Mid‐dosing interval concentration is important for polymyxin B exposure and acute kidney injury in critically ill patients

Abstract

This study aimed to evaluate the association between polymyxin B (PMB) exposure and acute kidney injury (AKI) and analyze the risk factors for PMB‐induced AKI in critically ill patients. Plasma concentrations of PMB were determined using an ultraperformance liquid chromatography–tandem mass spectrometer in intensive care unit patients who were administered PMB. Univariate and multivariate analyses were conducted to identify risk factors. A receiver operating characteristic curve was constructed to assess the discriminant power of the factors and to identify the cutoff value for AKI. The white blood cell count and estimated area under the concentration–time curve (AUC) of patients administered PMB were independent risk factors for PMB‐induced AKI, where AUC were calculated using a first‐order pharmacokinetic equation based on the mid‐dosing interval concentration (C_1/2t) and peak concentration. The area under the receiver operating characteristic curve of the final model was 0.805 (95% confidence interval, 0.690–0.921). The cutoff value for the combined predictor was 0.57. Alternatively, when using C_1/2t, which was strongly correlated with AUC, as the only independent risk factor, the analysis showed that the 3.47 μg/ml threshold provides favorable differentiation between the AKI and non‐AKI groups. These results provide insightful information for therapeutic drug monitoring–guiding PMB dosing in clinical practice.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Although several studies have identified risk factors for polymyxin B (PMB)–induced acute kidney injury (AKI), such as sex, age, and weight, they have considered the link between PMB exposure and AKI.

• WHAT QUESTION DID THIS STUDY ADDRESS?

Compared with the trough and peak concentrations, mid‐dosing interval concentration (C_1/2t) may be more important for the early prediction of PMB‐induced AKI.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

White blood cell count and the estimated area under the curve based on the C_1/2t and peak concentration using a first‐order pharmacokinetic equation were independent risk factors for PMB‐induced AKI. A C_1/2t of 3.47 μg/ml was observed to be an alternative cutoff value for predicting PMB‐induced AKI.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

Contrary to previous studies and recommendations, our study demonstrated that C_1/2t may be a critical concentration point for predicting AKI.

INTRODUCTION

In recent years, multidrug‐resistant gram‐negative bacteria (MDR‐GNB) have become an increasing threat to human health, particularly Pseudomonas aeruginosa, Acinetobacter baumannii, and Enterobacteriaceae. ¹ Because of the lack of other effective antibiotics, polymyxins have become the last resort for treating infections caused by MDR‐GNB. ² Among the polymyxins, polymyxin B (PMB) and colistin are commonly used in clinical practice owing to their satisfactory efficacy and relatively low nephrotoxicity. A systematic review and meta‐analysis has reported that PMB has lower nephrotoxicity than colistin and that no significant difference in mortality was observed between patients treated with the two drugs. ³ However, PMB has more significant advantages than colistin and is widely used in intensive care units. PMB is a polypeptide antibiotic that alters outer membrane permeability of bacterial cells. Commercially available PMB is a mixture in which polymyxin B1 (PMB1) and polymyxin B2 (PMB2) are the major components, accounting for >85% of the mixture.

Despite decades of clinical use, the most common adverse clinical effect of PMB is dose‐dependent nephrotoxicity, which mainly manifests as acute kidney injury (AKI) and acute renal tubular necrosis. The incidence of AKI in patients receiving PMB ranges from 20% to 60%. ⁴ , ⁵ , ⁶ , ⁷ Several studies have demonstrated the risk factors for PMB‐induced AKI, including sex, age, weight, loading dose, daily dosage, duration of treatment, baseline serum creatinine, infection site, and concomitant antibiotic use. ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ However, these studies did not consider the relationship between PMB exposure and AKI.

In 2019, international agencies and academic organizations jointly issued international consensus guidelines for the optimal use of polymyxins. The guidelines recommend achieving a target for the area under the concentration–time curve (AUC) within 24 h at a steady state of 50 to 100 mg·h/L, corresponding to an average steady‐state plasma concentration of 2 to 4 mg/L to reduce the risk of AKI. ¹⁴ However, the recommended targets are mainly based on in vitro and animal data rather than clinical results. ¹⁵ Recently, two studies have evaluated the association between plasma concentrations of PMB and AKI; however, the results are inconsistent. Han et al. ¹⁶ reported on the association between PMB plasma concentration and AKI development and suggested that the trough concentration of PMB should be controlled at <3.13 mg/L to reduce the risk of AKI. Interestingly, Deng et al. ¹⁷ reported that the peak concentration rather than the trough concentration of PMB and PMB1 is a significant predictor for the development of AKI. If the peak concentration of PMB1 was >5.23 mg/ml, the probability of AKI would be >50%. The inconsistent findings motivated us to explore the relationship between PMB exposure in vivo and AKI.

