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. Author manuscript; available in PMC: 2023 Apr 1.
Published in final edited form as: Pharmacotherapy. 2022 Feb 17;42(4):284–291. doi: 10.1002/phar.2670

Comparison of Bayesian-derived and first-order analytic equations for calculation of vancomycin area under the curve

Katie B Olney 1,2, Katie L Wallace 1,2, Ryan P Mynatt 1, David S Burgess 2, Kaitlyn Grieves 2, Austin Willett 2, Johann Mani 2, Alexander H Flannery 1,2
PMCID: PMC9750735  NIHMSID: NIHMS1854577  PMID: 35134264

Abstract

INTRODUCTION:

Consensus guidelines recommend targeting a vancomycin area under the curve to minimum inhibitory concentration (AUC24:MIC) ratio of 400-600 to improve therapeutic success and reduce nephrotoxicity. Although guidelines specify either Bayesian software or first-order equations may be used to estimate AUC24, there are currently no large studies directly comparing these methods.

OBJECTIVE:

To compare calculated AUC24 using first-order equations with two drug concentrations at steady state to Bayesian two and one-concentration estimations.

METHODS:

This was a single center, retrospective cohort study of 978 adult hospitalized patients receiving intravenous vancomycin between 2017-2019. Patients were included if they received at least 72 hours of vancomycin and had two serum drug concentrations obtained. AUC24 was calculated using first-order analytic (linear), Bayesian two-concentration, and Bayesian one-concentration methods for each patient. The InsightRx™ software platform was used to calculate Bayesian AUC24. Pearson’s correlation and clinical agreement (based on AUC24 classified as subtherapeutic, therapeutic, or supratherapeutic) were used to assess agreement between methods. Bland-Altman plots were used to assess mean difference (MD) and 95% limits of agreement (LOA).

RESULTS:

Excellent agreement was observed between linear and Bayesian two-concentration methods (r=0.963, clinical agreement=87.42%) and Bayesian two-concentration and one-concentration methods (r=0.930, clinical agreement=88.45%), however, a degree of variability was noted with 95% LOA −99 to 76 (MD=−11.5 mg*hr/L) and −92 to 113 (MD=10.4 mg*hr/L), for the respective comparisons. The agreement between linear and Bayesian one-concentration approaches was less than prior comparisons (r=0.829, clinical agreement=76.78%), and demonstrated the greatest amount of variability with 95% LOA −197 to 153 (MD=−21.9 mg*hr/L).

CONCLUSIONS:

Linear and Bayesian two-concentration methods demonstrated high-level agreement with acceptable variability and may be considered comparable to estimate AUC24. As linear and Bayesian one-concentration methods demonstrated significant variability and suboptimal agreement, concerns exist surrounding the interchangeability of these methods in clinical practice, particularly at higher extremes of AUC24.

Keywords: Therapeutic drug monitoring, Pharmacokinetics, Pharmacodynamics, Vancomycin, Area under the Curve, Bayesian

INTRODUCTION:

Effective therapeutic drug monitoring of intravenous (IV) vancomycin therapy is essential to mitigate the risk of acute kidney injury (AKI), estimated to be as high as 43% in the general population, as well as improve efficacy and therapeutic success (1-11). The 2020 consensus guidelines for therapeutic drug monitoring of vancomycin in methicillin-resistant Staphylococcus aureus (MRSA) infections recommend a goal area under the curve from 0 to 24 hours to minimimum inhibitory concentration (AUC24:MIC) ratio of 400-600 be achieved within the first 24 to 48 hours of therapy to improve therapeutic success and reduce nephrotoxicity (12). Recommendations towards appropriate methods for calculation of AUC24 include either first-order analytic calculations (using two drug concentrations at steady state) or Bayesian methods (preferably using two concentrations) (12).

Currently robust clinical and pharmacokinetic data comparing first-order analytical and Bayesian methods are lacking. The primary benefits of using a first-order analytic method for AUC24 calculation include decreased implementation cost and reliance on fewer assumptions, as compared to Bayesian software (12). The advantages of Bayesian software include the potential to decrease sampling burden (i.e. only one concentration required for calculation) and the ability to calculate estimated AUC24 prior to steady state (13-15). Although decreased sampling burden is a potential advantage of Bayesian software monitoring, consensus guidelines preferentially recommend utilization of two concentrations as data validating Bayesian one-concentration AUC24 estimations are currently lacking. Pharmacokinetic studies assessing Bayesian software suggest this method can underestimate AUC24, when compared to traditional first-order steady state calculations, although few data are available to estimate the clinical implications of such underestimation and the extent to which Bayesian estimates relate to first-order calculations in a real-world setting (13, 14). The aim of this study was to assess the overall agreement and associated variability in calculated AUC24 from a real-world cohort of patients with two vancomycin concentrations at steady state.

