FormalPara Key Points

This study found a strong association between patient-specific and population-based pharmacokinetic parameters that guide the initial dosing of vancomycin in most hospitals.

Our study findings show that in hospitalized patients who cannot have patient-specific pharmacokinetic parameters calculated, clinical algorithms based on population-predicted pharmacokinetic parameters can be used for vancomycin dosing.

1 Introduction

Vancomycin is a glycopeptide antibiotic used in the treatment of Gram-positive aerobic and anaerobic bacteria such as Enterococcus, Staphylococcus, Streptococcus, and Clostridium. Since the 1950s, this antibiotic has served as the first-line therapy for methicillin-resistant Staphylococcus aureus strains and ampicillin-resistant Enterococcus species [1].

Vancomycin empiric dose selection is weight based and the selection of dosing frequency is often adapted from population-predicted pharmacokinetic parameter estimates and/or using patient-specific pharmacokinetic parameters when two vancomycin concentrations are obtained [1, 2]. Matzke et al. have proposed the most common population-predicted pharmacokinetic elimination rate constant (Ke) used in the calculation of half-life (t1/2) and clearance for vancomycin elimination [2]. This equation (Ke = [0.00083 × creatinine clearance (CrCl)] + 0.0044) is used routinely in many hospitals to develop clinical algorithms for selecting initial vancomycin dose frequency [2]. Alternatively, after two vancomycin concentrations are obtained, the patient-specific pharmacokinetic Ke can be calculated using a patient’s vancomycin concentrations and can inform more precise selection of vancomycin dose frequency.

In a recent study, using the Matzke population-predicted Ke formula = 0.00083 × CrCl + 0.0044 [2], Oswalt et al. found that population and patient-specific Ke and half-life were similar in 158 patients with acute brain injury. More specifically, the study found statistically significant differences between the mean population-predicted and patient-specific Ke and t1/2; however, these were negligible clinical differences with a mean Ke difference of 0.0211 h−1 and a mean t1/2 difference of 1.01 h [3]. The study authors concluded that population-predicted pharmacokinetics may be an accurate empiric dosing strategy for selecting vancomycin dose frequency given the small clinical difference between population-predicted and patient-specific Ke. Additionally, Murphy and colleagues evaluated seven methods for estimating vancomycin pharmacokinetic parameters (Ke, volume of distribution, and vancomycin clearance) and concluded that these methods varied widely in their ability to predict vancomycin concentrations with measured vancomycin concentrations. The authors noted that the seven methods were not reliable to replace therapeutic monitoring of vancomycin concentrations [4]. However, the authors found that out of all the seven methods for estimating vancomycin pharmacokinetic parameters, the Matzke method had the least bias and best precision compared with the other six methods assessed [2, 4].

Previous studies have shown that factors such as age, renal function, and body weight influence vancomycin clearance and modulate vancomycin pharmacokinetics [5,6,7,8,9]. Various studies have looked at several equations used in estimating CrCl in obese patients with evolving divergent findings on the best equations and body weight to use [10,11,12,13,14,15]. The Salazar–Corcoran (S–C) equation had been proposed as the best method for estimating CrCl in obese patients with a body mass index ≥ 30 kg/m2 and this finding was corroborated by the study by Spinler et al. [10, 11]. However, more recent studies have been testing the use of the Cockcroft–Gault (C–G) equation to estimate CrCl [12] using ideal body weight, actual body weight, lean body weight, and 40% adjusted body weight [adjusted body weight = ideal body weight + 0.4 × (actual body weight − ideal body weight)] [13,14,15]. Initially, using lean body weight in the C–G equation was promising [14]; however, using the 40% adjusted body weight in the C–G equation has emerged as the least biased and most accurate method for calculating the C–G CrCl [15].

The primary objective of this case series is to evaluate the correlation between patient-specific vs population-predicted vancomycin pharmacokinetic parameters (Ke and t1/2) in a case series of hospitalized patients at an academic medical center. We aim for findings from this study to contribute to the literature and influence clinicians’ confidence on the use of population-predicted vancomycin pharmacokinetics Ke and t1/2 when obtaining patient-specific Ke and t1/2 is impractical or impossible.