Furthermore, a recent study reported that the intermediate concentration of the dosing interval may be the best choice for predicting the adverse effects of antibiotics. ¹⁸ In the two studies mentioned previously, only trough and peak concentrations were collected, and therefore the relationship between mid‐dosing interval concentration (C_1/2t) of PMB and AKI could not be assessed. Moreover, although the guidelines advise the range of AUC values, how to estimate the AUC with a limited sample strategy remains unclear. The relationship between the AUC estimated using different methods and PMB‐induced AKI remains unknown. Therefore, further research on the relationship between PMB exposure and AKI is required.

This study primarily aimed to identify the relationship between PMB exposure and AKI and determine the cutoff value of PMB when both AUC and plasma concentrations including C_1/2t were considered. We also analyzed the risk factors for PMB‐induced AKI in critically ill patients.

METHODS

Study design and ethics

This single‐center, real‐world cohort study was conducted in patients admitted in the intensive care unit of Nanjing Drum Tower Hospital from August 2020 to July 2022. The study protocol was approved by the Ethics Committee of Nanjing Drum Tower Hospital (no. 2021‐466‐01). The inclusion criteria were as follows: (1) adult patients (>18 years) who received intravenous PMB (sulfate; polymyxin B injection, Shanghai First Biochemical Pharmaceutical Co., Ltd., China), (2) patients with confirmed MDR‐GNB infections, (3) PMB was used for at least 2 days, and (4) plasma concentrations were monitored. The exclusion criteria were as follows: (1) baseline serum creatinine of >1.5 mg/dl or renal replacement therapy was used before PMB treatment; (2) maintenance dose of PMB was changed during treatment; and (3) critical data were missed, such as serum creatinine.

Clinical data and sample collection

Demographic characteristics, PMB therapy, baseline routine laboratory examination data, infection sites, pathogens, concomitant nephrotoxic drugs, comorbidities, prognoses, and adverse events were obtained from the hospital information system. Concomitant nephrotoxic drugs included tigecycline, carbapenems, vancomycin, and cefoperazone/sulbactam. Serious and treatment‐emergent adverse events included infectious shock, respiratory failure, respiratory cardiac arrest, and thoracic hemorrhage. Nonserious adverse events included ventilatory dysfunction, aggravation of infection, elevated troponin levels, and progressive elevation of bilirubin levels. Creatinine clearance was estimated using the Cockcroft–Gault equation. ¹⁹ According to Kidney Disease: Improving Global Outcomes, AKI was defined as an increase of ≥0.3 mg/dl in serum creatinine level within 48 h, a >1.5 times increase in serum creatinine level within 7 days, or a urine output of <0.5 ml/kg/h for >6 h. ²⁰

The present study did not interfere with the physicians' decisions to administer PMB. The physician determined the dose according to the patient's body weight and the pharmaceutical instructions. A loading dose was typically administered at the time of PMB treatment initiation to quickly achieve a steady‐state serum concentration that provides effective infection control. Generally, 2.5 mg/kg was administered as the loading dose, followed by a 2.5–3 mg/kg/day maintenance dose in two divided doses. However, some patients were not administered a loading dose because of the risk of AKI or other clinical causes.

After at least 48 h of therapy, when steady‐state plasma concentrations were approximately reached even when a loading dose was not administered, three blood samples were collected from each patient: trough concentration (C_min) of PMB before the next administration, C_1/2t 6 h after administration, and peak concentration (C_max) of PMB immediately after the end of administration. All blood samples were centrifuged at 885 g for 10 min, and the supernatant was obtained and stored at −80°C until analysis.

