2.1 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 (C0) was 0.5 h before intravenous drip, and for peak concentration (CP) was 0.5–1 h after intravenous drip. A 2 ml venous blood was collected and centrifuged at 3500 rpm. The supernatant was taken for determination.

2.2 Establishment and validation of vancomycin PPK model in patients with hematological diseases and neutropenia

Patients in the Department of Hematology of Hainan General Hospital from 1 January 2018, to 1 January 2020, were selected as the research subjects. The inclusion criteria were as follows: 1) diagnosed with hematological diseases; 2) ≥14 years old; 3) developed neutropenia (neutrophil count, ANC < 0.5 × 109/L) during the study; 4) received intravenous vancomycin intermittently. The exclusion criteria were: 1) <14 years old; 2) non-neutropenic state; 3) receiving any blood purification treatment; 4) incorrect samples. The body weight (BW), age, creatinine (CR), white blood cell count (WBC), 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. All procedures were performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments. 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 fitted by the additive model, proportional model, and mixed model. The fitting results of different error models were compared according to the objective function value (OFV), the goodness of fit 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 final 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 final 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 final model. When the degree of freedom n = 1 and the increase of OFV was more than 10.83, the covariate was saved. The final model was established following this approach.

The goodness of fit (GOF) and model predictive diagnostic chart (VPC) were drawn for model-based verification. The nonparametric bootstrap method was used for internal verification. In our study, the 95% confidence 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 final 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 verification. 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 F20 and F30 (PE% between ± 20% and ±30% percentage) were used to evaluate the precision of the model. When MDPE ≤ ±20%, MAPE ≤ ±30%, F20 ≥ 35%, and F30 ≥ 50%, the prediction performance of the model was considered acceptable. The calculation formulas are shown in formulas (1)–(5)-(1)–(5). (1) (2) (3) (4) (5) 2.3 Monte Carlo simulation of PPK model

Based on the established PPK model, Monte Carlo simulation was used to simulate the steady-state trough concentration of neutropenic patients with different CLCR under different vancomycin administration schemes.

When CLCR was 30, 60, 90, 120 ml/min/1.73 m2, 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.

2.4 Clinical application of PPK model

Patients with hematologic disease and neutropenia who had a CLCR ≥ 90 ml/min/1.73 m2 were selected as the research subjects and were treated by intravenous vancomycin. The patients were randomly divided into two groups: the model administration group and the non-model administration group. The age, height, weight, CLCR, the first C0, medication days of vancomycin, dose adjustment times, the compliance rate of the first C0, the proportion of patients who received dose adjustments and in the two groups were compared.

2.5 Statistical analysis

NONMEM (icon development solutions, USA, version 7.3) software was used for model establishment and simulation. Perl speak NONMEM (PSN version 3.4.2) was used for model validation. R software (version 2.12.0) was used for statistical testing and drawing, and SPSS 19.0 was used for data analysis.