2 Methods

2.1 Study Design and Patient Population

This is a single-center case series of patients who received vancomycin pharmacokinetic monitoring at University Medical Center, New Orleans, Louisiana from 1 July, 2018 to 30 May, 2019. This study was approved by the Institutional Review Board of Xavier University of Louisiana and the University Medical Center Research Review Committee. The target sample size proposed for this case series is approximately 20–40 patients based on a priori estimates on the number of patients who will meet inclusion criteria over the specified study timeframe.

All patients who were 18 years of age and older and received vancomycin therapy were included in the study. Patients were included if they were on the vancomycin monitoring list serviced by the primary investigator, had serum creatinine for calculation of population-predicted pharmacokinetic parameters, and had two vancomycin concentrations for calculation of patient-specific pharmacokinetic parameters. Patients were included if their vancomycin concentrations and serum creatinine were obtained within a 1-day period. Patients were excluded if vancomycin doses were given in between the two vancomycin concentrations.

2.2 Data Collection

The following demographic and clinical variables were collected on patients: age, sex, race, height, actual body weight (ABW), ideal body weight (IBW), adjusted body weight (AdjBW), body mass index, serum creatinine, C–G CrCl using IBW (C–G CrCl-IBW), C–G CrCl using ABW (C–G CrCl-ABW), C–G CrCl using AdjBW (C–G CrCl-AdjBW), S–C CrCl using ABW (S–C CrCl-ABW), first serum vancomycin concentration during elimination phase, second serum vancomycin concentration during elimination phase, hours apart between vancomycin concentrations for patient-specific pharmacokinetics, and time from last vancomycin dose to first serum vancomycin concentration during elimination phase. In addition, the following predictor variables were collected: Ke using C–G CrCl-IBW, Ke using C–G CrCl-ABW, Ke using C–G CrCl-AdjBW, Ke using S–C CrCl ABW, t1/2 using C–G CrCl-IBW, t1/2 using C–G CrCl-ABW, t1/2 using C–G CrCl-AdjBW, and t1/2 using S–C CrCl-ABW. Collected outcome variables were patient-specific Ke and patient-specific t1/2. All diagnoses were supported with a documented physician diagnosis and confirmed on the electronic medical record using the definition criteria below. Acute kidney injury was defined, based on the Kidney Disease: Improving Global Outcomes guideline, as an increase in serum creatinine by ≥ 0.3 mg/dL within 48 h; or an increase in serum creatinine to ≥ 1.5 times the baseline, which is known or presumed to have occurred within the prior 7 days; or urine volume < 0.5 mL/kg/h for 6 h [16]. Chronic kidney disease was defined, based on the Kidney Disease: Improving Global Outcomes guideline, as the presence of either kidney damage or decreased kidney function for 3 or more months, irrespective of cause [17]. The chronic kidney disease definition accounted for: duration—duration≥ 3 months, predicted on documentation or inference; function – glomerular filtration rate < 60 mL/min/1.73 m2 (glomerular filtration rate categories G3a–G5); and damage—kidney damage, as defined by structural abnormalities or functional abnormalities other than decreased glomerular filtration rate such as albuminuria (albumin excretion rate ≥ 30 mg/24 h; albumin-to-creatinine ratio ≥ 30 mg/g [≥ 3 mg/mmol]), urine sediment abnormalities, electrolyte and other abnormalities due to tubular disorders, abnormalities detected by histology, structural abnormalities detected by imaging, and history of kidney transplantation. End-stage renal disease was defined as chronic kidney failure in which a person’s kidneys cease functioning on a permanent basis leading to the need for a regular course of long-term dialysis or a kidney transplant to maintain life. [18].

