# Vancomycin Calculator

## Pharmacokinetic calculator with Bayesian modeling

### Patient Parameters

 Actual body weight: kg lbs Height: in cm Gender: Male Female Patient is critically ill No Yes

### Pharmacokinetic Modeling

 Clearance method: Bayesian modeling population estimates Bauer (CLvanco = 0.695*CrCl+0.05) Matzke (CLvanco = 0.689*CrCl+3.66) Volume of distribution (Vd): Bayesian modeling population estimates Bauer (0.7 L/kg) Matzke (0.89 or 0.72 L/kg) Rushing-Ambrose (0.17*Age+0.22*TotalBW+15) Morbidily obese (0.52 L/kg) User-specified Vd (enter a custom Vd) User-specified Vd L/kg Recommend loading dose: No Yes

Renal function:
Creatinine:
Age:

### Vancomycin Drug Levels

Drug levels available:

Empiric, initial vancomycin dosing will be calculated using population pharmacokinetic parameters. Two vancomycin drug concentrations (such as a peak and trough) should be obtained to optimize therapy. Learn more about the timing of vancomycin drug levels.

Looking for the previous version of this calculator? See the retired version that uses trough-based vancomycin goals without advanced modeling techniques.
Press 'Calculate' to view calculation results.

This vancomycin calculator uses pharmacokinetic population estimates, Bayesian modeling, and the Sawchuk-Zaske method to calculate a vancomycin dosing regimen for an adult patient. Vancomycin regimens can be calculated both empirically (without any prior doses) or using one or two vancomycin levels.

This calculator determines pharmacokinetic parameters and vancomycin dosing strategies using the following steps:

1. Estimate CLvanco and Vd

Empiric dosing (no drug levels): CLvanco and Vd are determined using population estimates from pharmacokinetic models. CLvanco is determined using whichever "Clearance method" is selected (see Methods for Determining Vancomycin Clearance). Vd is determined using the selected Vd method (see Methods for Determining Vancomycin Volume of Distribution).

One drug level available (trough): Vd is assumed using either a population estimate or a user-specified Vd. Clearance is then determined using the following steps:

1. Using a population estimate of clearance, extrapolate a true trough (if drug level drawn early or late)
$$Cp = Cp^0*e^{-kt}$$
2. Using a population estimate of Vd, extrapolate a peak value:
$$Extrapolated\;Peak = \frac{Dose/T_{inf}}{Kel*Vd}*(1-e^{-Kel*T_{inf}})+Trough$$
3. Using the extrapolated peak and trough values, calculate Kel and CLvanco:
$$\\Kel = ln(Peak/Trough)/(Tau-T_{inf}) \\CL_{vanco} = Vd*Kel$$

Two drug levels available (peak and trough): This is the most accurate method of calculating a patient-specific CLvanco and Vd; however, it requires two drug levels to be drawn. These patient-specific pharmacokinetic values can be calculated using the Sawchuk-Zaske method.

2. Optimize CLvanco and Vd using Bayesian modeling (if selected)

If a single drug level is available, Bayesian modeling can be used to optimize the population estimates of CLvanco and Vd. This feature can be disabled by selecting "Population Estimates" in the "Preferred modeling method" setting.

Bayesian modeling uses a population estimate of CLvanco and Vd (called a Bayesian prior) and optimizes these estimates using a single drug level. As an example, Bayesian modeling may optimize a Vd value from 0.98 L/kg (the population estimate) to 1.11 L/kg (an optimized value based on the patient's drug level). See Vancomycin Bayesian Modeling for more information.

Bayesian modeling is not conducted when no drug levels are available (a level is necessary for the model) nor when two drug levels are available (the Sawchuk-Zaske method is more reliable).

