Does calculation method matter for targeting vancomycin area under the curve?

Abstract

Objectives

To assess differences in vancomycin AUC estimates from two common, clinically applied first-order pharmacokinetic equation methods compared with Bayesian estimates.

Methods

A cohort of patients who received vancomycin and therapeutic drug monitoring was studied. First-order population pharmacokinetic equations were used to guide initial empirical dosing. After receipt of the first dose, patients had peak and trough serum levels drawn and steady-state AUC was estimated using first-order pharmacokinetic equations as standard care. We subsequently created a Bayesian model and used individual Empirical Bayes Estimates to precisely calculate vancomycin AUC_24–48, AUC_48–72 and AUC_72–96 in this cohort. AUC at steady state (AUC_SS) differences from the first-order methods were compared numerically and categorically (i.e. below, within or above 400–600 mg·h/L) to Bayesian AUCs, which served as the gold standard.

Results

A total of 65 adult inpatients with 409 plasma samples were included in this analysis. A two-compartment intravenous infusion model with first-order elimination fit the data well. The mean of Bayesian AUC_24–48 was not significantly different from AUC estimates from the two first-order pharmacokinetic equation methods (P = 0.68); however, Bayesian AUC_48–72 and Bayesian AUC_72–96 were both significantly different when compared with both first-order pharmacokinetic equation methods (P < 0.01 for each). At the patient level, categorical classifications of AUC estimates from the two first-order pharmacokinetic equation methods differed from categorizations derived from the Bayesian calculations. Categorical agreement was ∼50% between first-order and Bayesian calculations, with declining categorical agreement observed with longer treatment courses. Differences in categorical agreement between calculation methods could potentially result in different dose recommendations for the patient.

Conclusions

Bayesian-calculated AUCs between 48–72 and 72–96 h intervals were significantly different from first-order pharmacokinetic method-estimated AUCs at steady state. The various calculation methods resulted in different categorical classification, which could potentially lead to erroneous dosing adjustments in approximately half of the patients.

Introduction

Recent updates to the vancomycin therapeutic monitoring guidelines for MRSA infections recommend the use of AUC monitoring. In order to maximize efficacy and minimize nephrotoxicity, the recommended daily AUC for MRSA infections is 400–600 mg·h/L.¹ Multiple strategies for calculating AUC are recommended in the guidelines, including first-order pharmacokinetic equations and Bayesian models.^2–4 Clinically applied first-order pharmacokinetic equations for vancomycin monitoring utilize two serum levels to determine the daily AUC value; a post-distributional peak (drawn 1–2 h post-infusion) and a trough (drawn 30 min prior to the next infusion).^3,5 The main advantages of first-order pharmacokinetic equations are ease of implementation and widespread familiarity among clinicians. However, first-order pharmacokinetic equations can only provide a snapshot of the patient’s AUC at steady state (AUC_SS) when assumptions are made that patient dosing and clinical status remain constant. As a result, AUC estimations derived from first-order pharmacokinetic equations can vary widely if individual patient factors, such as renal function or volume of distribution (V_d), change during or after the sampling period. Bayesian models differ because they utilize Bayesian priors (prior knowledge about how the drug behaves in similar patients) combined with individual patient data, to more accurately predict individual patient drug exposures.^4,6–8 Bayesian models with well-developed priors offer additional flexibility in vancomycin monitoring compared with first-order pharmacokinetic equations, since timing of levels is less critical and one level can provide accurate AUC estimates in some cases.^4,8,9 Covariates, such as renal function and weight-adjusted V_d, can also be incorporated into Bayesian models to provide adaptive AUC estimates that reflect ‘real-time’ variability and patient-specific drug disposition.¹⁰

Differences in calculated vancomycin AUC between these methods are largely unexplored. Both methods are recommended in the guidelines, which may lead clinicians to assume that they result in similar AUC estimates. The purpose of this study was to compare two clinically applied first-order pharmacokinetic equation methods that estimate AUCss with Bayesian estimates of vancomycin AUC over three distinct timepoints that approach steady state.

