Vancomycin population pharmacokinetic modeling in children using Bayesian estimation and a Non Parametric Approach

To analyze microbiological effectiveness of vancomycin in children from a pediatric hospital through population pharmacokinetic modelling, as well as to propose dose adjustment, a cross-sectional study was performed in children under vancomycin treatment from the John Paul II Children’s Hospital, MG. In order to establish a model, concentrations versus time curves were analyzed using a population pharmacokinetic approach with Pmetrics® . Seventeen blood samples of 10 patients were collected. The best model to describe vancomycin population pharmacokinetic (PK) consisted of a two-compartment linear intravenous absorption model. The R² value and bias for population and individuals in observed versus predicted plot was 0.642 vs. 0.992 and the bias of 0.41 mg/L and 0.0778 mg/L, respectively. The covariables creatinine clearance, age, and body mass index were related to vancomycin PK. A relevant PK variability for vancomycin in pediatric patients was verified, which was significantly influenced by creatinine clearance, age, and body mass index. This result justifies the formulation of dosing recommendations for vancomycin in pediatric patients to achieve adequate pharmacodynamics targets.


INTRODUCTION
Vancomycin is classified as a glycopeptide antibiotic with activity predominantly against Gram-positive bacteria,. Known since 1956, it is the drug of choice in the treatment of methicillin-resistant Staphylococcus aureus (MRSA) infections both in adult and pediatric populations, despite its ototoxic and nephrotoxic effects (Liu et al., 2011). Previous reports have demonstrated that for adults and serious susceptible MRSA infections, a vancomycin exposure target of area-under-the-curve of the serum concentrations vs. time over 24 h to minimum inhibitory concentration (AUC/MIC) ratio ≥ 400 improves treatment success, which correlates to trough concentrations between 15 and 20 mcg/mL (Rybak et al., 2009;Kullar et al., 2012;Dalton et al., 2020).
To optimize vancomycin exposure, current Infectious Diseases Society of America (IDSA) guidelines recommend vancomycin of 60 mg/kg/day empirically for treating suspected serious MRSA infections in children. In Brazil, the empirical dose usually used to treat these infections is 40 mg/kg/day (Liu et al., 2011;Hoang et al., 2014). A large population-based pharmacokinetic (PK) study in pediatric patients demonstrated that a vancomycin dose of 60 to 70 mg/kg/day was necessary, depending on age, SCr, and MIC distribution to achieve the therapeutic Anna Luísa Oliveira Silveira, Geisa Cristina da Silva Alves, Jiao Xie, Jason A Roberts, Cristina Sanches target of AUC/MIC ≥ 400 (Le et al., 2013). However, available data for vancomycin dosing in children is still scarce (Alves et al., 2017) Although European and North American guidelines provide an excellent reference for the treatment of MRSA infections, the ideal would be to guide this therapy by local factors, including the probable sources of infection and the risk factors associated with the patient. Additionally, to guide the empirical choice of initial antibiotic therapy, as well as to make it easier for adequate treatment, updated epidemiological data on the local incidence of pathogens and resistant strains, as well as a precise microbiological diagnosis and antibiotic susceptibility tests are necessary. Therefore the present study sought to analyze vancomycin microbiological effectiveness in children from a local pediatric hospital, through population pharmacokinetic modelling.

Setting
This was a cross-sectional PK study conducted at the John Paul II Children's Hospital (HIJPII/FHEMIG, 2016) between April 2016 and December 2016.

Ethics
Ethics approval was obtained from the Ethics Committee of the Hospital Foundation of Minas Gerais (approval reference number: 3388/22712016) and from the local Ethics Committee of the Federal University of São João del Rei (approval reference number: 1,422,909), both in March 2016. Informed consent was obtained from all participants included in the study. Children and legal guardians were invited to participate and to sign the Written Informed Consent and Term of assent. All procedures were in accordance with the Helsinki Declaration and with the 466/2012 resolution.

Study population
The inclusion criteria were: age between 2 and 12 years and antibiotic treatment with vancomycin for at least five biological half-lives (steady-state). Exclusion criteria were: renal replacement therapy patients and/or burns patients.

Dosing, administration, and data collection
Vancomycin dosing was at the physician's discretion according to the recommendations of the local Hospital Infection Control Committee. Antibiotic infusion was performed by infusion pump or micro drops.
Clinical and demographic data included age, gender, weight, height, body mass index, admission, admission unity, treatment, antibiotic infusion time, culture results, minimum inhibitory concentration, surgeries, drains, central and peripheral venous catheters, intra-arterial puncture, catheterization, naso-orotracheal intubation, and main exams. Height and BMI, when not available in medical records, were estimated from the values of anthropometric data available at the National Center for Health Statistics from the Centers for Disease Control and Prevention (CDC, 2017), where the data are estimated according to the age of each child and compared with the table of weight and height from NCHS 77/8 of the Brazilian pediatric society. Additionally, renal clearance (ClCr) was calculated trough the Schwartz et al. (1976) equation, which applies a constant related to age and gender; pharmacokinetic parameters of volume of distribution (V), elimination constant ratio (Kel), and drug clearance (Cl) were calculated by the model.

Sample collection, handling, storage, and measurement
Respecting the period of five half-lives to reach steady-state, two blood samples were taken from a venous catheter and / or arterial catheter (2 mL / collection in Vacutainer / Sodium EDTA bottle), with a minimal interval of 2 h for each patient. Blood samples were centrifuged (Centrifuge Excelsa Baby® I 206) within 15 minutes at 3500 rpm. The plasma supernatant (500 μl) was transferred to an eppendorf tapered tube with a 10 % solution (500 μl) of MOPS (3-[N-morpholino] -propanesulfonic acid, J.T.Baker®) and stored at -80 ºC until analysis, not exceeding six months. Samples were analyzed by high performance liquid chromatography (HPLC) according to Alves, Chequer and Sanches (2019).