Weight was calculated using one of the following equations:

$$ \begin{aligned}& A{\text{ctual body weight }}\left( {\text{ABW}} \right)\,\, {\text{for male and female patients}} \\ &\quad= {\text{Measured weight using weighing scale}}\end{aligned} $$
$$ \begin{aligned}&{\text{Ideal body weight }}\left( {\text{IBW}} \right){\text{for male patients}}\\ &\quad = 50 + 2.3\,\, ({\text{height in inches}} > 60 {\text{ inches}})\end{aligned} $$
$$ \begin{aligned}&{\text{Ideal body weight }}\left( {\text{IBW}} \right)\,\, {\text{for female patients}} \\ &\quad= 45.5 + 2.3 \,\,({\text{height in inches}} > 60 {\text{ inches}})\end{aligned} $$
$${\text{Adjusted body weight for male patients}} = I{\text{BW for male patients}} + 0.4\,\, \left( {{\text{ABW}} - {\text{IBW for male patients}}} \right)$$
$${\text{Adjusted body weight for female patients}} = {\text{IBW for female patients}} + 0.4 \,\,\left( {{\text{ABW}} - {\text{IBW for female patients}}} \right)$$

where weight is in kilograms, and height is in inches.

Creatinine clearance was calculated using one of the following equations:

$$ \begin{aligned}&{\text{Cockcroft}}{-}{\text{Gault }}\left( {C{-}G} \right) \,\,{\text{equation for male patients}} \\ &\quad= \frac{{\left( {140 - {\text{age}}} \right)\,\,\left( {\text{weight}} \right)}}{{\left( {72} \right)\,\,\left( {\text{serum creatinine}} \right)}}\end{aligned} $$
$$ \begin{aligned}&{\text{Cockcroft}}{-}{\text{Gault }}\left( {{\text{C}}{-}{\text{G}}} \right) {\text{equation for female patients}} \\ &\quad= \frac{{\left( {140 - {\text{age}}} \right)\,\,\left( {\text{weight}} \right)}}{{ \left( {72} \right)\,\,\left( {\text{serum creatinine}} \right)}} \times 0.85\end{aligned} $$
$$ \begin{aligned}&{\text{Salazar}}{-}{\text{Corcoran}}\,\, \left( {{\text{S}}{-}{\text{C}}} \right)\,\, {\text{equation for male patients}} \\ &\quad= \frac{{\left( {137 - {\text{Age}}} \right)\,\,\left( {0.285 \times {\text{weight}}} \right) + \left( {12.1 \times {\text{height}}^{2} } \right)}}{{\left( {51} \right)\,\,\left( {\text{serum creatinine}} \right)}}\end{aligned} $$
$$ \begin{aligned}&{\text{Salazar}}{-}{\text{Corcoran}} \,\,\left( {{\text{S}}{-}C} \right)\,\, {\text{equation for female patients}} \\ &\quad= \frac{{\left( {146 - {\text{Age}}} \right)\,\,\left( {0.287 \times {\text{weight}}} \right) + \left( {9.74 \times {\text{height}}^{2} } \right)}}{{\left( {60} \right)\,\,\left( {\text{serum creatinine}} \right)}}\end{aligned} $$

where age is in years, weight is in kilograms, height is in meters, and serum creatinine is in milligram (mg)/deciliter (dL). Weight is either actual body weight (ABW), ideal body weight (IBW), or adjusted body weight (AdjBW) for the C–G equation and weight is actual body weight (ABW) for the S–C equation.

Population-predicted pharmacokinetic parameters were calculated using the following equations [2]:

$$K_{\text{e}} = \left( {0.00083 \times CrCl} \right) + 0.0044$$
$$t_{1/2} = \frac{0.693}{{K_{\text{e}} }},$$

where Ke is the first-order elimination rate constant, CrCl is the creatinine clearance in mL/min based on the C–G equation or S–C equation, and t1/2 is the half-life.

Patient-specific pharmacokinetic parameters were calculated using the following equations [19]:

$$K_{\text{e}} = \frac{{\ln \left( {\frac{C1}{C2}} \right)}}{{{\text{time hours between }} C1 {\text{ and }} C2}}$$
$$t_{1/2} = \frac{0.693}{{K_{\text{e}} }},$$

where Ke is the first-order elimination rate constant, C1 is the first vancomycin concentration drawn at least 2 h after vancomycin is fully administered to ensure vancomycin post-administration distribution phase is complete [20], C2 is the second vancomycin concentration drawn after C1, and t1/2 is the half-life. Vancomycin doses were not given in between C1 and C2.