Methods

Analyses in this report are from data collected as a retrospective cohort study of adult patients who received vancomycin at the University of Maryland Medical Center (UMMC), Baltimore, MD, USA from 1 February 2017 to 31 January 2018. Initial empirical dosing was by first-order population pharmacokinetic equations based on total body weight and calculated creatinine clearance using the Cockcroft–Gault equation (capped at 120 mL/min), targeting an AUC of 500 mg·h/L at steady state. Subsequent two-level AUC dosing was based on first-order patient-specific parameters (i.e. calculated with two concentrations drawn around the peak and trough). This was standard practice for vancomycin dosing and monitoring at UMMC during the study period. All patients had peak and trough vancomycin levels drawn after the first dose on day one. Peak levels were drawn approximately 2 h after the end of infusion and trough levels were drawn at least 5 h after the first dose, ideally within 30 min of the next scheduled infusion. With these two concentrations, AUC_SS was calculated using first-order equations and patient-specific parameters (see the Supplementary data available at JAC Online).¹¹ Vancomycin doses and schedules were then adjusted as needed to target AUC_SS between 400–600 mg·h/L.¹

Subsequently, we employed a Bayesian estimation approach using Monolix 2021R1 (Lixoft, Antony, France); a two-compartment model served as the base.¹² Evaluated covariates included height, weight, creatinine clearance and concomitant receipt of nephrotoxins. Pharmacological and physiologically plausible covariates were considered for addition in the model based on a stepwise approach. Continuous covariates were log-transformed and an allometric scaler for weight was applied to clearance with a linear scaler for volume. Selection of the final model was based on the Akaike Information Criterion (AIC), between-subject variability of the population estimates, goodness-of-fit plots for observed versus predicted and the rule of parsimony. Using the finalized model structure, Empirical Bayes Estimates (EBEs) for each patient (i.e. individual Bayesian posteriors), all available serum vancomycin levels and known doses and administration times, we calculated 24 h AUCs between 24–48, 48–72 and 72–96 h of vancomycin therapy for each patient that completed dosing through the end of the time period (Simulx 2021R1, Antony, France).

Differences between calculated AUCs from the three different methods were compared using a repeated measures one-way ANOVA test with the Geisser–Greenhouse correction and Dunnett’s test for multiple comparisons (GraphPad Prism 9.3.1, San Diego, CA, USA). Bayesian calculations were designated as the reference group (i.e. the ‘true’ exposure), since real-time changes in dosing, schedule and renal function were captured in these calculations. Calculated AUCs for each of the different methods were also compared by classification into the following categories: below target (AUC <400 mg·h/L), within target (AUC 400–600 mg·h/L) or above target (AUC >600 mg·h/L). AUCs estimated by each of the first-order pharmacokinetic equation methods were then compared with Bayesian-estimated AUCs to determine classification concordance between methods. To exclude partial exposures and/or treatment days, patients were only included in each analysis for which they received all scheduled doses in the 24 h interval for the calculated AUC period.

‘Categorical agreement’ was achieved if both calculation methods resulted in the same AUC classification for an individual patient. A ‘minor error’ indicated that one method resulted in a ‘within-target’ AUC estimate while the comparator method resulted in either an ‘above-target’ or ‘below-target’ estimate, while a ‘major error’ signified that one method resulted in an ‘above-target’ AUC estimate while the comparator method resulted in a ‘below-target’ estimate (or vice versa). We hypothesized that different AUC estimation methods would result in differing dose-adjustment decisions.

Results

A total of 65 adult inpatients provided 409 plasma samples for analysis. The cohort consisted of general medicine patients (n = 52) and critical care patients (n = 13); mean age of 53 years, 44% male, 58% Caucasian and median (IQR) BMI of 25.9 kg/m² (21.8–32.6). Each patient had an average of six vancomycin plasma levels, constituting three separate occasions of therapeutic drug monitoring. AUC_SS estimates based on the first-order population pharmacokinetic method resulted in a median (IQR) AUC of 496 mg·h/L (76). Subsequent AUC_SS estimates made by first-order pharmacokinetic equations with peak and trough levels resulted in a median (IQR) AUC of 498 mg·h/L (107).

