of patients, including critically ill patients. The search was conducted on November 2, 2024, in PubMed, LILACS, OVID Medline, Scopus, Web of Science, SAGE Journals, and Google Scholar, including reports published after January 1998 and some previously known reports in other similar publications. Search terms submitted to each database are presented in Table 1. Only articles published in English, Spanish, or Portuguese were included in the search. The founded references were uploaded into Rayyan ( http://rayyan.qcri.org; Headquarter: Cambridge, Massachusetts, U.S.A.), which is a free web and mobile app, that helps expedite the initial screening of abstracts and titles using a process of semi-automation while incorporating a high level of usability. ¹³ First the detected duplicates in data summary was eliminated by preliminary revision, then the reports were screened and selected for the full text screening to check over the inclusion and exclusion criteria.

We identified 180 records in databases and 10 registers previous included in others publications. ¹⁴ After removing duplicates, 155 records remained for screening; 100 were eliminated due to exclusion criteria and 55 reports were assessed for eligibility for full text review; finally, 36 studies were included for this review ( Figure 1).

In order to organize the information, they were divided into 8 groups of patients, general (12), ^{15 – 26} surgical (5), ^{27 – 31} with impairment kidney function (7), ^{32 – 38} obese (3), ^{39 – 41} geriatrics (4), ^{42 – 45} with cancer (4), ^{15 , 46 – 48} patients with cystic fibrosis (1) ⁴⁹ and trauma patients (1). ⁵⁰ Studies published from 1998 to 2024 were found, the mean study by year was 2.3 with an standard deviation (SD) of 1.6 and the years with the highest number of publications were, 2018 (6), 2020 (5), 2019 (4) and 2024 (4). Predominantly, publications of Asian, Middle Eastern, North American and European origin were found; the countries with the highest number of publications were China (9), Japan (6), South Korea (5) and the United States of America (USA) (5). Regarding the design of the study, 27 (75%) were retrospective and 9 (25%) were prospective; the mean of sample size was 217 and SD of sample size was 434,4 (biased by the study of Pai and DeBacker ³⁶ with 2640 patients). 22 (61.1%) of the models were one-compartment and 14 (38.9%) were two-compartment.

The most commonly used software was NONMEM in 28 studies (77.8%), followed by Monolix 5 (13.9%), Phoenix 2 (5.6%) and R environment with Pmetrics package 1 (2.8%), therefore, 32 (88.9%) of the studies performed a primary analysis and development of the model with Nonlinear mixed-effects modeling (NLME), followed by 3 (8.3%) that used stochastic approximation expectation maximization (SAEM) and 2 (2.8%) performed with nonparametric adaptive grid (NPAG); the most used secondary analyses were first-order conditional estimation (FOCE), first-order conditional estimation with interaction (FOCEI) and first-order conditional estimation with extended least square method (FOCE-ELS) with 19 (52.8%) studies, in addition to objective function value (OFV) with 17 (47.2%) studies and generalized additive model (GAM) with 1 study (7.7%). Almost all models reported internal evaluations, 35 (97.2%) studies, 25 (86.2%) of which reported bootstrap simulations and the methods generally used were goodness-of-fit plots model (GOF), visual predictive checks (VPC), prediction- and variability-corrected VPC (pvcVPC) and numerical predictive check (NPC); only 4 studies reported external evaluations. ^{19 , 21 , 47 , 50} A summary of demographics and PopPK modeling methods for all the included studies is presented in Table 2.

The combined mean and combined SD of age did not differ much from the combined means and SD by groups, being for all 59.74 years and 17.24 years respectively; as for the total body weight (TBW) the obese group presented a combined mean of 131.62 kg with a combined SD of 31.59 kg, while the total of the groups had a combined mean of 76.98 kg and a combined SD of 21.25 kg; for the estimated glomerular filtration rate (eGFR) greater heterogeneity was found, since in the group with impaired kidney function the combined means and SD were 59.55 ml/min and 44.54 ml/min respectively, while in the total the combined mean of the eGFR was 80.42 ml/min and the combined SD was 54.07 ml/min (see Extended data E2 Additional results tables).