The default vancomycin infusion durations were 1 h for vancomycin ≤ 1000 mg, 1.5 h for vancomycin 1250–1500 mg, 2 h for vancomycin 1750–2000 mg, and 3 h for vancomycin 2250–3000 mg. Data on whether vancomycin concentration was collected at steady state were assessed. Steady-state concentration was defined as a vancomycin concentration obtained prior to the fourth maintenance dose for patients with normal renal function and prior to the third dose for patients with renal dysfunction (acute kidney injury, chronic kidney disease, and end-stage renal disease); consistent with our hospital protocol [21].

2.3 Study Objectives

The primary objective of this study is to evaluate the correlation between population-predicted and patient-specific pharmacokinetic parameters (Ke and t1/2). The secondary objectives of this study is to evaluate the mean bias and precision between the population-predicted and patient-specific pharmacokinetic parameters (Ke and t1/2) in select adult medicine patients. A subgroup analysis was performed to assess the correlation between population-predicted and patient-specific pharmacokinetic parameters (Ke and t1/2) in special populations—obese patients with a body mass index ≥ 30 kg/m2 and patients with renal dysfunction (acute kidney injury, chronic kidney disease, and end-stage renal disease). All correlation analyses were performed on the population-predicted pharmacokinetics using diverse methods of estimating renal function (S–C and C–G methods using either ideal, actual, and adjusted body weights).

2.4 Statistical Analyses

Descriptive statistics were used to describe the study demographic characteristics. Simple linear regression analysis was performed to assess the Pearson correlation coefficient (r) and the unstandardized coefficient (β) ± standard error between population-predicted and patient-specific pharmacokinetic parameters: Ke and t1/2. The Student’s t test was used to compare mean differences between the population-predicted and patient-specific pharmacokinetic parameters (Ke and t1/2) in patients. An F-test is used to test if the ratio of the two precision estimates between the two groups is different. All significance testing was set at an α of < 0.05. IBM SPSS Statistics version 25 and SAS version 9.4 were used to conduct all statistical analyses.

3 Results

A total of 30 patients were included in the study. 33.3% (10/30) of the patients were obese and 56.7% (17/30) of the patients had renal dysfunction (11 had acute kidney injury, 1 had chronic kidney disease, 3 had both acute kidney injury and chronic kidney disease, and 2 had end-stage renal disease). Of the 30 patients, 23 patients (76.7%) were at steady state when the vancomycin concentration was drawn, six patients did not reach steady state when the vancomycin concentration was drawn, and for 1 patient, we could not decide whether the patients was at steady state because the patient received the vancomycin dose at an outside hospital and had no documented record of the vancomycin doses received at the outside hospital. Out of the 23 patients who were at steady state, only four were counted as reaching steady state prior to the third dose as the patients had renal dysfunction. Seven patients were hospitalized in the intensive care unit and 23 patients were admitted in non-intensive care unit inpatient settings when the vancomycin concentration was drawn. Tables 1, 2, and 3 provide information on our hospital’s vancomycin protocol and patients’ baseline information.

Table 1 Vancomycin dosing guide protocol used at the University Medical Center, New Orleans [21]
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Table 2 Baseline characteristics
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Table 3 Infections treated in all patients
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Tables 4 and 5 show the relationship between the population-predicted pharmacokinetic parameters (Ke and t1/2) and patient-specific pharmacokinetic parameters (Ke and t1/2) in all patients. All the calculated population-predicted Ke and t1/2 using all four CrCl estimation methods were each significantly correlated with patient specific Ke and t1/2; with the population-predicted Ke and t1/2 calculated using C–G CrCl-AdjBW showing the strongest association with patient-specific Ke and t1/2. Figures 1, 2, 3 and 4 provide a simple linear regression graph of the relationship between the patient-specific Ke and population-predicted Ke calculated using different methods for estimating CrCl.