For the Bayesian approach, the two-compartment intravenous infusion base model with first-order elimination fit the data well. Addition of log-transformed weight as a covariate in the model for central compartment volume (V1) improved the base model and allometrically scaled log-transformed weight on clearance improved the model fit. The final model’s population mean (SD) parameter values for linear elimination (CL), central compartment (V1), peripheral compartment (V2) and intercompartmental transfer (Q) were 4.08 L/h (0.4), 53.8 L (0.33), 48.9 L (1.34) and 3.53 L/h (0.55), respectively. V1 and CL were standardized to log-adjusted weight, with V1 scaled to weight^1 and CL allometrically scaled to weight^0.75. The linear regression of the Bayesian posterior population predictions versus observed concentrations resulted in an intercept of 7.81, where the ideal is 0; the slope was 0.56, where the ideal is 1, and the R² value was 0.35. The linear regression of the Bayesian posterior individual predictions versus observed concentrations resulted in an intercept of 3.29, where the ideal is 0; the slope was 0.82, where the ideal is 1, and the R² value was 0.65. AUCs derived from the EBEs (as the basis for the Bayesian model) resulted in a median (IQR) AUC_24–48 of 484 mg·h/L (173), AUC_48–72 of 541 mg·h/L (161) and AUC_72–96 of 574 mg·h/L (189).

The majority of AUCs calculated by first-order population pharmacokinetic equations were classified as ‘within target’ [62/65 (95%)], with several classified as ‘above target’ [3/65 (5%)]. For calculations made by first-order pharmacokinetic equations with peak and trough levels, 9/65 (14%) were ‘below target’, 48/65 (74%) were ‘within target’ and 8/65 (12%) were ‘above target.’ For Bayesian AUC_24–48 calculations (i.e. the assumed true exposures), 11/65 (17%) were ‘below target’, 39/65 (60%) were ‘within target’ and 15/65 (23%) were ‘above target’ (Figure 1). Bayesian AUC_24–48 was not significantly different from AUC estimates from the two first-order pharmacokinetic equation methods (P = 0.68). When categorical classifications of Bayesian AUC_24–48 estimates were compared with categorical classifications from the first-order population pharmacokinetic method, 38/65 (58%) patients had categorical agreement between the methods, 26/65 (40%) had a minor categorical error and 1/65 (2%) had a major categorical error. Similarly, when categorical classifications of Bayesian AUC_24–48 estimates were compared with those from the first-order pharmacokinetic method with peak and trough levels, 39/65 (60%) patients had categorical agreement and 26/65 (40%) had a minor categorical error.

Figure 1.

Comparison of AUC estimation methods. This figure appears in colour in the online version of JAC and in black and white in the print version of JAC.

For Bayesian AUC_48–72 calculations, 5/53 (9%) were ‘below target’, 30/53 (57%) were ‘within target’ and 18/53 (34%) were ‘above target.’ Bayesian AUC_48–72 was significantly different from AUC estimates from the two first-order pharmacokinetic equation methods (P < 0.01). When categorical classifications of Bayesian AUC_48–72 estimates were compared with categorical classifications from the first-order population pharmacokinetic method, 28/53 (53%) patients had categorical agreement between the methods and 25/53 (47%) had a minor categorical error. Similarly, when categorical classifications of Bayesian AUC_48–72 estimates were compared with those from the first-order pharmacokinetic method with peak and trough levels, 24/53 (45%) patients had categorical agreement and 29/53 (55%) had a minor categorical error.

For Bayesian AUC_72–96 calculations, 5/42 (12%) were ‘below target’, 19/42 (45%) were ‘within target’ and 18/42 (43%) were ‘above target.’ Bayesian AUC_72–96 was significantly different from AUC estimates from the two first-order pharmacokinetic equation methods (P < 0.001). When categorical classifications of Bayesian AUC_72–96 estimates were compared with categorical classifications from the first-order population pharmacokinetic method, 19/42 (45%) patients had categorical agreement between the methods and 23/42 (55%) had a minor categorical error. Similarly, when categorical classifications of Bayesian AUC_72–96 estimates were compared with those from the first-order pharmacokinetic method with peak and trough levels, 14/42 (33%) patients had categorical agreement, 27/42 (64%) had a minor categorical error and 1/42 (2%) had a major categorical error. See Figure 2.

Figure 2.

Comparison of categorical classifications of AUC estimates from two first-order pharmacokinetic equation-based methods versus Bayesian-method estimations. ^aCategorical agreement: both AUC estimation methods resulted in the same AUC classification. ^bMinor error: one AUC estimation method resulted in a ‘within-target’ AUC estimate while the comparator method resulted in an ‘above-taregt’ or ‘below-target’ AUC classification. ^cMajor error: one AUC method resulted in a ‘below-target’ AUC estimate while the comparator method resulted in an ‘above-target’ estimate. This figure appears in colour in the online version of JAC and in black and white in the print version of JAC.

