# Vancomycin AUC Calculation

### In this article:

Vancomycin is a glycopeptide antibiotic with activity against methicillin-resistant *Staphylococcus aureus *(MRSA)as well as other clinically important gram-positive organisms.^{1}

Vancomycin has found significant use in clinical practice due to its activity against these organisms. Just like any other medication, however, safe and effective dosing and monitoring of vancomycin is essential.

Vancomycin dosing must be tailored to the patient and closely monitored given its narrow therapeutic index^{2} and risky adverse effects.

In the clinical setting, patients often present with multiple comorbidities, varying ranges of body weight and body mass index (BMI), and rapidly changing creatinine clearance (CrCl).

Due to this, clinicians can be faced with significant challenges in providing just the right amount of medication at doses and frequencies that will effectively treat the patient without causing harm.

To most effectively and consistently do this, clinicians must have a thorough understanding of the available therapeutic drug monitoring guidelines, pharmacokinetics, and the tools and calculation methods at their disposal.

*To calculate vancomycin dosage, please view the DoseMeRx calculator.*

## A brief History of Vancomycin Pharmacokinetics

### What is AUC for Vancomycin?

Though vancomycin has been used since the 1950s, there was no formal guidance available to assist clinicians with evaluating and dosing the medication until 2009. If drug levels were collected, there was not a well-established method of determining if the patient was adequately treated or at risk for acute kidney injury (AKI).

When the 2009 vancomycin consensus guidelines for the therapeutic monitoring of vancomycin were released, available literature that could be used to determine the therapeutic monitoring goal for vancomycin was limited.

While there were some small studies conducted in humans, most were in animals or in a laboratory setting (in vitro).^{3}

Even with the paucity of available human data, the authors of the 2009 consensus guidelines were able to come to some conclusions regarding dosing recommendations.

This included recommendations on empiric dosing according to the patient’s body weight, adjusting the dose of vancomycin based on the patient’s CrCl, and intensifying the dosing strategy if the patient had a confirmed, serious infection caused by MRSA such as endocarditis.

They concluded that based on the pharmacokinetics of vancomycin, the monitoring parameter of choice for the drug should be the vancomycin area under the concentration-time curve (AUC) divided by the minimum inhibitory concentration (MIC), with an AUC/MIC ratio ≥400 needed for reliable efficacy.^{3}

### How do you Monitor AUC for Vancomycin?

In 2009 when this consensus guidance was released, the only AUC calculation method that was available for the hospital clinician required two serum concentrations to perform pharmacokinetic calculations by hand.

The readily available software we have now for the busy clinician to rapidly and accurately estimate the AUC:MIC ratio using Bayesian estimation did not exist.

Hand calculations were cumbersome and the several steps involved increased the risks for errors. Seeing that this was not reasonable for clinical practice at the time, the authors decided to recommend trough-only monitoring as a convenient surrogate marker for this ratio.

By targeting a trough level of at least 15 mcg/mL and ideally no greater than 20 mcg/mL, the clinician could assume that the AUC/MIC would be ≥400 assuming an *S. aureus *vancomycin MIC of 1 mcg/mL. Thus, the single trough level became the gold standard for vancomycin monitoring.

While this was a necessary step towards more appropriate dosing and monitoring of vancomycin, patients were still at risk for side effects from the drug.^{4-7}

These side effects were prevalent even when kept within the trough goals of 15-20 mcg/mL for severe infections and most commonly involved AKI.

AKI can be a very unfortunate finding in patients receiving vancomycin. First, since vancomycin is primarily cleared in the kidneys,^{1} AKI makes dosing the patient’s vancomycin much more difficult and imprecise.

AKI has also been associated with progression to dialysis, longer length of stay, and significantly higher costs for the health system.^{8,9}

It is in the interest of patients, providers, pharmacists, and stakeholders that AKI is prevented. From 2009 to 2020, several articles and meta-analyses evaluating the safety and efficacy of trough-only monitoring were released.^{4-13}

In these articles, trough-only monitoring was not well correlated with improved clinical outcomes and maintaining a trough level in the range of 15-20 mcg/mL consistently failed in predicting clinical cure and AKI risk.