Table 4 Relationship between population-predicted elimination rate constant (Ke) and patient-specific Ke in all patients (n = 30)
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Table 5 Relationship between population-predicted half-life (t1/2) and patient-specific t1/2 in all patients (n = 30)
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Fig. 1
figure 1

Relationship between population-predicted elimination rate constant (Ke) using Cockcroft–Gault creatinine clearance-ideal body weight (C–G CrCl-IBW) and patient-specific Ke (r = 0.718; coefficient of determination [R2] = 0.516; n = 30)

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Fig. 2
figure 2

Relationship between population-predicted elimination rate constant (Ke) using Cockcroft–Gault creatinine clearance-actual body weight (C–G CrCl-ABW) and patient-specific Ke (r = 0.711; R2 = 0.505; n = 30)

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Fig. 3
figure 3

Relationship between population-predicted elimination rate constant (Ke) using Cockcroft–Gault creatinine clearance-adjusted body weight (C–G CrCl-AdjBW) and patient-specific Ke (r = 0.729; R2 = 0.532; n = 30)

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Fig. 4
figure 4

Relationship between population-predicted elimination rate constant (Ke) using Salazar–Corcoran creatinine clearance-actual body weight (S–C CrCl-ABW) and patient-specific Ke (r = 0.725; R2 = 0.525; n = 30)

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When evaluating the mean difference in bias between the population-predicted parameter; Ke (Table 6), there was no significant mean difference between the patient-specific Ke and population-predicted Ke calculated using C–G CrCl-IBW and C–G CrCl-AdjBW. The mean patient-specific Ke was significantly different from the population-predicted Ke calculated using C–G CrCl-ABW and S–C CrCl-ABW; however, the mean differences observed were small at 0.018 h−1 and 0.016 h−1, respectively. There were no significant differences in precision between any of the population-predicted Ke and the patient-specific Ke. Table 7 shows the t1/2 calculation derived from the Ke from Table 6. All population-predicted t1/2 were significantly different from patient-specific t1/2. Likewise, the precision of all the population-predicted t1/2 were smaller than the patient-specific Ke.

Table 6 Mean bias and precision between population-predicted elimination rate constant (Ke) and patient-specific Ke in all patients (n = 30)
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Table 7 Mean bias and precision difference between population-predicted half-life (t1/2) and patient-specific t1/2 in all patients (n = 30)
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Tables 8 and 9 show the relationship between the population-predicted Ke and t1/2 and patient-specific Ke and t1/2 in obese patients. All the population-predicted Ke using different CrCl methods were significantly correlated with patient-specific Ke. The population-predicted t1/2 was significantly correlated with patient-specific t1/2 using three different CrCl methods with the population-predicted t1/2 derived from C–G CrCl-ABW not showing a strong correlation with patient-specific t1/2. The population-predicted Ke and t1/2 calculated using C–G CrCl-IBW showed the strongest association with patient-specific Ke and t1/2 in obese patients. Among patients with renal dysfunction (Tables 10 and 11), all the population-predicted Ke and t1/2 were significantly correlated with patient-specific Ke and t1/2. The population-predicted Ke using C–G CrCl-ABW had the strongest correlation to the patient-specific Ke, while the population-predicted t1/2 using C–G CrCl-AdjBW had the strongest correlation to the patient-specific t1/2 in patients with renal dysfunction.

Table 8 Relationship between population-predicted elimination rate constant (Ke) and patient-specific Ke in obese patients (n = 10)
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Table 9 Relationship between population-predicted half-life (t1/2) and patient-specific t1/2 in obese patients (n = 10)
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Table 10 Relationship between population-predicted elimination rate constant (Ke) and patient-specific Ke in patients with renal dysfunction (n = 17)
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Table 11 Relationship between population-predicted half-life (t1/2) and patient-specific t1/2 in patients with renal dysfunction (n = 17)
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4 Discussion