Quantification of PMB concentrations

Quantification of the PMB concentration is a regular clinical laboratory test for patients treated with PMB, and an internal quality assessment was performed. Briefly, PMB1 and PMB2 plasma concentrations were determined using an ultraperformance liquid chromatography–tandem mass spectrometer (Qlife Lab 9000 UPLC system), and the PMB plasma concentration was calculated as the sum of PMB1 and PMB2. A Phenomenex Kinetex XB‐C18 (2.6 μm, 3.0 × 50 mm) was used for chromatographic separation. Mobile Phase A consisted of 0.1% formic acid in water and Mobile Phase B consisted of acetonitrile. The gradient elution was performed as follows: 0~1 min, 1%~30%B; 1~2.5 min, 30%~98%B; and 2.5~3 min, 98%B. Column temperature and flow rate were 40°C and 0.3 ml/min. The PMB peaks in blank samples were <2% of the lower limit of quantitation level for PMB1 and PMB2. The calibration curve demonstrated a good linear relationship with correlation coefficients of 0.998 and 0.999 in the range of 35–14,000 ng/ml for PMB1 and 15–6000 ng/ml for PMB2, respectively. For PMB1, the intrabatch and interbatch precisions of the quality control samples ranged from 2.1% to 6.1%, and the corresponding accuracy ranged from −1.1% to 8.1%. For PMB2, the intrabatch and interbatch precisions of quality control samples ranged from 2.3% to 11.9%, and the corresponding accuracy ranged from −1.2% to 7.4%.

Estimation of PMB AUC

The trapezoidal area method and first‐order pharmacokinetic equation method were used to estimate AUC in this study. ²¹ For the first‐order pharmacokinetic equation method, we employed a formula based on the one‐compartment model with linear elimination because it can adequately explain the pharmacokinetics of PMB. ²² Two timed steady‐state plasma concentrations (C_min–C_max) or three‐timed steady‐state plasma concentrations (C_min–C_1/2t–C_max) are used in the trapezoidal area method. Any two timed steady‐state plasma concentrations (C_min–C_max, C_min–C_1/2t, or C_1/2t–C_max) are used in the first‐order pharmacokinetic equation method. The relevant formulas are as follows:

$$\mathrm{AUC}=\sum \frac{\left(t_i-t_{i-1}\right)\times \left(C_i+C_{i-1}\right)}{2}$$ (1)

Equation (1) uses the trapezoidal area method to estimate the AUC, where t _i and t _i−1 are adjacent sampling times, and c _i and c _i−1 are the corresponding plasma concentrations.

$${\mathrm{K}}_{\mathrm{e}}=\frac{\mathrm{Ln}\left(\frac{C_1}{C_2}\right)}{t}$$ (2)

$$\mathrm{AUC}=\frac{t^{\prime }\times \left({\text{Ceoi}}^{\prime }+\mathrm{Ct}\right)}{2}+\frac{{\text{Ceoi}}^{\prime }-\mathrm{Ct}}{{\mathrm{K}}_{\mathrm{e}}}$$ (3)

Equations (2) and (3) use the first‐order pharmacokinetic equation method to estimate AUC, which refers to Equations (1) and (4) from Pai et al. ²¹ K_e is the elimination rate constant, C₁ and C₂ represent any two of the three concentrations, and t is the interval between the two concentrations. Where t' is infusion time, Ceoiʹ and Ct are the theoretical approximate steady‐state peaks and trough concentrations.

Data analysis

Continuous variables with normal distribution are described as means ± standard deviations (SDs), and a Student's t‐test was used to compare the two groups. Continuous variables with non‐normal distribution are presented as medians and interquartile ranges, and the Mann–Whitney U test was used to compare the two groups. Categorical variables are summarized as frequencies and percentages, and comparisons among groups were performed using the chi‐square test or Fisher's exact test.

A logistic regression analysis was performed to determine the risk factors associated with AKI. Variables with p < 0.05 in the univariate analysis were included in the multivariate analysis. The forward stepwise method was used to determine risk factors in the multivariate analysis. The Hosmer–Lemeshow test was adopted to evaluate the goodness of fit of logistic regression models, and a nonsignificant test (p ≥ 0.05) indicated a good fit. ²³

A receiver operating characteristic (ROC) curve was constructed to assess the discriminant power of the factors and to identify the cutoff value for AKI. Areas under the curve of 0.7–0.79 were considered a satisfactory performance and those of 0.8–0.89 was considered optimum performance. ²⁴ The Youden index is used to measure overall diagnostic effectiveness, ranging between 0 and 1, with a value of 1 indicating perfect diagnostic effectiveness and 0 indicating an ineffective test. ²⁵ Pearson correlation analysis was performed to evaluate the relationship between AUC and plasma concentration. Significance was set at p < 0.05. The IBM SPSS Statistics software (Version 25.0) was used for data analysis, and graphs were prepared using GraphPad Prism (Version 9.0).