Population PK modelling
In order to develop a model, one-and twocompartment models were tested in the Nonparametric Adaptive Grid algorithm with Pmetrics®, a package for R® (Los Angeles, CA, USA). Lambda and Gamma error models were tested for inclusion. Additionally, demographic and clinical characteristics, such as weight, age, gender (male), serum creatinine, intensive care unit, creatinine clearance, and body mass index, for affecting vancomycin pharmacokinetics were also tested for inclusion as covariates when they lead to any improvement in the coefficient of determination of linear regression (R²), or also in a reduction of the bias of the goodness-of-fit plots, as well as in a statistically significant reduction in log-likelihood (P<0.05). A similar analysis was performed for each run, where those same parameters were taken into account for the goodness-of-fit evaluation.

Model diagnostics
To evaluate the predictive performance, mean biasadjusted squared prediction error (imprecision) and the bias of the population and individual prediction models were analyzed. Visual predictive check plot and the normalized prediction distribution errors, as well as weighted residual plots versus time and concentration were used to test the suitability of the final covariate model.

Pharmacokinetic model building
Based on the model building, the best model consisted of a two-compartment linear intravenous absorption model with an additive error to describe the concentration-time data of the total plasma concentrations of vancomycin. The R² value and bias for population and individuals in observed versus predicted plot was 0.642 vs. 0.992 and the bias of 0.41 mg/L and 0.0778 mg/L, respectively (Figure 1 (A), (B)).  The inclusion of the normalized covariables creatinine clearance, age, and body mass index resulted in a statistically significant improvement of log-likelihood, the goodness-of-fit plots from the former model (R²< 0.2), as well of the R² value, being thus included in the final equation. The final model was represented by the following equation: CL=CLni*((CLcr/218)**0.75)*((age/7)**0.75)*16.7/BMI &IF(ICU.EQ.1) THEN CL=CLi*((age/7)**0.75)*16.7/BMI V=Vni &IF(ICU.EQ.1) THEN V=Vi Ke=CL/V Where, CL ni is the clearance for patients not admitted to the ICU; ClCr is the covariable creatinine clearance; BMI is the covariable body mass index; CL i is the clearance for patients admitted to the ICU; V is the volume of distribution; ICU is the covariable intensive care unit; V i is the volume of distribution for patients admitted to the ICU; V ni is the volume of distribution for patients not admitted to the ICU and Ke is the elimination rate constant.
The mean (SD) population PK parameter estimates from the final equation are displayed in Table II.
The goodness-of-fit of the chosen model are displayed in Figure 1 (C).   Grace (2012) found an altered volume of distribution of vancomycin in obese patients when compared with non-obese patients associated with those factors. Finally, a higher drug transfer rate from the central compartment to peripheral compartment than peripheral compartment to central compartment was verified, evidencing the wide vancomycin distribution in tissues, with a decreased return, despite its hydrophilicity (Hanrahan, Lipman, Roberts, 2016).
Two-compartment pharmacokinetic models for vancomycin in pediatric patients have been previously described in the literature (Seay et al., 1994;Capparelli et al., 2001;Marsot et al., 2012;Moffett et al., 2018). Similarly, Neely et al. (2014), describes a twocompartment model for vancomycin, parameterized with first order elimination (Ke) from the central compartment with a volume (Vc) and linear transfer to (KCP) and from (KPC) the peripheral compartment.
Nevertheless, there are a few methodological limitations in this report. First the sample size, which can compromise the model predictive capacity. Second, this study was not delineated to measure clinical outcomes, such as the development of bacterial resistance. However, this study can provide a strong positive impact on the patient's prognosis, since the knowledge of their pharmacokinetics and pharmacodynamics influence control of the infection.

DISCUSSION
Although there are a few previous reports evaluating vancomycin kinetics in children (Hoang et al., 2014;Moffet et al., 2018;Hahn et al., 2015;Krivoy et al., 1998;Tkachuk, Collins, Ensom, 2018), this is a pioneering study conducted in Brazilian patients. The results show that glycopeptide pharmacokinetics is related to creatinine clearance, age, and body mass index. In addition, the proposed model has a good predictive capacity, both for individuals (r²= 0.992) or population (r²= 0.642) and predicts individual concentrations well, supporting its choice for Gram-positive pathogens that remain resistant, such as MRSA.
Several factors affect vancomycin pharmacokinetics, especially the covariable age. Studies on preterm newborns have shown that the pharmacokinetic parameters of vancomycin are influenced not only by gestational age, but also and more significantly, by post conceptual age and body weight. In older children, an increased vancomycin body clearance with age, with a peak around 4 years was demonstrated (Spivey, Gal, 1986;Schaad, McCracken, Nelson, 1980;Sande, Mandell, 1991), justifying a higher final clearance than the initial clearance. n addition, the body mass index influence on vancomycin kinetics has been described in previous reports (Pan et al., 2020;Leong, Boro, Winter, 2011;Vance-Bryan et al., 1993;Bauer, Black, Lill, 1998). Vance-Bryan et al. (1993) verified that an increase of 10 Kg in total body weight would increase the CONCLUSION In this study, we verified a relevant pharmacokinetic variability for vancomycin in pediatric patients, more significantly for the final volume of distribution, which showed the highest coefficient of variation. Further studies are required to validate our findings.