Clinical Application of Vancomycin PPK Model in Patients with Neutropenia

Background: To explore the clinical application of a population pharmacokinetics (PPK) model of vancomycin in patients with hematological diseases who developed neutropenia. Methods: Patients with neutropenia treated at the Department of Hematology in our hospital were included in the PPK model study. A nonlinear mixed effect modeling approach (NONMEM) was used to establish the PPK model of those patients. Monte Carlo simulation was also carried out. A total of 64 patients were divided into model group and non-model group for clinical application research. The model group was given the rst dose of 1g q8h, and the non-model group was given 1g q12h as the empiric therapy; the follow-up dose adjustment was made according to the concentration results. Results: This two-compartment model showed good stability and accuracy. The average concentrations in the model group and the non-model group were signicantly different, i.e., 13.45±4.07 μg/ml, 60.71% reaching the target concentration vs. 9.85±3.76 μg/ml, 27.78% reaching the target concentration, respectively (all P<0.05). This suggested that for patients with neutropenia and CLCR ≥ 90 ml/min/1.73m 2 , the rst dose of 1g q8h may help to reach the target concentration as soon as possible. Conclusions: Our PPK model of vancomycin in patients with hematologic diseases who developed neutropenia can be used to realize the individualized application of vancomycin in this population. the drug concentration Viva-E. The quantitative range was 2.0 ~ 50.0 µg/ml. was 0.5 h before for peak, was 0.5-1 h after intravenous drip. A 2ml venous blood was collected and centrifuged at 3500 rpm. The supernatant was taken for determination. neutrophil hemoglobin platelet serum total protein (TP), serum albumin (ALB), alanine aminotransferase (ALT), aspartate aminotransferase (AST), vancomycin dosage (mg/d), administration (h), serum concentration (µg/ml)


Background
Vancomycin is the rst-line drug in the treatment of methicillin-resistant Staphylococcus aureus (MRSA) infection that has been clinically used for a very long time. Because of its narrow therapeutic window and obvious individual differences in pharmacokinetics, there are many guidelines and expert consensuses that guide the clinical application of vancomycin in recent years [1][2][3][4][5][6][7]. With the development of quantitative pharmacology, numerous researches have shown clinical signi cance in optimizing the drug delivery scheme of vancomycin by using the PPK model, which could quickly help to improve the target rate of TDM [8][9][10][11][12]. The difference of pharmacokinetics was obvious in different pathological states.
Over recent years, there has been an increasing interest in PPK of vancomycin in patients of different pathological states. However, there are only a few model studies on adult neutropenic patients.
More and more attention has been paid to the pharmacokinetics of vancomycin in patients with hematological tumors. Our previous research showed that vancomycin exposure was often inadequate in these populations. It is also mentioned in the guideline of vancomycin treatment drug monitoring of China revised in 2020 that neutropenic patients with fever are recommended to accept TDM, and the PPK model is helpful to realize the implementation of individualized drug delivery scheme. We had recently established a PPK model for patients with hematologic malignancy and neutropenia, and it showed good stability and prediction performance. In this paper, the clinical application of this PPK model was studied in order to promote the individualized application of vancomycin in this special population.

Determination of vancomycin concentration in serum
Vancomycin concentration in serum was tested by using the Siemens automatic drug concentration analyzer Viva-E. The quantitative range was 2.0 ~ 50.0 µg/ml. The time for trough concentration was 0.5 h before intravenous drip, and for peak, concentration was 0.5-1 h after intravenous drip. A 2ml venous blood was collected and centrifuged at 3500 rpm. The supernatant was taken for determination.