One potential cause for this finding was with the inability of the trough to function as a surrogate for the AUC.

While a trough goal between 15 and 20 mcg/mL usually represented an AUC of at least 400, it also had the tendency to overshoot the therapeutic range of the drug, predisposing patients to the aforementioned complications of kidney damage.

Clinicians and researchers were then faced with a challenge. With the literature further supporting the AUC as the ideal monitoring parameter for the drug, and the trough level not being sufficient as a surrogate marker of the AUC, how should the new therapeutic dosing guidelines proceed?

The only solution was to forego surrogate markers and calculate the AUC directly.

In the 2020 update to the consensus guidelines for the therapeutic monitoring of vancomycin, trough-only monitoring was officially no longer recommended with direct monitoring of the AUC used in its place.^{14}

For health systems, this meant that anyone monitoring and adjusting vancomycin doses needed to move away from the traditional trough goals and towards a method of calculating the AUC. To get from trough to AUC, clinicians needed to have a thorough understanding of pharmacokinetics.

## Zero Order and First Order Pharmacokinetics

Drug elimination pharmacokinetics can be divided into two main categories: zero order and first order.

Zero order kinetics is a time-dependent process where the same amount of drug is eliminated from the body per unit time regardless of the concentration of the drug in the patient.^{15}

Drugs that follow a zero order model will at low doses appear to follow first order (linear) elimination up until the point that the elimination mechanism becomes saturated.

Alcohol is a commonly used example of zero order (nonlinear) kinetics. Alcohol dehydrogenase, one of the major enzymes involved in alcohol metabolism, has a low Km, which is a measure of the affinity of the substrate for an enzyme. Translated – this suggests that the alcohol dehydrogenase enzyme has a high affinity for alcohol.^{16}

This high affinity causes the enzyme to be saturated with substrate at low concentrations. When this saturation takes place, the rate of alcohol metabolized through this pathway no longer increases in relationship to increasing alcohol amounts.^{15,16}

Increasing alcohol ingestion will also prolong the elimination half-life, as the elimination rate no longer increases proportionally with the drug concentration.^{15,17}

These factors contribute to increasing the complexity of estimating the concentrations of alcohol at a given time point.

The distinguishing factor between zero order and first order pharmacokinetics is the ability of the elimination system to become saturated by the drug.^{15}

When administered intravenously, vancomycin is eliminated renally with >80% of the administered drug recoverable unchanged in the urine.^{1}

While there are other means of vancomycin elimination, renal function plays the most central role in determining how quickly a patient can remove vancomycin from the central compartment. Luckily, patients of average weight receiving vancomycin at appropriate doses and frequencies for their renal function will exhibit first order elimination kinetics.^{1,3,5,6}

In first order (linear) pharmacokinetic models, drug elimination can be represented as a straight line on a logarithmic scale. In an ideal scenario where elimination of drug is consistent, drug concentration can be estimated at any time point by the first order equation C = C_{0} * e^{-kt} where C = drug concentration, C_{0 }= initial drug concentration (extrapolated), e = the base of the natural logarithm, k = the elimination rate constant, and t = time.^{18}

If two drug levels are collected over the same dosing interval, the clinician can then solve for the elimination rate constant (k) and use this equation to provide an estimation of vancomycin concentration.

The simple first order equation above for vancomycin dosing does have limitations.

First, it can only be used to inform the clinician of the drug concentration at a certain time point. While this can be an effective method for drug monitoring of some medications, it alone cannot be used to determine the AUC.

Since drug level monitoring alone was found to be less effective than directly monitoring the AUC, more complex calculations are needed.

## How do you Calculate AUC MIC Ratio for Vancomycin?

### Calculation of the AUC Using the Sawchuk-Zaske Method

To hand calculate the AUC using first order equations, the Sawchuk-Zaske method can be used.^{18}

This method relies on having two post-dose drug levels from the same dosing interval ideally collected at steady state.

Typically, the first level will be a post infusion peak and the second level is a trough level. This equation also allows the elimination rate constant of the drug to be calculated, starting with the following equation:

k = *ln*(C_{peak}/C_{trough})/∆t

Where k = the elimination rate constant, C_{peak }is the observed peak level collected, C_{trough }is the observed trough level, and ∆t is the difference in time in hours between the C_{peak }and the C_{trough }levels.