3. Use one-compartment PK equations to estimate peak, trough, and AUC/MIC

Once CLvanco, Vd, and Kel are determined, one-compartment pharmacokinetic equations can be used to determine the peak, trough, and AUC/MIC for a given regimen:

Predicted Peak and Trough
$$\\ C_{peak} = \frac{Dose * (1-e^{(-K_{el}*T_{inf})})}{T_{inf}*Vd*K_{el}*(1-e^{(-K_{el}*Tau)})} \\ C_{trough} = C_{peak} * e^{(-k * (Tau - T_{inf}))}$$
AUC Method #1
$$\\ Lin\;trap = \frac{C_{trough}+C_{peak}}{2}*(T_{inf}) \\ Log\;trap = \frac{(C_{peak}-C_{trough})*(Tau-T_{inf})}{\ln(\frac{C_{peak}}{C_{trough}})} \\ AUC_{0-Tau} = (Lin\;trap) + (Log\;trap) \\ AUC_{0-24} = AUC_{0-Tau}*(24/Tau) = AUC\;in\;mcg*h/mL$$
AUC Method #2
$$\\ CL_{vanco} = K_{el} * Vd \\ AUC_{0-24}=(Total\;daily\;vancomycin\;dose)/CL_{vanco}$$
Convert AUC to AUC:MIC ratio over 24 hours
$$\\ AUC_{0-24}:MIC = \frac{AUC_{0-24}}{MIC}$$

#### Vancomycin Pharmacokinetic Models and Population Estimates

When CLvanco or Vd are unknown, population estimates are used based on published literature. In many pharmacokinetic textbooks, a single Vd (such as 0.7 L/kg) or CLvanco (such as 70% of creatinine clearance) are recommended. Literature demonstrates that these population estimates vary widely in certain patient populations, such as morbidly obese or critically ill patients. Given that, this calculator selects one of four possible pharmacokinetic models to estimate a patient's pharmacokinetic parameters:

• Buelga et. al, 2005:1 Default model for general hospitalized adult patients
• Adane et. al, 2015:2 Extreme obesity model (BMI > 40 kg/m2 and body weight ≥ 120 kg)
• Roberts et. al, 2011:3 Critically ill patient model for ICU patients (BMI < 30 kg/m2)
• Masich et. al, 2020:4 Critically ill and obesity model (BMI ≥ 30 kg/m2 and body weight > 100 kg)

There are many models available for pharmacokinetic and Bayesian analyses.5,6 These models were selected based on being generalizable, one-compartment models with reasonable predictive performance in confirmatory publications.

These four models vary significantly between each other given the difference in patient populations modeled, emphasizing the importance that the most representative model is selected for an individual patient. Using an example patient weighing 100 kg with a creatinine clearance of 80 mL/min and BSA of 2.3 m2, the initial pharmacokinetic variables with each model would be:

 Model Intended patient population CLvanco (L/hr) Vd (L/kg) Half-life (hr) Buelga 2005 1 General hospitalized 5.18 0.98 13.1 Adane 2015 2 Extreme obesity 4.19 0.51 8.4 Roberts 2011 3 Critically ill 4.65 1.53 22.8 Masich 20204 Critically ill and obesity 5.21 0.78 10.4

#### Methods for Determining Vancomycin Clearance

The following methods can be used to estimate vancomycin clearance

##### Bayesian modeling population estimates [Preferred Method]

CLvanco is estimated using the most appropriate published pharmacokinetic model for a given patient. The following equations are used as part of these models:

 Model Intended patient population CLvanco Equation Buelga 2005 1 General hospitalized $$CrCl*60/1000*1.08$$ Adane 2015 2 Extreme obesity $$6.54*CrCl_{TotalBW}/125$$ Roberts 2011 3 Critically ill $$4.58*CrCl_{per\;1.73\;m^2}/100$$ Masich 20204 Critically ill and obesity $$3.23*(CrCl/40)^{0.69}$$
##### Bauer Method 7

CLvanco is estimated using a linear relationship to creatinine clearance while normalizing to total body weight:

$$CL_{vanco} = (0.695*CrCl/TotalBW + 0.05)*TotalBW*0.06$$
##### Matzke Method 8

CLvanco is estimated using a linear relationship to creatinine clearance:

$$\\CL_{vanco} = (0.698*CrCl+3.66)*0.06$$

Note that this method comes from the same manuscript that published the linear relationship between Kel and CrCl (Kel=0.00083*CrCl+0.0044), sometimes called the Creighton equation.