Establishment and validation of vancomycin PPK model in patients with neutropenia
Patients in the Department of Hematology of Hainan General Hospital from January 1, 2018, to January 1, 2020, were selected as the research subjects. The inclusion criteria were as follows: 1) diagnosed with hematological diseases; 2) ≥ 14 years old; 3) neutrophil de ciency during the study; 4) received intravenous vancomycin. The exclusion criteria were: 1) 14 years old; 2) non-neutropenic state; 3) receiving any blood puri cation treatment; 4) incorrect sampling. The body weight (BW), age, creatinine (CR), white blood cell count (WBC), neutrophil count (ANC), hemoglobin (HGB), platelet count (PLT), serum total protein (TP), serum albumin (ALB), alanine aminotransferase (ALT), aspartate aminotransferase (AST), vancomycin dosage (mg/d), administration time (h), serum concentration (µg/ml) of the patients were collected and recorded. The above indexes were measured on the same day or within 3 days before and after the monitoring of vancomycin serum concentration. Creatinine clearance rate (CLCR) was calculated using the CKD-EPI formula developed by the US chronic kidney disease epidemiology cooperative working group. This study was approved by the Medical Ethics Department of our hospital (approval number [2018]68), and all patients had informed consent.
The PPK model of the neutropenic population was established by the nonlinear mixed-effects model (NONMEM). The exponential model was used to describe the variation among individuals, and the residual variation was tted by the additive model, proportional model, and mixed model. The tting results of different error models were compared according to the objective function value (OFV), the goodness of t graph, and the rationality of parameters. The basic model was established based on these same approaches. In the basic model, a stepwise regression method was used to add covariates and establish the nal model. When the degree of freedom n = 1 and the decrease of OFV was more than 3.84 after adding a certain covariate, this covariate was kept in the nal model. The covariates, which included age, gender, BW, creatinine, CLCR, WBC, ANC, HGB, PLT, TP, ALB, ALT, and AST, were eliminated one by one from the nal model. When the degree of freedom n = 1 and the increase of OFV was more than 10.83, the covariate was saved. The nal model was established following this approach.
The goodness of t (GOF) and model predictive diagnostic chart (VPC) were drawn for model-based veri cation. The nonparametric bootstrap method was used for internal veri cation. In our study, the 95% con dence interval of population parameters and the estimated values of population parameters were obtained by 1000 times bootstrap method and were compared with the estimated values of the nal model parameters. In addition, patients who were not included in the model group with the same entry conditions in the same period were used for external veri cation. The prediction performance was judged by the prediction error (PE%) of the model. The median relative prediction error (MDPE) was used to evaluate the model's accuracy, and the median absolute prediction error (MAPE) was used to evaluate the precision of the model. Composite indexes F 20 and F 30 (PE% between ± 20% and ± 30% percentage) were used to evaluate the precision of the model. When MDPE ≤ ± 20%, MAPE ≤ ± 30%, F 20 ≥ 35%, and F 30 ≥ 50%, the prediction performance of the model was considered acceptable. The calculation formulas are shown in formulas 1 to 5. When CLCR was 30, 60, 90, 120 ml/min/1.73m 2 , respectively, the following drug delivery schemes (including 1g q12h, 1g q8h, 0.5g q8h, 0.5g q6h) were simulated. One thousand sets of simulation data were generated for each combination of the dosing scheme and CLCR. If the vancomycin trough concentration was maintained at 10 ~ 20 µg/ml, it was considered that the scheme was feasible with this CLCR.

Clinical Application Of Ppk Model
Patients with hematologic diseases accompanied by neutropenia and CLCR ≥ 90 ml/min/ 1.73m 2 were selected as the research subjects and were treated by intravenous vancomycin. The patients were randomly divided into two groups: the non-model administration group and the model administration group. The mean and standard rates of the rst trough concentration of vancomycin in the two groups were compared.