Most of the equations presented by the PopPK models are in the form in which the expressions for clearance (CL), distribution volumes (V _i), intercompartmental clearance (Q) and elimination transfer rate constants (k ₁₂, k ₂₁), are equal to the estimates of the population mean of each study (CLpop, V _ipop, Qpop, k ₁₂pop, k ₂₁pop) or typical values (TVCL, TVV _i, TVQ, TVk ₁₂, TVk ₂₁), which as in the case of CL are generally affected proportionally or additively by covariates, in greater proportion by the renal clearance (CL _CR) or the estimated glomerular filtration rate (eGFR) by Cockroft-Gault, although the studies by Chung et al. ¹⁷ and Ling et al. ⁴² uses cystatin C to affect the TVCL or the study by Medellín-Garibay ⁵⁰ and Wei et al. ³¹ they associate furosemide or mannitol respectively as factors that alter eGFR, for these models serum creatinine or CLCR are also included as covariates. Furosemide was not directly used to estimate the glomerular filtration rate (GFR). Instead, it was administered as part of a furosemide stress test, which has been proposed as a functional marker of renal reserve. This test assesses renal response to a standardized dose of furosemide and has been used to predict acute kidney injury (AKI) progression in critically ill patients. However, in the context of the referenced study, cystatin C was the primary biomarker used for GFR estimation.

To a lesser extent, total body weight (TBW) or age are reported as covariates for TVCL, other models include clinical conditions such as the use of hemodialysis (HD), ^{16 , 35} continuous renal replacement therapy (CRRT) ¹⁶ or intermittent renal replacement therapy (IRRT) ³⁷ ; there are models such as that of Kim et al. ²⁹ that includes as covariates being a neurosurgical patient, presenting underlying liver cirrhosis or co-administration of nephrotoxic drugs; the most recent model such as that of Tsuda et al. ⁴⁸ even includes quick SOFA (qSOFA) as a covariate. Other covariates only presented once per model, such as sex, ⁴⁰ daily dose of vancomycin and AST, ³⁸ albumin ²⁷ and post-craniotomy meningitis. ⁴⁴

Regarding distribution volumes, they are most commonly reported as equal to TVVi if expressed in liters (L) or as the relative TVVi by TBW if expressed in L/kg. In some equations, age can also influence these values. The most reported equation patterns for CL, V _i, Q, k12, and k21 are: CL = TVCL × CL CR / CL ¯ CR θ CL CR CL = θ CL CR × CL CR CL = TVCL CL = TVCL + θ CL CR × CL CR CL = TVCL × TBW / TBW ¯ θ TBW CL = TVCL × CL CR / CL ¯ CR CL = TVCL × CL CR / CL ¯ CR θ CL CR × TBW / TBW ¯ θ TBW V i = TVV V i = TVV × TBW Q = TVQ k 12 = TVk 12 k 21 = TVk 21

The main features and values of the equations, parameters, population mean (VT) and variability are shown in Table 3. Many of the studies do not explicitly show TV for which we calculate with measures of central tendency for the reported covariates and substituting them in the covariate equations in the final model; although most studies with two-compartment models reported parameters in the form of flow rates (CL and Q), two studies reported model parameters in the form of elimination, transfer rate constants (k ₁₂, k ₂₁) were presented, in order to make comparisons among studies, the conversion of parameters in the form of flow rates was implemented with the following equation: Q = k 12 × V 1

To perform an analysis of the TV, the combined means of all studies and also by compartments were calculated; the complete results are found in Supplementary data S2. The TVCL for all studies was 3.02 L/h; by groups the TVCL was 3.76 L/h for the general population, 7.08 L/h for surgical patients, 0.5 L/h for the group with impaired renal function, 5.61 L/h for obese patients, 3.31 L/h for geriatric patients, 4.38 L/h for patients with cancer, 5.52 L/h for cystic fibrosis and 2.6 L/h for trauma patients; when separating the patients without impaired renal function, the TVCL is 4.5 L/h, which differs substantially from that reported in the group with impaired renal function and shows the change with respect to the TVCL of all studies when eliminating those with the lowest clearance.