RESULTS

A total of 90 patients who underwent intravenous PMB were enrolled in this study. After excluding 35 patients (29 patients were undergoing renal replacement therapy or had renal insufficiency at baseline, five patients had dose changes but without therapeutic drug monitoring [TDM], and one patient had missing serum creatinine), 55 patients were finally included in the study. The PMB concentration was measured in 165 blood samples. The mean age of the patients was 61 years, and the median body weight was 62 kg. Of the patients, 64% were men, and the duration of therapy was 4–42 days. The Acute Physiology and Chronic Health Evaluation II and Sequential Organ Failure Assessment scores of patients at baseline were 20.6 ± 5.8 and 6.3 ± 3.0, respectively. Acinetobacter baumannii (n = 38, 69.1%) and Klebsiella pneumoniae (n = 22, 40.0%) were the predominant pathogenic bacteria. Of the patients, 34 received loading doses of 75, 100, 150, or 200 mg. Doses of 100, 150, and 200 mg were used to maintain the desired steady‐state drug concentration. The dosing regimens for the loading and maintenance doses in all patients are detailed in Table 1. The C_min of PMB ranged from 0.397 to 4.933 μg/ml, and C_1/2t of PMB ranged from 1.438 to 7.030 μg/ml, whereas C_max of PMB ranged from 2.976 to 14.155 μg/ml (Figure 1). The AKI group comprised 30 patients, and 25 were assigned to the non‐AKI group, with an overall AKI incidence of 54.5%. AKI occurred 3–17 days after the start of treatment; 46.7% of patients developed AKI within 7 days and 53.3% developed AKI after 7 days of treatment (Figure 2). Of the 30 patients included in the AKI group, eight patients developed declining renal function, and five patients died, and 15 patients demonstrated improved renal function. Two patients were voluntarily discharged from the hospital. The 30‐day mortality rate was 34.5% (20% in the non‐AKI group vs. 46.7% in the AKI group; p = 0.038). Regarding adverse events, 14 and 10 patients in the AKI and non‐AKI groups, respectively, experienced at least one adverse event during the PMB treatment period. Following are the final treatment outcomes of the 55 patients: nine died, 11 were discharged voluntarily, 34 improved, and one was cured. The detailed demographic and clinical data are presented in Table 1.

TABLE 1.

Characteristics and univariate analysis of patients in the AKI group and non‐AKI group.