From here, the true peak (C_{max}) can be extrapolated using the difference in time between the expected peak and the first drug level (C_{peak}) using the following equation:

C_{max }= C_{peak}/e^{-kt’}

In this case, t’ is the time between the “observed” peak (i.e., the drug level drawn from the patient) and the “true” peak, back-extrapolated.

From here, the true trough (C_{min}) can be calculated using the C_{max }from the following formula:

C_{min }= C_{max }* e^{-k(Tau-tinf)}

Where *Tau *is the dosing interval and tinf is the infusion time in hours.

Now, the AUC can be calculated. Commonly, the trapezoidal rule is used to calculate the AUC by hand. A full description of how to perform these calculations can be found here.

With all of the necessary parameters and an understanding of how to calculate the AUC, any adjustments to the dose of vancomycin or modifications in dosing frequency can all be calculated by the user.

It should be noted, however, that there are limitations to using the first order equations in the calculation of the area under the curve.

## Limitations of the First Order Equations

While the first order calculations can be performed “by hand”, they do have some significant limitations:

- These equations cannot account for rapid shifts in renal function, fluid or volume status, or for any other parameters which may influence the patient’s drug clearance. This means that when a patient experiences these shifts, a new set of pharmacokinetic parameters should be calculated.
- Unfortunately, this practice may result in significantly more drug levels being collected, specifically optimally timed peak and trough levels whenever possible.
- In the busy hospital environment, collection of a peak and trough level is often a challenging obstacle and involves many moving parts.
- Nursing team members must understand and be able to counsel the patient regarding why they need to draw another drug level, and the patient must be willing to submit to additional testing.
- Physician staff may need education regarding the timing of drug levels and their interpretation in relationship to the patient’s last vancomycin dose, especially considering that optimally timed peaks may flag as high or critically high results on the patient’s laboratory report.
- Preparing patients to discharge on vancomycin for outpatient parenteral antimicrobial therapy will present challenges if they are receiving their vancomycin through a home infusion company or are discharged to another facility that remains on a trough-only monitoring protocol.

In-hospital management, education, and transitions of care are not the only limitations of first order equations.

Unfortunately, vancomycin pharmacokinetics can be more complex and requires more finesse than the simple first order elimination equations can provide.

As with many drugs, vancomycin has been modelled as following two- or even three-compartment pharmacokinetics.^{1,5,13}

This presents a challenge for the first order equations, as these equations assume that the drug follows one compartment pharmacokinetics.

The one compartment model is the most simplistic way of describing how a drug distributes and is eliminated from the body.

In this model, it is assumed that the drug distributes completely and immediately to all other compartments in a homogenous fashion.^{13}

While this model simplifies calculations and is usually sufficient for most clinical applications, it may lose accuracy in some patient subsets such as patients with renal insufficiency.^{12}

In the critical care patient population, the availability of albumin to bind free drug decreases,^{17} volume of distribution increases as a result of excess fluid administration and “third spacing” of fluid, and renal function often decreases or undergoes rapid changes.

It is for these reasons that vancomycin pharmacokinetic studies in critically ill patients in the ICU often use a two-compartment model.^{19}

Finally, it should also be noted that the first order equations only provide a 24-hour snapshot of the vancomycin AUC. It cannot adapt to different conditions such as rapidly improving or declining renal function. This means that, ideally, additional samples are drawn with each significant change in vancomycin clearance.

## Implementation of Manual AUC Calculation with First Order Pharmacokinetics

While there are several limitations to consider when using first order pharmacokinetic equations, there are some potential benefits.

First, these equations are free to use and universal, such that anyone with access to the patient’s data can use them to derive an AUC. One approach used by some facilities is the creation of spreadsheet or electronic health record integrated calculators.