Discussion

In our study, significant variation was seen across categorical AUC estimates when using first-order, steady-state, pharmacokinetic equation methods, compared with Bayesian estimation. Since the first-order population pharmacokinetic equation method was used to guide initial vancomycin dosing, it is unsurprising that most patients were estimated to have AUC_SS between 400–600 mg·h/L. The first-order population pharmacokinetic equations demonstrated similar exposure estimates with a few outliers and 95% of patients had ‘within-target’ AUCs. However, these steady-state equations make assumptions, such as fixed dosing, perfect timing and consistent intervals. When comparing AUCs that make fewer assumptions (i.e. Bayesian AUCs that account for actual doses and intervals for each patient), we see that categorical agreement (classified as below, within or above target) is poor. This was true for all 24 h periods in which Bayesian AUCs were calculated (and for which vancomycin was likely at steady state for most patients). As a result of this poor categorical agreement, approximately half of the patients in this study would have potentially required different vancomycin dose adjustments depending on the utilized estimation method.

We are aware of one other study that compared Bayesian methods (Bayesian posteriors from one and two measured concentrations). Olney et al.¹³ demonstrated higher agreement than we have shown in this study. For example, they demonstrated 87.4% agreement between linear pharmacokinetic equations from steady-state samples and two-concentration Bayesian calculations. On the other hand, our study demonstrated ~50% agreement. Much of this difference may be attributed to the manner AUC calculations were performed. Our study utilized early concentrations to estimate steady-state AUCs, whereas Olney et al.¹³ compared concentrations measured directly at steady state. These differences are important and relevant to clinical care. Clinical studies have demonstrated that early vancomycin exposures (i.e. day 2 AUC) best predict kidney outcomes.^14–16 Our study demonstrated that using early estimates of patient vancomycin exposures (i.e. from first 24 h) did not project well to actual realized exposures (i.e. AUCs at steady state). Taken together, the clinical implication is that traditional pharmacokinetic equations are best performed proximal to the timepoint at which AUC is desired to be estimated (e.g. one measure at steady state if steady-state AUC is desired and calculated with traditional pharmacokinetic equations). Bayesian methods may provide an improved opportunity to project actual steady-state exposures from early measurements.^13–16

Differences between the methodologies arise because Bayesian-guided estimation uses a prior embedded pharmacokinetic model and incorporates actual patient exposures, while first-order pharmacokinetic equations rely on population estimates and/or idealized dose timing to predict AUCs. Bayesian-guided estimation can be a more accurate reflection of ‘real-world’ factors that affect individual AUC exposures, such as V_d, renal function and changes in dose and/or administration frequency. This gives Bayesian AUC estimation methods added flexibility when accounting for these individual patient factors and thus can improve the predictive accuracy of individual patient AUCs, when compared with traditional first-order pharmacokinetic equation methods that rely on more assumptions. Although Bayesian-guided AUC monitoring is preferred per the current guidelines, both Bayesian and first-order pharmacokinetic equation methods are currently recommended for vancomycin monitoring. Clinicians should be aware of potential variability in vancomycin AUC calculations related to the utilized method. Bayesian methods result in more accurate AUC estimations when compared with first-order pharmacokinetic equations, thus potentially allowing for better recognition and management of vancomycin-associated nephrotoxicity. Limitations of this study include the single-centre, retrospective nature, which may limit the generalizability of findings. In addition, not all the categorical differences between the groups might trigger differences in dosing (e.g. one clinician may dose adjust for an AUC_24–48 of 395 mg·h/L, whereas another may not). In this study, only two patients had ‘borderline’ Bayesian-calculated AUCs outside the therapeutic range of 400–600 mg·h/L, which does not significantly impact our findings.

Conclusions

Bayesian-estimated AUCs (i.e. 48–72 h and 72–96 h) were significantly different from first-order pharmacokinetic equations that projected AUCs at steady state. AUCs calculated by the three different methods differed by categorical classification, which could potentially lead to erroneous dosing adjustments in approximately half of the patients.

Funding

This work was supported in part by the National Institute of Allergy and Infectious Diseases of the National Institutes of Health [R21AI149026 (M.H.S.)].

Transparency declarations

M.H.S. has ongoing research contracts with Nevakar and SuperTrans Medical as well as having filed patent US10688195B2. All other authors: none to declare.

Disclaimer

The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Supplementary data

Supplementary data are available at JAC Online.