Variable	Overall (n = 55)	Non‐AKI (n = 25)	AKI (n = 30)	p value
Baseline demographics
Sex
Male	35 (63.6)	13 (52.0)	22 (73.3)	0.101
Female	30 (36.7)	12 (48.0)	8 (26.7)
Age, y	61.0 ± 16.7	60.4 ± 15.6	61.4 ± 17.9	0.834
Body weight, kg	62.0 (55.0, 73.0)	64.0 (50.0, 72.5)	60.5 (57.3, 73.3)	0.806
Duration of treatment, days	11.0 (8.0, 15.0)	11.0 (8.5, 14.0)	12.5 (8.0, 15.3)	0.524
APACHE II score	20.6 ± 5.8	20.6 ± 5.8	20.6 ± 5.9	0.997
SOFA score	6.3 ± 3.0	6.0 (4.0, 7.5)	6.0 (4.0, 8.3)	0.507
PMB treatment
Infusion time, h				0.678
1	48 (87.3)	23 (92.0)	25 (83.3)
2	5 (9.1)	2 (8.0)	3 (10.0)
2.5	2 (3.6)	0 (0.0)	2 (6.7)
Loading dose, mg				0.138
0	21 (38.2)	9 (36.0)	12 (40.0)
75	3 (5.5)	3 (12.0)	0 (0.0)
100	24 (43.6)	11 (44.0)	13 (43.3)
125	1 (1.8)	1 (4.0)	0 (0.0)
150	6 (10.9)	1 (4.0)	5 (16.7)
Maintenance dose, mg				0.031*
100	15 (27.3)	11 (44.0)	4 (13.3)
150	39 (70.9)	14 (56.0)	25 (83.3)
200	1 (1.8)	0 (0.0)	1 (3.3)
Laboratory examination data
Procalcitonin, g/L	0.3 (0.1, 1.2)	0.3 (0.1, 0.7)	0.4 (0.2, 1.7)	0.310
White blood cell, 109/L	9.6 (7.3, 13.4)	8.5 (5.8, 11.3)	10.8 (8.1, 17.2)	0.041*
Neutrophil, 109/L	10.6 ± 10.7	7.2 (4.5, 9.9)	9.5 (5.9, 15.6)	0.106
Neutrophil %	82.0 (77.2, 89.1)	79.6 (75.7, 83.8)	86.3 (79.4, 91.7)	0.041*
Alanine transaminase, U/L	27.7 (16.8, 43.2)	30.0 (14.7, 52.9)	25.3 (17.2, 41.7)	0.654
Aspartate transaminase, U/L	27.2 (20.1, 37.0)	27.6 (17.7, 44.3)	26.9 (20.2, 33.8)	0.630
Alkaline phosphatase, U/L	104.3 (67.4, 156.7)	97.4 (66.3, 144.6)	108.9 (73.6, 165.3)	0.447
Glutamyl transpeptidase, U/L	69.2 (27.1, 134.7)	57.9 (24.0, 113.3)	91.5 (32.0, 164.8)	0.190
Total bilirubin, μmol/L	12.4 (8.2, 22.7)	12.4 (7.9, 19.7)	12.8 (8.6, 26.3)	0.457
Direct bilirubin, μmol/L	4.6 (2.6, 10.8)	3.3 (2.3, 9.2)	5.3 (2.9, 13.5)	0.217
Total proteins, g/L	57.8 ± 8.0	57.3 (49.5, 64.9)	57.5 (52.3, 62.9)	0.594
Serum albumin, g/L	33.0 (30.2, 35.5)	33.2 (29.8, 37.0)	33.0 (30.8, 34.6)	0.987
Blood urea nitrogen, mmol/L	10.3 ± 4.9	9.1 (6.5, 12.4)	8.1 (6.9, 14.0)	0.980
Serum creatinine, μmol/L	52.0 (35.0, 64.0)	56.0 (30.0, 67.5)	51.5 (37.8, 62.3)	0.618
Uric acid, μmol/L	176.0 (108.0, 236.0)	137.0 (102.0, 238.5)	185.5 (111.0, 242.8)	0.437
C‐reactive protein, mg/L	79.6 ± 66.9	52.7 (7.5, 100.0)	86.7 (33.2, 131.0)	0.052
Estimated glomerular filtration rate, ml/min·1.732/m2	162.2 ± 75.9	127.3 (101.9, 254.0)	146.4 (106.1, 194.2)	0.660
Creatinine clearance, ml/min	129.6 ± 62.8	119.0 (83.1, 175.8)	127.0 ± 60.9	0.839
Infection site
Lung	38 (69.1)	17 (68.0)	21 (70.0)	0.873
Bloodstream	15 (27.3)	7 (28.0)	8 (26.7)	0.912
Abdomen	4 (7.3)	1 (4.0)	3 (10.0)	0.740
Others	9 (16.4)	6 (24.0)	3 (10.0)	0.302
Pathogenic bacteria
Klebsiella pneumoniae	22 (40.0)	10 (40.0)	12 (40.0)	1.000
Acinetobacter baumannii	38 (69.1)	19 (76.0)	19 (63.3)	0.311
Pseudomonas aeruginosa	2 (3.6)	1 (4.0)	1 (3.3)	1.000
Concomitant nephrotoxic drugs	16 (29.1)	6 (24.0)	10 (33.3)	0.448
Comorbidities
Hypertension	25 (45.5)	12 (48.0)	13 (43.3)	0.729
Type 2 diabetes	9 (16.4)	4 (16.0)	5 (16.7)	1.000
Drug concentrations
Cmin(B1), μg/ml	1.9 ± 0.9	1.6 ± 0.7	2.1 ± 0.9	0.017*
Cmin(B2), μg/ml	0.3 ± 0.2	0.3 ± 0.1	0.4 ± 0.2	0.036*
C1/2t(B1), μg/ml	3.0 ± 1.1	2.5 ± 0.8	3.4 ± 1.1	0.001*
C1/2t(B2), μg/ml	0.6 ± 0.2	0.5 ± 0.2	0.6 ± 0.2	0.003*
Cmax(B1), μg/ml	6.3 ± 1.9	5.6 ± 1.8	6.9 ± 1.9	0.013*
Cmax(B2), μg/ml	1.1 (0.9, 1.3)	1.0 (0.8, 1.2)	1.1 (1.0, 1.4)	0.035*
Cmin(B), μg/ml	2.2 ± 1.0	1.9 ± 0.8	2.5 ± 1.1	0.019*
C1/2t(B), μg/ml	3.6 ± 1.3	3.0 ± 0.9	4.1 ± 1.3	0.001*
Cmax(B), μg/ml	7.5 ± 2.3	6.6 ± 2.1	8.1 ± 2.2	0.014*
AUC0–24, trapezoidal area, μg · h/ml
Based on Cmin(B), C1/2t(B), and Cmax(B)	99.1 ± 30.8	85.4 ± 24.4	110.4 ± 31.3	0.002*
Based on Cmin(B) and Cmax(B)	115.9 ± 36.0	101.9 ± 30.9	127.6 ± 36.2	0.007*
AUC0–24, first‐order pharmacokinetic equation, μg · h/ml
Based on Cmin(B) and Cmax(B)	104.1 ± 34.4	90.2 ± 28.4	115.7 ± 35.1	0.005*
Based on C1/2t(B) and Cmax(B)	91.9 ± 30.1	77.7 ± 21.8	103.7 ± 31.2	0.001*
Based on Cmin(B) and C1/2t(B)	88.1 ± 32.3	72.8 ± 21.2	100.7 ± 34.8	0.001*
Outcome
30‐day mortality	19 (34.5)	5 (20.0)	14 (46.7)	0.038*
Adverse events				0.623
Serious adverse events	14 (25.5)	4 (16.0)	10 (33.3)
No serious adverse events	10 (18.2)	6 (24.0)	4 (13.3)