If a hand-calculated AUC is the best choice for your practice site, consider reviewing some of the available literature summarizing how this method may be implemented, such as the article by Meng *et al.*

The following are a few considerations adapted from this article that can be used for transitioning from trough-based dosing to the two-level AUC method:

- Provide education to staff pharmacists, nurses, and physicians regarding the need to add vancomycin peaks for all patients being monitored on vancomycin therapy
- Create a dosing calculator that can either be used within the electronic medical record or on a shared spreadsheet file
- Update any dosing protocols and monitoring sheets to reflect the updated guidance which reviews how the AUC can be hand calculated should a situation arise where the above calculator is not available
- After implementation, continuously evaluate the workflow impact and patient outcomes of this method of AUC dosing

Although hand calculating the AUC is feasible, the same problems that swayed the 2009 guidelines away from this method of AUC calculation still exist today: it may take more time and increase the risk of clerical errors. The 2020 consensus guideline updates recommend Bayesian estimation as the preferred approach to monitoring the AUC.

## Implementation of a Bayesian Dosing Software Program

In addition to the research that was released between 2009 and 2020, there was also a very significant development in the realm of AUC estimation: the creation of commercially available Bayesian estimation software programs.

Bayesian estimation is based on Bayes’ Theorem. This theorem is a mathematical formula that can be used to determine the probability of an event occurring based on the condition(s) placed on the event and the probability model (Bayesian prior) used as a guide.

There are several models available that can be used as the Bayesian prior.^{21-25} These include models for the standard, critically ill, or obese, the adult patient on hemodialysis, and pediatric/adolescent and preterm/neonate models.

When applied to vancomycin dosing, a Bayesian software program will analyze the patient’s height, weight, age, serum creatinine values and trends, and compare these values against the model selected as the Bayesian prior.

By inputting a single drug level collected at any time point into the system, the program can calculate the volume of distribution, half-life, elimination rate constant, clearance, and the AUC.

Using this information and the predictive power of Bayesian estimation, the program can use this information to provide a new dosing regimen to arrive within the goal AUC.

These programs are also able to work with any dosing strategy the patient previously received.

For example, if a patient received a loading dose of vancomycin or doses that were given early or late, the program can provide a recommended dose adjustment based on the amount and timing of drug administration.

If the clinician wants to adjust the patient’s daily vancomycin dose or change from a twice daily to a daily or every other day regimen, these programs are customizable to allow for this flexibility. They also can forecast the expected drug levels and daily AUC based on the new regimen selected.

It should be noted that while the collection of a single drug level at any time point is likely within reason for a Bayesian software program to provide a valid dosing recommendation, the 2020 consensus guidelines do recommend the collection of two drug levels, specifically in patients that may be at risk of altered pharmacokinetics.

This recommendation is of most importance when considering patients that are critically ill and need more intensive drug monitoring for a serious infection.

If the implementation of a Bayesian software program is your goal, consider reviewing this complete AUC conversion toolkit. This toolkit provides helpful advice and strategies to completing the following implementation steps and more. Some of these steps are summarized below:

- Create an implementation timeline. This step should not be skipped as it lays out the necessary groundwork to ensure that the project will be successful.
- Conduct an extensive literature review of AUC vancomycin dosing, specifically literature sources that utilize a Bayesian program if possible.
- Identify a team of super users and physician champions. If your health system has an infectious disease physician team and/or antimicrobial stewardship program, rally for their support.
- Obtain approval from members of management and other key stakeholders. Bayesian software programs such as DoseMeRx require a paid, yearly contract.
- Present plans to pharmacy, nursing, and physician teams
- Decide on a go-live date and discuss live training programs if applicable with the selected AUC dosing software company.
- Complete training and ensure all super users are present for the implementation date and at minimum for one-week post-implementation to answer questions.
- Consider performing post-implementation auditing to ensure the program is being used effectively.

## Key Takeaways

The 2020 dosing guidelines for vancomycin dosing have made the transition from attaining a target trough to instead focusing on the AUC.

Even in patients with a baseline normal renal function, the risk of nephrotoxicity from vancomycin is too great to go without collection and monitoring of vancomycin levels. While the therapeutic monitoring parameters have removed the trough surrogate, the underlying pharmacokinetic principles of vancomycin remain unchanged. By understanding applied pharmacokinetics, clinicians can decrease the risk of AKI from this drug while still effectively treating serious MRSA infections. With readily accessible and easy-to-use Bayesian estimation software, healthcare systems and clinicians are empowered to make this change from trough to AUC for the betterment of their patients.

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