The TV of the central distribution volume (TVVc) for all studies was 58.24 L, by groups the TVVc was 42.74 L for the general population, 57.93 L surgical, 64.8 L for the group with impaired renal function, 71.01 L obese, 82.3 L geriatric, 47 L with cancer, 31.5 L with cystic fibrosis and 74.4 L for trauma patients; the TVVc without the obese, geriatric and trauma group is 54.78 L, while in the obese, geriatric and trauma group the TVVc was 78 L. The TVCL for single compartment models was 4.38 L/h and TVV was 61.26 L. The TVCL for two compartment models was 2.63 L/h, TVQ was 8.71 L/h, TVV1 and TVV2 were 38.59 L and 96.97 L respectively.

Regarding the variability of the TV, the mean between-subject variability coefficients of CL (ωCL) were 31.44% (max: 99.20%; min: 5.30%), of the central distribution volume (ωVc) 27.29% (max: 54.99; min: 6.34%) and peripheral (ωVp) 49.45% (max: 72.80%; min: 6.80%); and finally the means of additive ( a) and proportional ( b) errors were 6.67 mg/L (max: 55.00 mg/L; min: 6.34 mg/L) and 27.29% (max: 54.99; min: 0.70%) respectively. The previously mentioned results are summarized in Supplementary data S2.

In the precision dosing, the TDM and development of PopPK within the MIPD is relevant to improve efficacy and/or lower toxicity in special populations with high variability, like pediatrics, elderly, those with renal or hepatic impairment and comedicated patients. The translation of this approach personalized medicine requires the implementation of new dosing scenarios, new working paradigms and clinical pharmacology experts and researchers, that are not limited only to the academic area. ⁵¹

NONMEM (ICON, Dublin, Ireland), Monolix (Lixoft, Paris, France) and Phoenix NLME (Certara, Princeton, NJ) are the most widely used nonlinear mixed effects modeling (NLMEM) tools in pharmacometrics. They are commercial offerings with fees substantial licensing costs, and while all have programs aimed at reducing or eliminating licensing costs in educational institutions or low-income countries, the administrative hurdles and associated delays in availability can be cumbersome when conducting analysis and training students and researchers to use these tools in resource-limited settings. Implementation of open-source software based on R and the nlmixr package may be a credible and capable alternative to commercial PK/PD modeling software to fit compartmental of pharmacokinetic/pharmacodynamic (PK/PD) models described by ordinary differential equations (ODEs). Parameter estimation algorithms implemented in nlmixr currently include relatively mature implementations of NLMEM, SAEM, and first-order, first-order with interaction, FOCE, and FOCEI. ⁵²

About the development of PopPK models we can observe for vancomycin it is expected that CL _CR would be the most important covariable in most models and could affect the CL and the prediction of serum vancomycin concentration, it is because vancomycin is excreted 80% to 90% as an unchanged drug in urine ¹⁹ ; conventionally, the eGFR is calculated by the Cockroft-Gault equation, however, the CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration), Modification of Diet in Renal Disease (MDRD) and Berlin Initiative Study 2 (BIS-2) equations has been shown to be more accurate, especially in youngest. ⁵³ This is because, although the Cockcroft-Gault equation is widely used in pharmacokinetic studies and drug dosing adjustments, it has several limitations. It was developed in a specific population, primarily adult males, which limits its applicability to other groups, such as elderly individuals, patients with altered body composition (e.g., obesity, cachexia), or critically ill patients. Additionally, since it relies on serum creatinine levels, it is influenced by factors such as muscle mass, diet, and hydration status, potentially leading to inaccurate estimations of renal function. The equation also lacks standardization across different creatinine assay methods, and its accuracy diminishes in patients with very low or highly fluctuating glomerular filtration rates (GFR), such as those with acute kidney injury (AKI). Moreover, the use of actual body weight can introduce further errors, particularly in patients with obesity or fluid overload. Despite these limitations, the Cockcroft-Gault equation remains widely used due to its historical application in drug dosing guidelines and its inclusion in many pharmacokinetic models.