Note: Variables are presented as means ± standard deviations, medians (interquartile ranges), or numbers (percentage).

Abbreviations: AKI, acute kidney injury; APACHE II, Acute Physiology and Chronic Health Evaluation II; AUC_0–24, area under the concentration–time curve over a 24‐h period; C_1/2t, mid‐dosing interval concentration; C_max, peak concentration; C_min, trough concentration; PMB, polymyxin B; PMB1, polymyxin B1; PMB2, polymyxin B2; SOFA, Sequential Organ Failure Assessment.

^*Significant at p < 0.05.

FIGURE 1.

Distribution of C_min, C_1/2t and C_max in patients. C_1/2t, mid‐dosing interval concentration; C_max, peak concentration; C_min, trough concentration.

FIGURE 2.

Date and frequency of polymyxin B–induced acute kidney injury.

Univariate analysis

The univariate analysis identified several factors associated with PMB‐induced AKI. The maintenance dose (p = 0.031), white blood cell count (WBC; p = 0.041), and neutrophil% (p = 0.041) differed significantly between the two groups. In addition, all plasma concentrations measured and the AUC estimated by the different methods were significantly higher (p < 0.05) in the AKI group than in the non‐AKI group.

Multivariate analysis

The multivariate logistic regression analysis revealed that WBC count (odds ratio [OR], 1.123; 95% confidence interval [CI], 1.000–1.260; p = 0.050) and AUC (OR, 1.040; 95% CI, 1.013–1.06; p = 0.003), estimated using a first‐order pharmacokinetic equation based on C_1/2t and C_max (AUC_1/2t,max), were independent risk factors for AKI (Table 2). According to the results of the multivariate analysis, the final model is presented in Equation 4, and the Hosmer–Lemeshow test indicated that the model had a better fitting degree (p = 0.749).

$$\begin{array}{c}\text{Probability}\left(\mathrm{AKI}\right)=\hfill \\ 1/\left[1+\exp \left(4.623-0.116\times \mathrm{WBC}-0.040\times {\mathrm{AUC}}_{1/2\mathrm{t},\max }\right)\right]\hfill \end{array}$$ (4)

TABLE 2.

Multivariate analysis to identify risk factors for polymyxin B–induced acute kidney injury.

Risk factor	OR	95% CI	p value
White blood cell, 109/L	1.123	1.000–1.260	0.0499
AUC0–24, first‐order pharmacokinetic equation, μg·h/ml
Based on C1/2t(B) and Cmax(B)	1.040	1.013–1.068	0.003

Abbreviations: AUC_0–24, area under the concentration–time curve over a 24‐h period; C_1/2t, mid‐dosing interval concentration; C_max, peak concentration.