#### Methods for Determining Vancomycin Volume of Distribution

The following methods can be used to estimate vancomycin volume of distribution (Vd)

##### Bayesian modeling population estimates [Preferred Method]

Vd is estimated using the most appropriate published pharmacokinetic model for a given patient. The following Vd values are used as part of these models:

 Model Intended patient population Vd (L/kg TotalBW) Buelga 2005 1 General hospitalized 0.98 Adane 2015 2 Extreme obesity 0.51 Roberts 2011 3 Critically ill 1.53 Masich 20204 Critically ill and obesity 0.78
##### Bauer Method 7

Vd is a fixed value of 0.7 L/kg. This value is commonly used in pharmacokinetic textbooks.

##### Matzke Method 8

Vd estimates are determined based on creatinine clearance:

CrCl (mL/min) Vd (L/kg)
> 60 0.72
≤ 60 0.89
##### Rushing-Ambrose Method 9

Vd estimates are determined using an equation incorporating age (in years) and total body weight (in kg):

$$\\ Vd\;(liters) = 0.17*Age + 0.22*TotalBW + 15 \\ Vd\;(L/kg) = Vd\;(liters) / TotalBW\;(kg)$$
##### Morbid Obesity 2,10

Among non-critically ill, morbidly obese patients (defined as BMI > 40 kg/m2 and body weight ≥ 120 kg), Vd (L/kg) is smaller per kilogram of total body weight. Although values are highly variable, a Vd of 0.52 L/kg is a reasonable population estimate supported by the literature.

##### User-Specified Vd

For users who would like to use a specific volume of distribution value (L/kg), this option can be selected.

#### Vancomycin Bayesian Modeling for CLvanco and Vd

Bayesian modeling can be used to estimate a patient's vancomycin clearance (CLvanco) and volume of distribution (Vd) on the basis of one single vancomycin level either at steady state or even after one single dose. Bayesian modeling is a mathematically complex process that involves the following steps:

1. Identify a publication describing mean and variance of vancomycin clearance and volume of distribution. This publication should include subjects with similar characteristics to the patient who will be receiving vancomycin.
2. One or more vancomycin concentrations are drawn from a patient.
3. An algorithm identifies values for CLvanco and Vd that are most likely (using probability) to explain the patient's serum drug concentrations. These values are optimized based on the original publication's mean and variances of CLvanco and Vd.
4. With a known CLvanco and Vd, an elimination constant (Kel) can be calculated ($$Kel=CL_{vanco}/Vd$$)
5. Once the most likely values of Kel and Vd have been estimated, one-compartment pharmacokinetic equations are used to identify a dose and its associated peak, trough, and AUC/MIC values.

#### Sawchuk-Zaske Method for Kel and Vd

When multiple vancomycin drug concentrations are available, traditional pharmacokinetic equations can be implemented to calculate patient-specific pharmacokinetic parameters. This approach is called the Sawchuk-Zaske method.11 Unlike in Bayesian analysis, this method does not utilize population estimates of kinetic parameters and should provide more reliable results, particularly in patients with very altered pharmacokinetics values.

The Sawchuk-Zaske method uses two post-dose concentrations (regardless of being at steady state) using the following approach:11

##### 1. Determine Kel
$$\\ Cp = Cp^0*e^{-kt} \\ (rewritten\;to\;solve\;for\;k) \\ k = ln(Cp^0/Cp)/t$$
Cp0 is the first (higher) concentration; Cp is the second (lower) concentration; t is the time elapsed between Cp0 and Cp; k is the elimination constant (Kel)
##### 2. Extrapolate to Cmax (peak) and Cmin (trough)

Using the first-order elimination equation ($$Cp = Cp^0*e^{-kt}$$), a true peak (Cmax) can be calculated using the time elapsed between the end of the vancomycin infusion and the first drug concentration (Cp0). Similarly, a true trough (Cmin) can be calculated using the time elapsed between the second drug concentration (Cp) and the when the next dose is due to begin infusing.