METHODS:

Patient Identification

Adult patients ≥18 years of age admitted to University of Kentucky HealthCare between 10/1/2017-9/12/2019 who received at least 72 hours of IV vancomycin therapy with two steady state concentrations obtained within 96 hours of vancomycin initiation were included. AUC24 monitoring using two steady state concentrations (peak drawn 2 hours following the end of infusion and trough drawn 30 minutes prior to the next dose) assessed using linear equations was the standard of care for vancomycin monitoring during this time. Patients were excluded if they had underlying renal dysfunction (creatinine clearance ≤30 mL/min estimated using the Cockcroft-Gault equation), were receiving renal replacement therapy, or had AKI (using the Kidney Disease Improving Global Outcomes (KDIGO) definition) prior to initiation of IV vancomycin. Baseline serum creatinine (SCr) was defined as the SCr measured immediately prior to the first dose of IV vancomycin. If no SCr was obtained prior to the first dose, the first measured SCr following initiation of therapy was used. Critically ill patients were defined as any patient admitted to an intensive care unit (ICU) at any point during the course of IV vancomycin therapy. For the purpose of this study, the abbreviation “AUC24” will be used interchangeably with AUC24:MIC, assuming a vancomycin MIC of 1 mg/L.

Data Collection

All data were extracted from the University of Kentucky Center for Clinical and Translational Science and coding was completed by a data analyst with Biostatistics, Epidemiology, & Research Design (BERD) at the University of Kentucky. Approximately 10% of included patients were selected at random and had vancomycin concentrations manually validated through review of the electronic medical record (EMR). All pharmacokinetic parameters were calculated utilizing two vancomycin concentrations obtained at steady state utilizing the equations detailed in Table 1A in the Supplementary Appendix.

At the conclusion of the study period, patient-specific characteristics including weight, height, sex, age, serum creatinine, vancomycin administration data, and vancomycin concentration data were manually entered into the InsightRx™ software platform in a retrospective fashion to determine AUC24 by both Bayesian two-concentration and one-concentration methods. Seven pharmacokinetic models are incorporated into the InsightRx™ platform: Goti et al., Thomson et al., Buelga et al., Drusano et al., Neely et al., Rodvold et al., and Carreno et al (16-22). The InsightRx™ software platform recommends the most appropriate population-based pharmacokinetic model based on patient-specific age, weight, height, and serum creatinine data. These recommended models were used in the retrospective calculation of Bayesian two-concentration and one-concentration AUC24. The most commonly used model, Thomson et al., serves as the default for all non-critically ill patients (16). Goti et al. was defaulted for critically ill patients and Carreno et al. was defaulted for obese patients (17, 22).

Initially, the vancomycin dosing data and trough concentration were entered into the InsightRx™ platform to calculate the Bayesian one-concentration AUC24. Following extraction of the Bayesian one-concentration AUC24, the peak concentration was input and the Bayesian two-concentration AUC24 was subsequently calculated. After input of all dosing and concentration data, the AUC24 corresponding with time of concentration attainment and linear AUC24 calculation was recorded. For example, if a patient had vancomycin concentrations obtained around the fifth dose of IV vancomycin, the real-time InsightRx™ AUC24 following the fifth dose of vancomycin was used for comparison to linear methods.

Statistical Analysis

Correlations between AUC24 estimated by all three methods (linear, Bayesian two-concentration, and Bayesian one-concentration) were assessed using Pearson’s correlation. To compare the calculated AUC24 values, we employed a similar approach to that of Narayan et al (23). Agreement was estimated using the mean difference (MD) between Bayesian and linear AUC24 methods while the 95% limits of agreement (LOA) based on Bland-Altman plots were used to determine variability.

Categorical matching was used to determine the clinical decision agreement and characterize the concordance for which linear, Bayesian two-concentration, and Bayesian one-concentration resulted in AUC24 estimations classified as subtherapeutic (AUC24 <400 mg*hr/L), therapeutic (AUC24 400-600 mg*hr/L), or supratherapeutic (AUC24 >600 mg*hr/L). The clinical decision agreement provides an estimation of the extent to which the different methods would have influenced clinical decision making in practice (dose increase, no change, or dose reduction, respectively). Data analyses were conducted using Stata (StataCorp. 2019. Stata Statistical Software:Release 16; StataCorp LLC, College Station, Texas, USA).