ROC curve analysis

The ROC curve analysis (Figure 3a) revealed that the model had acceptable predictability. The area under the ROC curve (AUROC) of the model was 0.805 (95% CI, 0.690–0.921), which was larger than that of the WBC count (AUROC, 0.661; 95% CI, 0.518–0.805) and AUC_1/2t,max (AUROC, 0.757; 95% CI, 0.630–0.885). The Youden index was obtained using the coordinates of the ROC curve, and the maximum value corresponded to the cutoff value. The cutoff value of the model was 0.57, with a sensitivity of 70% and a specificity of 80%. Considering that it may be more convenient to collect a single blood sample during clinical operations, we also analyzed the AUROC of PMB concentrations at different timepoints separately. The results revealed an AUROC of C_1/2t (0.747) > C_max (0.675) > C_min (0.672), indicating that C_1/2t had a better performance in predicting AKI than C_min and C_max (Figure 3b). The univariate logistic regression analysis further revealed a correlation between the probability of AKI induction and C_1/2t (Figure 4). The optimal cutoff value of C_1/2t was 3.47 μg/ml (p = 0.002), with a 66.7% sensitivity and a 72% specificity. The probability of AKI was >50% when C_1/2t was ≥3.24 mg/L according to Equation 5.

$$\text{Probability}\left(\mathrm{AKI}\right)=1/\left[1+\exp \left(2.742-0.845\times {\mathrm{C}}_{1/2\mathrm{t}}\right)\right]$$ (5)

FIGURE 3.

ROC curve of polymyxin B plasma concentrations, the final model, and other factors for predicting AKI. (a) ROC curve of the final model and other factors for predicting AKI. (b) ROC curve of polymyxin B plasma concentrations for predicting AKI. AKI, acute kidney injury; AUC_1/2t,max, area under the concentration–time curve estimated using a first‐order pharmacokinetic equation based on C_1/2t and C_max; AUROC, area under the receiver operating characteristic curve; C_min, trough concentration; C_1/2t, mid‐dosing interval concentration; C_max, peak concentration; ROC, receiver operating characteristic; WBC, white blood cell count.

FIGURE 4.

Univariate logistic regression analysis for the probability of polymyxin B–induced AKI. C_1/2t, mid‐dosing interval concentration; AKI, acute kidney injury.

Correlation between AUC and plasma concentration

The Pearson's correlation analysis further revealed a correlation between C_1/2t, C_max, and AUC_1/2t,max (Figure 5). Compared with C_max (r = 0.726), AUC_1/2t,max and C_1/2t had a higher significant correlation (r = 0.985).

FIGURE 5.

Pearson correlation analysis between the mid‐dosing interval concentration (C_1/2t) of polymyxin B, the peak concentration (C_max) of polymyxin B, and the area under the concentration–time curve (AUC_1/2t,max). AUC_1/2t,max was estimated using a first‐order pharmacokinetic equation based on C_1/2t and C_max.

DISCUSSION

Currently, PMB‐induced AKI is a major clinical concern. TDM is necessary for the use of PMB, and this study aimed to explore the exposure–AKI cutoff value of PMB to predict AKI. The results indicated WBC count and estimated AUC_1/2t,max estimated using a first‐order pharmacokinetic equation were independent risk factors for PMB‐induced AKI. Additionally, C_1/2t was strongly correlated with AUC and the threshold of 3.47 μg/ml is an alternative satisfactory choice for predicting AKI.

Several studies have reported the incidence of AKI. Different definitions of AKI and the wide range of PMB doses administered may account for these different results. The incidence of AKI in the current study was 54.5%, which is at the higher end of the aforementioned studies. Great efforts have been made to determine the cause of AKI caused by PMB, and the results have demonstrated that PMB can selectively accumulate in renal proximal convoluted tubule epithelial cells, inducing apoptosis and resulting in decreased kidney function. ²⁶ Additionally, animal studies have revealed that PMB can cause reduced renal blood flow and increased vascular resistance in rats, which may also be related to AKI. ²⁷ The studies on the mechanism of AKI induced by PMB will help guide clinical administration.

The development of AKI during treatment has been reported to be associated with worse prognosis, including higher mortality. ¹² We also demonstrated that AKI was significantly associated with 30‐day mortality. A higher incidence of chronic renal failure in patients who develop AKI has been demonstrated in previous studies. ²⁸ Thus, reducing exposure to AKI‐related risk factors is important. The current dosing strategy for PMB is based on the overall weight; however, it may not fully consider the factors affecting drug exposure. The AUC or plasma concentrations may better reflect drug exposure in vivo.