Basic information of patients
A total of 77 patients, including 42 males and 35 females, were included in this PPK model study. One hundred nine trough concentrations and 43 peak concentrations were monitored. The primary diseases were 34 cases of acute myeloid leukemia, 16 cases of acute lymphoblastic leukemia, 10 cases of lymphoma, 5 cases of aplastic anemia, 5 cases of myelodysplastic syndrome, 4 cases of chronic myeloid leukemia, 2 cases of multiple myeloma, and 1 case of chronic monocytic leukemia. A total of 26 patients were included in the external validation. The basic information of patients is shown in Table 1. The nal PPK model One compartment model and a two-compartment model were used to t the data. The OFV of the twocompartment model was lower than that of the one-compartment model. After considering the rationality of the objective function value, the goodness of t graph, and parameters, the two-compartment model was nally used as the basic model. The mixed model was used to describe the variation among individuals, and the OFV was 532.06. The estimated values of CL, V 1 , Q, and V 2 were 6.43 L /h, 18.9 L, 19.5 L /h, and 37.1 L /h, respectively. Inter-individual variation of CL (ω 2 CL) was 0.0615, and the interindividual variation of V 1 (ω 2 V 1 ) was 0.126. The stepwise regression method and stepwise elimination method were used to screen the covariates. Only CLCR was retained so that the nal model was obtained.
The formula for the nal model was as follows: CL = 6.84* (BW/70) θBW_CL * (CLCR/116) θCLCR_CL * exp (η 1 ) Formula 6 CL was the clearance rate, 6.84 in formula 6 was the typical value of Cl, BW was the bodyweight of patients. η 1 represented the difference between the patient clearance rate and the typical value of the population. The parameters of the nal model are shown in Table 2.

Model validation
The goodness of t map (GOF) was drawn, including scatter plot of basic model observations (DV) and population predicted values (PRED), scatter plot of DV and individual predictive value (IPRED), scatter plot of DV and conditional weight residuals (CWRES), scatter plot of DV and time. According to DV and PRED scatter plots, the coincidence degree of the trend line and reference line was high; the distribution of scatter plot of predicted value and conditional weight residual and scatter plot of predicted value and time were symmetrical, and there was no obvious trend change, which indicated that the nal model had a good predictive ability. The nal model GOF and predictive diagnosis diagram are shown in Fig. 1 and Fig. 2.
The Bootstrap method was used to verify the nal model. Repeated sampling 1000 times from the original data was performed in order to generate multiple sets of Bootstrap data. Then tted the Bootstrap data and estimated the model parameters, summarized all the results of successful operation, and compared those with the nal model parameters. There was no signi cant difference between the nal model parameters and bootstrap median, and the success rate of convergence was 90%, indicating that the model was reliable. The validation results were shown in Table 3.

Results Of Monte Carlo Simulation
According to Monte Carlo simulation, the predicted trough concentration of vancomycin in neutropenic patients with different CLCR under different administration regimens is shown in Fig. 3. When CLCR was 30 ml/min /1.73m 2 , the recommended dosage regimen of vancomycin was 0.5g q8h; when CLCR was 60 ml/min/1.73m 2 , the recommended dosage regimen was 1g q12h, 0.5g q6h or 0.5g q8h; when CLCR was ≥ 90 ml/min/1.73m 2 , vancomycin 1g q8h could reach a satisfactory concentration.

Clinical Application Results Of The Ppk Model
As the CLCR of neutropenia patients was generally high [13,14], the CLCR ≥ 90ml/ min /1.73m 2 was taken as the entry condition. A total of 64 adult patients with neutropenia, including 35 males and 29 females, were included in the clinical study. Among them, 28 were in the model group, and 36 were in the non-model group. All of them had a CLCR ≥ 90 ml/min/1.73m 2 . The model group was given 1g q8h directly, while the non-model group was given 1g q12h based on the experience, after which the dosage regimen was adjusted after monitoring the concentration. After 48 h of administration, serum samples were collected 30 minutes before the next administration to monitor the rst trough concentration, with 10 ~ 20 µg/ml being the target concentration. The average concentration in the model group was 13.45 ± 4.07 µg/ml; the compliance rate for the rst time was 60.71%. The average concentration in the nonmodel group was 9.85 ± 3.76 µg/ml; the compliance rate for the rst time was 27.78%. Independent sample t-test was used for age and CLCR between the two groups; Kruskal Wallis test was used for blood concentration, and Chi-square test was used for compliance rate. The results showed no signi cant difference between the two groups in age and CLCR. The mean and the rate of reaching the standard of the rst blood concentration in the model group was higher than that in the non-model group. These results suggested that for patients with neutropenia and CLCR ≥ 90 ml/ min /1.73m 2 , the rst dose of 1g q8h could be used to quickly reach the target concentration. The clinical application results are shown in Table 4.