To our knowledge, this is the first study examining the correlation between vancomycin population-predicted and patient-specific pharmacokinetic parameters. This study noted that regardless of the CrCl method used, the Matzke population-predicted Ke was reliable and strongly correlated to the patient-specific Ke. Our study findings were consistent with findings from the Oswalt et al. and Murphy et al. studies [3, 4]. The Oswalt study found small, clinically negligible differences between the population-predicted and patient-specific pharmacokinetics and concluded that using population-predicted pharmacokinetics may be an accurate empiric dosing strategy for determining vancomycin dosing frequency in patients with acute brain injury. 3 Similar to the Oswalt et al. study, our study found two small and clinically negligible significant differences between patient-specific and population-predicted pharmacokinetics using C–G CrCl-ABW and S–C CrCl-ABW, while there was no significant bias between patient-specific and two population-predicted pharmacokinetics using C–G CrCl-IBW and C–G CrCl-AdjBW. The Murphy et al. study also noted that the Matzke population-predicted pharmacokinetic parameter (which was used in our study) performed best compared with the other six methods evaluated in their study.

In our study, we observed that regardless of the CrCl estimation method used, the population-predicted Ke was significantly correlated with patient-specific Ke. However, population-predicted Ke using C–G CrCl-AdjBW had the strongest correlation with patient-specific Ke in all patients in our case series. In the subgroup analyses of special populations, population-predicted Ke using C–G CrCl-IBW had the strongest correlation with patient-specific Ke in obese patients and the population-predicted Ke using C–G CrCl-ABW had the strongest correlation in patients with renal dysfunction. This slightly stronger favoring of the C–G CrCl-IBW as the best method for calculating population-predicted Ke is somewhat inconsistent with other studies, which have previously reported that the C–G CrCl-IBW underestimates CrCl in obese patients [14, 22]. This finding of the better performance of the C–G CrCl-IBW for the calculation of population-predicted Ke in obese patients should be interpreted cautiously given the limitations of our small study. The S–C equation was also not the best method in obese patients as supported by prior studies [10, 11]. The population-predicted Ke using C–G CrCl-ABW had the best correlation to patient-specific Ke in patients with renal dysfunction. The assessment of the correlation between patient-specific and population-predicted pharmacokinetics in patients with renal dysfunction was an exploratory subgroup analysis in our case series. It is worth noting that two methods, not used in our case series, have been previously proposed for calculating CrCl in patients with renal dysfunction, although these methods are dated and need validation in a larger population [23, 24].

Our study has some strengths and limitations. The strength of this study is that it evaluated a mix of adult patients that is similar to patients encountered in real-life clinical settings, with different infections, comorbid status (obesity, renal dysfunction), and vancomycin concentrations obtained pre- and post-steady state. The study limitations include that this is a single-center study, which reduces the external validity and generalizability of our study. The study sample size is small (N = 30); although the risk of a type 2 statistical error is low as the study sufficiently identified a significant correlation between population-predicted and patient-specific pharmacokinetic parameters (Ke and t1/2). There is a risk of selection bias in our study given that patients with renal dysfunction may have been oversampled as this population typically requires multiple vancomycin concentrations to help in the selection of an appropriately individualized vancomycin dose frequency. The equations used in this study for measuring CrCl provide CrCl estimates compared to 24-h urine collection and these equations do not account for rapid changes in CrCl among patients with renal dysfunction. Additionally, we acknowledge that not assessing the area under the curve to minimum inhibitory concentration is a limitation of our study as emerging evidence is pointing to this measure as a better pharmacokinetic/pharmacodynamic marker for monitoring vancomycin efficacy while ensuring patient safety and guiding vancomycin dose optimization [25,26,27,28,29].

5 Conclusions

The study found that regardless of the CrCl estimation method used, population-predicted Ke was significantly correlated with patient-specific Ke. Population-predicted Ke using C–G CrCl-AdjBW had the strongest correlation with patient-specific Ke in all patients. Among special populations assessed, population-predicted Ke using C–G CrCl-IBW had the strongest correlation with patient-specific Ke in obese patients and population-predicted Ke using C–G CrCl-ABW had the strongest correlation in patients with renal dysfunction. The vancomycin population-predicted pharmacokinetic formula can be used safely to estimate a patient’s vancomycin pharmacokinetics in hospitalized adult patients.