Although TDM is currently recommended for PMB dosing, evidence regarding the association between exposure and PMB‐induced AKI is limited. In the present study, we included plasma concentrations and AUC calculated using the two methods in the analysis. The study indicated that the baseline WBC count and AUC_1/2t,max were independent risk factors for AKI development during PMB administration in critically ill patients. WBC count is a known infection indicator, and previous literature has reported that WBC count was positively correlated with the change in renal tubular score. ²⁹ Although WBC count was included in the final multivariable logistic regression model, the univariate analysis demonstrated an AUROC of only 0.661, indicating a relatively low diagnostic value. Previous studies have reported strong associations between AKI and AUC for many antibiotics. D'Amico et al. demonstrated that AUC monitoring had a significant effect on reducing AKI incidence compared with vancomycin trough concentration. ³⁰

Furthermore, our results revealed that more attention should be paid to AUC_1/2t,max to reduce AKI in PMB. In addition, the combined predictor based on WBC count and AUC_1/2t,max was an excellent predictor of AKI in critically ill patients, with an AUROC of 0.805, which is similar to that of the final models of Han et al. (0.813) and Deng et al. (0.799). ¹⁶ , ¹⁷ A combined predictor value of >0.57 suggests that the patient was at a higher risk of developing AKI.

In clinical practice, a single sampling strategy is preferred. Therefore, we further analyzed the predictive performance of PMB single plasma concentration in AKI. The univariate analysis revealed that the C_1/2t, C_max, and C_min were significantly different between the two groups. Among the concentrations at different timepoints, the AUROC of C_1/2t (0.747) was close to that of AUC_1/2t,max (0.757) and larger than those of C_min and Cmax, which were lower than 0.7. Another finding of the present study was that C_1/2t was strongly correlated with AUC_1/2t,max, with r > 0.98. A similar conclusion was drawn by Chen et al., ³¹ in which the AUROC based on limited sampling concentrations in 42 Chinese patients treated with PMB was evaluated, and blood samples were collected at 0, 1.5, 2, 4, 6, 8, and 12 h after PMB administration. The results indicated that C_1/2t was the most accurate predictor of AUC (r ² = 0.984). ³¹ Consistently, we identified C_1/2t as an important risk factor for PMB‐induced AKI and can be used as an alternative to predict AKI when only one sample can be obtained. Although the current guidelines do not recommend monitoring C_1/2t, our results and those of previous clinical studies indicate the importance of C_1/2t.

Another important finding of our study was that AKI occurred 3–17 days after PMB administration, and 13.3% of the patients developed AKI on Day 3, which was similar to the results reported by Deng et al. ¹⁷ Moreover, a previous study has reported that early AKI is a favorable predictive factor for later AKI. ³² Of the patients, 47% experienced AKI within 7 days, indicating that renal function should be examined at an early stage when using PMB.

This study had several limitations. First, this was a single‐center study, and the number of included patients was limited. Renal insufficiency because PMB administration limited the sample size. Further studies with larger sample sizes should support the robustness of our conclusions. Second, owing to the lack of clinical indicators for patients after the end of treatment, we did not analyze the relationship between PMB exposure and clinical efficacy, which is a direction for future research.

CONCLUSION

Our findings suggest that WBC count and AUC_1/2t,max are independent risk factors for PMB‐induced AKI, and the optimal cutoff value of the model was 0.57 to predict AKI. In addition, C_1/2t is an important risk factor for PMB‐associated AKI and could be controlled at <3.47 μg/ml during treatment, serving as an alternative to predict AKI.

AUTHOR CONTRIBUTIONS

J.W., Y.L., and S.H. wrote the manuscript. H.Z. and N.Y. designed the research. L.J., J.W., M.W., X.C., and X.L. performed the research. J.W., Y.L., and S.H. analyzed the data.

FUNDING INFORMATION

This project was funded by National Key R&D Program of China (no. 2020YFC2008303), Nanjing Medical Science and Technique Development Foundation (no. YKK17075), and Jiangsu Province Youth Medical Talents Project (no. QNRC2016013).

CONFLICT OF INTEREST STATEMENT

The authors declared no competing interests for this work.

ETHICS STATEMENT

This study was approved by the Ethics Committee of the Drum Tower Hospital affiliated with the Medical School of Nanjing University (no. 2021‐466‐01).

Supporting information

Data S1

Appendix S1

Wang J, Li Y, Huang S, et al. Mid‐dosing interval concentration is important for polymyxin B exposure and acute kidney injury in critically ill patients. CPT Pharmacometrics Syst Pharmacol. 2023;12:1911‐1921. doi: 10.1002/psp4.13040