Introduction Of A Typical Case
A 50-year-old female patient weighing 47kg, with a CLCR of 128.6 ml/min/1.73m 2 was diagnosed with acute myeloid leukemia. She developed neutropenia with fever after chemotherapy and was diagnosed with Streptococcus bovis infection in the blood. From February 18, 2021, she received 1g q12h of vancomycin. The rst concentration of vancomycin was 6.0 µg/ml 48 h after the prescription. PPK model was used to predict that the concentration of 1 g q8h after adjustment was 11.8µg/ml, and the real measured concentration was 10.2 µg/ml. The prediction error was 13.56%. A week later, the blood culture showed that the pathogen was negative. If the patient had received 1g q8h at the rst dose, this would have helped to quickly reach the target blood concentration and control the infection.

Discussion
The phenomenon of insu cient concentration of vancomycin is commonly found in patients with hematological diseases. Kergueris reported that the vancomycin elimination rate, which is constant in patients with neutropenia, was higher than that in the general population and had no signi cant correlation with serum creatinine and urine volume in such patients [15]. Michiel B. haeseker's study revealed that the clearance rate of vancomycin in patients with neutropenia was signi cantly higher than that in patients without neutropenia (CL = 67 ± 26ml/min vs. CL = 50 ± 22ml/min). They suggested that the average dose of vancomycin should be increased by one-third in neutropenic patients [16]. Choi et al used multiple logistic regression, which showed that neutropenia was the main cause of insu cient vancomycin exposure (OR = 1.75, p = 0.029) [17]. Our previous study revealed that the incidence of renal hyperfunction (ARC) in patients with hematologic diseases was 37.88%, while that in patients without hematologic diseases was only 21.56% (p = 0.001) [13]. Patients with neutropenia often have a severe infection and high mortality, thus requiring timely anti-infection treatment [18,19]. Therefore, it is very important to make individual medication plans for vancomycin in this population.
In a meta-analysis conducted by Wang et al, which included 100 vancomycin PPK models, the median value of clearance (CL) in the PPK model for adults, the elderly, and children was 3.  [20]. The estimated CL value of neutropenia patients in this study was 6.84l/h, which was higher than that reported above. As shown by the results, such patients had a higher vancomycin clearance rate. According to the PPK model and Monte Carlo simulation, acute renal hyperfunction (ARC) is de ned as CLCR ≥ 130 ml/min/1.73m 2 [14].
When the CLCR of neutrophil de ciency patients was ≥ 90 ml/min/1.73m 2 , the initial regimen of 1g q8h helped to achieve su cient drug exposure quickly. The CLCR value was lower than the de nition of ARC, which should be considered in clinical practice. After long-term chemotherapy and other treatment, patients with hematological malignancies tend to lose weight gradually, which may affect the detection of serum creatinine. How to eliminate these effects needs to be further studied. In general, establishing the PPK model in line with the characteristics of patients with neutropenia has certain signi cance for optimizing the clinical application of vancomycin. The clinical application research of the model established in this study needs to be further researched to accumulate su cient experience and promote the individualized application of vancomycin.
Conclusions PPK models of vancomycin in adult patients with hematologic diseases and neutropenia are few. The model established in this study is helpful to promote the individualized application of vancomycin in this population.  Figure 1 Goodness-of-t plots of nal.

Figure 2
Visual predictive checks of the nal model.