RESULTS:

In total, 1085 patients met baseline inclusion criteria and 978 patients were included in the final analysis. More than 60% of included patients were male and the median age was 52 years (IQR 39, 62). Of the included patients, 69% were critically ill and the median BMI was 27 kg/m2 (IQR 23, 32). The median total daily dose of IV vancomycin was 2,500 mg (IQR 2000, 3000) and the median time from first dose to first serum vancomycin concentration was 47.2 hours (IQR 35.7, 58.9). Baseline demographics are displayed in Table 1.

Table 1:

Baseline Characteristics

Patient Demographics (n=978)
Age, years
Median (Interquartile Range) 		52 (39, 62)
Male Gender
Total (%) 		588 (60.1%)
Critically ill
Total (%) 		675 (69%)
Body mass index, kg/m2
Median (Interquartile Range) 		27 (23, 32)
Baseline serum creatinine, mg/dL
Median (Interquartile Range) 		0.8 (0.7, 1.0)
Dosing and Therapeutic Drug Monitoring Data
Total daily dose, mg
Median (Interquartile Range) 		2500 (2000, 3000)
Dosing interval
 8 hours
 Total (%) 		47 (4.8%)
 12 hours
 Total (%) 		795 (81.3%)
 18 hours
 Total (%) 		1 (0.1%)
 24 hours
 Total (%) 		137 (14%)
Time from first dose to first serum concentration, hours
Median (Interquartile Range) 		47.2 (35.7, 58.9)
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Linear versus Two-Concentration Bayesian

Excellent correlation was observed between linear and Bayesian two-concentration methods (r=0.963) with 87.4% clinical decision agreement (Figures 1 and 2). Based on Bland-Altman plotting, the MD was −11.5 mg*hr/L and 95% LOA was −99 to 76 (Figure 2). In patients with an AUC24 considered subtherapeutic by linear method, the Bayesian two-concentration method predicted a therapeutic AUC24 14.9% of the time. In patients with a linear AUC24 classified as supratherapeutic, the Bayesian two-concentration method resulted in an AUC24 classified as therapeutic 21.4% of the time. Although agreement was strong on average between the two methods, increasing variability was seen with AUC24 exceeding 600 mg*hr/L (Figure 2).

Figure 1: Scatterplot of AUC24 Estimations by method.

Figure 1:

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A: Linear AUC24 versus Bayesian 2-Level AUC24; B: Linear AUC24 versus Bayesian 1-Level AUC24; C: Bayesian 1-Level AUC24 versus Bayesian 2-Level AUC24

Figure 2: Comparison of AUC24 Methods by Bland-Altman Plotting and Clinical Decision Agreement.

Figure 2:

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A: Linear AUC24 versus Bayesian 2-Level AUC24; B: Linear AUC24 versus Bayesian 1-Level AUC24; C: Bayesian 1-Level AUC24 versus Bayesian 2-Level AUC24

Linear versus One-Concentration Bayesian

Correlation between linear and one-concentration Bayesian methods was moderately high (r=0.823), but less so than the other comparisons and had the lowest overall clinical decision agreement of only 76.8% (Figures 1 and 2). Linear and one-concentration Bayesian methods demonstrated the largest differences on average and the highest variability in their differences with MD of −21.9 mg*hr/L and 95% LOA −197 to 153 (Figure 2).

When linear AUC24 was classified as subtherapeutic, the Bayesian one-concentration method predicted a therapeutic AUC24 26.6% of the time (Figure 2). When linear AUC24 was classified as supratherapeutic, the corresponding Bayesian one-concentration AUC24 was classified as therapeutic or subtherapeutic 31.5% and 2.1% of the time, respectively (Figure 2). Again, increasing variability was seen when AUC24 exceeded 600 mg*hr/L (Figure 2).

Two-Concentration Bayesian versus One-Concentration Bayesian

Correlation between Bayesian two-concentration and one-concentration methods was strong (r=0.931), with 88.5% clinical decision agreement (Figures 1 and 2). MD was 10.4 mg*hr/L and 95% LOA for Bayesian two-concentration and Bayesian one-concentration methods was −92 to 113 based on Bland-Altman plotting (Figure 2). In patients with an AUC24 considered subtherapeutic by Bayesian two-concentration method, the Bayesian one-concentration method predicted an AUC24 that was therapeutic 12.8% of the time (Figure 2). When Bayesian two-concentration AUC24 was classified as supratherapeutic, the corresponding Bayesian one-concentration AUC24 was classified as therapeutic or subtherapeutic 14.6% and 1.0% of the time, respectively.