Ling et al. used to covariate the model CKD-EPIcys and BIS-2 eGFR with specific equations for each one. ⁴² Beyond that, models have always been compared to the CL _CR, including the studies like Tanaka et al. which uses cystatin C, those who consider that this may be more accurate and sensitive than creatinine for calculating eGFR, suggesting that it could be a good predictive marker of CL and vancomycin concentrations. ²³

Great difference was found in TV estimates, the population with significantly higher TVCL and TVV are obese and surgical patients; in both, this finding in TVCL are explained by the augmented renal clearance (ARC) in early stage of the surgical approach or in obese by the compensatory vasodilation of the afferent arteriole, ⁵⁴ also in neurological patients the brain lesions and the loss of autoregulation induced by brain injury may impair the kidney autoregulatory process ²⁹ ; in the obese population because the volume of distribution is linked to weight and also to the constants of CL _CR, it is expected that both the TVCL and the TVV increase. ³⁹ The trauma and elderly have also the highest TVV (central and peripheral) but lowest TVCL; Variability in trauma patients CL is due to the fact that the elimination of vancomycin depending on tubular secretion and the concomitant administration of other drugs, such as furosemide ⁵⁰ ; the renal function of the elderly gradually decreases with age and the larger volume of distribution may be by the changes in the peripheral circulation usually due to poor nutrition, hypoalbuminemia and internal environmental disorders such as hypokalemia, hyponatremia and metabolic acidosis that increased tissue affinity for vancomycin, and the TVV is high because they are attached to the weight. ⁴⁵ In patients with impairment kidney function the heterogenicity of the TVCL it is due to changes in the central compartment generated by renal effect of the vancomycin, dialysis and changes in the ultrafiltration rate of each session, for this reason eGFR estimated by Cockroft-Gault equation is not a reliable marker of renal function. ^{33 , 36 , 37} Patients with above-the-mean vancomycin clearance and volume of distribution typically exhibit pharmacokinetic profiles associated with increased drug elimination and expanded drug distribution. Several factors may contribute to these elevated parameters, including younger age, preserved or augmented renal function, higher body weight, and conditions associated with hyperdynamic circulation, such as sepsis or burns. Higher clearance rates may result in subtherapeutic vancomycin concentrations, potentially reducing efficacy and increasing the risk of treatment failure, particularly in infections caused by less susceptible pathogens. Similarly, an increased volume of distribution may lead to lower peak concentrations, which could impact the drug’s time-dependent antibacterial activity. Given these considerations, patients with above-the-mean clearance and volume of distribution may require individualized dosing strategies, such as higher initial doses, more frequent administration, or therapeutic drug monitoring to ensure optimal target attainment while minimizing the risk of underexposure. ^{55 – 57}

To end when we look at the variability of the models is striking that for the patients undergoing allogeneic transplantation, the models developed indicate a high variability due to high between-subject variability and the difficulty of maintaining the therapeutic range, due to the characteristics of these patients with extremely low hematocrit levels, increased intravascular volume, and increased renal clearance. ^{46 – 48} It is important to note that this review had several limitations. Some of the papers do not specify the clinical and pathological characteristics of the study subjects. The creatinine clearance formulas are different in every article making necessary the classification of every subpopulation before applying the model, the units of measure and the population have great variability. That is the main reason why the comparisons presented are indirect and the generalization of the data that we show must be read carefully.

This scoping review highlights the principal information of different PopPK models, which showed heterogeneity in the parameters and methods of analysis and evaluation, even if these methods can be used to guide the dosing regimen in different subpopulations, it is imperative to conduct experiments with local samples to define the best fit in the different subpopulation.