DISCUSSION:

In our real-world cohort study of patients with two steady state vancomycin concentrations, we found that, on average, the mean difference in AUC24 estimates between the three approaches was low overall. Variability was acceptable for the comparisons of linear versus Bayesian two-concentration and Bayesian two-concentration versus Bayesian one-concentration, but significant variability and low clinical decision agreement was noted in the linear versus Bayesian one-concentration. In general, agreement suffered the most at higher AUC24 values.

Bayesian software relies on population pharmacokinetic modeling, in combination with at least one patient-specific drug concentration, to provide an estimated AUC24 (12). The basis of Bayesian calculation software, the Bayes’ Theorem, is a mathematical equation designed to quantify the relationship between population-based probability distribution (i.e. the Bayesian prior) and patient-specific pharmacokinetics (i.e. the Bayesian posterior) (12-15). The Bayesian prior is estimated utilizing population kinetics and probability distribution; the adaptive functionality of the software improves the accuracy of estimated population kinetics as more patient-specific data is entered and stored (12-15). This adaptive functionality allows for a holistic, rather than “snapshot”, estimation of pertinent pharmacokinetic parameters.

When comparing methods, it is important to consider the implications of discordance in clinical decision classification. From a safety perspective, the most important relationship is represented by the discordance seen when one method predicts an AUC24 that is supratherapeutic while the other method estimates an AUC24 that is either therapeutic or subtherapeutic. As an AUC24 >600 mg*hr/L has been associated with an increased risk of nephrotoxicity, one could assume that misclassification of AUC24 as either therapeutic or subtherapeutic, resulting in no dose adjustment or subsequent dose increase, may result in augmented vancomycin exposure and increased risk of nephrotoxicity (24, 25). Conversely, from an efficacy standpoint, the most important relationship is represented by the discordance seen when one method predicts an AUC24 that is subtherapeutic while the second method estimates an AUC24 that is therapeutic or supratherapeutic. The consequences of such discordance may prompt the clinician to maintain or decrease the dose when actual exposure is considered suboptimal, thereby potentiating the risk for treatment failure and mortality (26-29).

Linear versus Two-Concentration Bayesian

Overall, linear and two-concentration Bayesian methods demonstrated the strongest correlation (r=0.963) while also maintaining strong clinical decision agreement, low mean difference, and reasonable variability. The increasing variability seen between methods when linear AUC24 exceeded 600 mg*hr/L is likely related to the predictive and adaptive functionality of Bayesian software translating into a “smoothed” curve and subsequently lessened predicted exposure. The impact of this increasing variability most notably results in a concern for increased nephrotoxicity in patients with an AUC24 >600 mg*hr/L by linear methods as more than one fifth of these patients had an AUC24 classified as therapeutic by the Bayesian two-concentration method. However, given the high correlation combined with acceptable variability seen between the two methods, it could be assumed that the actual numerical difference in AUC24 would be unlikely to impact clinical practice or outcomes, despite marginal discordance in clinical categorization (using strict cut-off values) seen at the extremes of AUC24.

Linear versus One-Concentration Bayesian

On average, these methods provided similar AUC24 values, however, there was significant variability when comparing linear calculations to one-concentration Bayesian estimations with 95% LOA −200 to 190 based on Bland-Altman plotting and only 76.8% clinical decision agreement (Figure 2). As such, if one was to assume a therapeutic vancomycin AUC24 of 500 mg*hr/L, a difference of more than 150 mg*hr/L in either direction may result in the potential for significant differences in the clinical management of a patient’s therapy.

There was highly concerning discordance seen, as it relates to risk of nephrotoxicity, in patients with an AUC24 classified as supratherapeutic by linear method. While a supratherapeutic AUC24 calculated by linear method may have resulted in a subsequent dose reduction, the one-concentration Bayesian estimate may have prompted the clinician to either maintain or increase the vancomycin dose approximately one-third of the time. This variation may be due in large part to the fact that only one drug-concentration is utilized to inform the Bayesian software for AUC24 predictions, resulting in substantial “blunting” of the simulated exposure curve. Neely et al. found that Bayesian AUC24 estimated from only trough concentrations required the use of richly sampled vancomycin data as the Bayesian prior to provide accurate estimations.(20) Although established pharmacokinetic models were used as the Bayesian prior within our study, one could postulate that the input of richly sampled vancomycin data over time may result in improved correlation and reduced variability of Bayesian one-concentration estimates, when compared to linear methods.

Two-Concentration Bayesian versus One-Concentration Bayesian

As anticipated, strong correlation was observed between Bayesian two-level and one-level methods (r=0.930), with overall 88.5% clinical decision agreement and a low mean difference. These findings are consistent with what has previously been reported in the literature and are expected given that these assessments are based on the same models and priors (13, 30). Although evidence supporting the real-world applicability of one-concentration Bayesian AUC24 calculations within the general population is limited, the advantages of this method include decreased sampling burden (i.e. only one drug concentration required for calculation) and the ability to calculate estimated AUC24 prior to steady state, allowing for more timely therapeutic drug monitoring (13-15). In general, the adaptable functionality of Bayesian dosing methods, utilizing population pharmacokinetics, may be beneficial to reduce the implications of confounding factors (such as non-physiologic volumes of distribution) when compared to first-order calculations.

Given the additional cost and logistical concerns associated with obtaining two concentrations to perform therapeutic drug monitoring, Bayesian one-concentration methods may offer an alternative method by which to predict AUC24 and reduce hospital spending (31). However, the assumption that one-concentration Bayesian is equivalent to two-concentration Bayesian only remains true if one were to assume that the “gold-standard” for calculation of AUC24 is the Bayesian two-concentration method. Additionally, Narayan and colleagues assessed the predictive performance of Bayesian modeling for IV vancomycin and found all Bayesian models exhibited low bias but also considerably low precision in the critically ill patient population (23). Our findings were similar as, on average, the three methods maintained reasonable correlation and low mean difference, but demonstrated fluctuating variability, particularly at the extremes of AUC24.

There are several limitations to this study including the retrospective nature of data collection and reliance on the electronic medical record to extract all data points. As this study represents a real-world cohort and does not utilize a “true measured” AUC24 for comparison, we were only able to describe agreement between the three different methods. Additionally, although the clinical decision agreement represents a simplified metric of clinical relevance, , it should be recognized that this analysis may overstate the true difference in AUC24 in some instances (i.e. a patient with AUC24 of 400 mg*hr/L would be categorized as therapeutic versus a patient with AUC24 of 399 mg*hr/L would be categorized as subtherapeutic), and is not an exact representation of what changes in vancomycin dosing were made by the clinician at the time of concentration assessment. As Bayesian AUC24 estimates were not compared to the calculated linear AUC24 at the time of vancomycin concentration assessment, this comparison did not impact clinical decision making for this cohort. Additionally, the current therapeutic drug monitoring guidelines at our institution recommend obtaining vancomycin concentrations at approximately steady-state around the fourth dose following initiation of therapy. As such, there is a chance that some patients may have had vancomycin concentrations obtained prior to true steady state based on the calculated patient-specific half-life. Furthermore, as the peak and trough concentrations are obtained around a single vancomycin dose, the linear calculations assume that prior doses were administered on time and at the appropriate dosing interval. Lastly, we used the software-recommended models on the the InsightRx™ software platform rather than a singular consistent Bayesian model. As this represented default use of the software, this does not reflect the adaptive functionality of the software to adjust the Bayesian prior based on a specific institution or specific unit’s data.

CONCLUSIONS:

Linear and Bayesian two-concentration methods provided a similar mean AUC24 with acceptable levels of agreement and may be considered comparable to estimate AUC24. Similarly, Bayesian two-concentration and Bayesian one-concentration methods may also be considered comparable. Overall, Bayesian methods resulted in underestimation of AUC24, when compared to linear calculations, particularly at higher linear AUC24 values. As linear and Bayesian one-concentration methods demonstrated significant variability and lacked high-level agreement, concerns exist surrounding the interchangeability of these methods in clinical practice.

Supplementary Material

Supplementary Table

Acknowledgements:

Statistical support was provided by Dr. Arnold Stromberg, PhD. The project described was supported by the NIH National Center for Advancing Translational Sciences through grant number UL1TR001998. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Footnotes

Disclosures: This publication is the result of research funded by the ACCP Foundation Futures Grant Resident Investigator Award (2020-2021). Bayesian software was provided on a trial basis by InsightRx™ at no cost.

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Supplementary Materials

Supplementary Table
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