##### 3. Calculate volume of distribution (Vd)

A patient-specific Vd can be calculated using Cmax and Cmin from the previous step. If a patient has only received one single dose (thus not at steady state), Cmin is set to 0 (zero).

$$\\ Vd = \frac{Dose/T_{inf}*(1-e^{-k*T_{inf}})}{k*(C_{max} - (C_{min} * e^{-k*T_{inf}}))}$$
Vd is the volume of distribution (in liters); dose is the vancomycin dose (in milligrams); Tinf is the vancomycin infusion time (in hours); k is the elimination constant (Kel, in hr-1); Cmax is the true peak concentration; Cmin is the true trough concentration (if at steady state) or is 0 (zero) if not at steady state
##### 4. Use patient-specific Kel and Vd for additional calculations

Once patient-specific values of Kel and Vd have been determined, traditional one-compartment pharmacokinetic equations are used to identify a dose and its associated peak, trough, and AUC/MIC values.

#### Vancomycin Drug Level Monitoring

The most optimal method of monitoring vancomycin therapy is to obtain two drug levels (such as a peak and trough concentration) during the same dosing interval. These drug levels can either be obtained after the first dose is given (non-steady state) or once steady state is achieved (after the third dose is administered). The use of two drug concentrations allows for patient-specific estimations of all pharmacokinetic parameters using the Sawchuk-Zaske method.

Two drug levels (peak and trough) collected after a single dose (non-steady state)

Two drug levels (peak and trough) collected at steady state (after at least three doses)

Because vancomycin trough levels alone (one drug concentration) has been the standard for so long, some institutions may prefer to monitor drug therapy using a single vancomycin level (typically a trough level). This single drug level may be obtained after the first dose is given (non-steady state) or once steady state is achieved (after the third dose is administered). While a single drug level is less costly and more convenient, it requires Bayesian modeling to estimate pharmacokinetic parameters and may not be as accurate as a two-level approach, particularly in patients with very altered pharmacokinetics (extreme obesity, critically ill, pregnancy, burns, etc.).

One drug level collected after a single dose (non-steady state)

One drug level collected at steady state (after at least three doses)

In selected patients, a loading dose (25-30 mg/kg of total body weight; maximum 3000 mg) may be considered in order to achieve rapid attainment of serum concentrations.12 Patients who should be considered for a loading dose include those who are critically-ill, those receiving renal replacement therapy, or those receiving a continuous infusion of vancomycin. Note that this recommendation is made on the basis of expert opinion and is not supported by clinical trial data.

#### Inappropriate Populations for This Calculator

This calculator is NOT appropriate for the following patient populations or may require a higher degree of clinical judgment:

• Pediatrics (< 18 years)
• Cystic fibrosis
• Severe burn injury

#### Dosing Recommendations for Renal Replacement Therapy (RRT)

Vancomycin dosing in patients receiving renal replacement therapy is complex and usually requires expert clinical judgment in conjunction with assessment of unique patient-specific factors. For example, blood flow rate, filter type, hemodialysis frequency or downtime, effluent rate, and residual renal function are among several factors that influence a patient's vancomycin dosing needs. The following are general considerations and recommendations for this patient population.

##### Intermittent Hemodialysis 12

An initial loading dose of 25 mg/kg is recommended followed by 7.5 to 10 mg/kg after each hemodialysis session. Blood samples may be collected before dialysis (pre-dialysis) or 1-2 hours after dialysis (post-dialysis) and should be used to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

##### Sustained Low Efficiency Dialysis (SLED) 12,13

An initial loading dose of 20 to 25 mg/kg is recommended followed by 15 mg/kg after the end of each hybrid hemodialysis session. Blood samples may be collected before hybrid dialysis (pre-dialysis) or 1-2 hours after hybrid dialysis (post-dialysis) and should be used to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

##### Continuous Renal Replacement Therapy (CRRT) 14

An initial loading dose of 15 to 25 mg/kg is recommended followed by a maintenance dose based on the CRRT modality (see below). Blood samples should be collected to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

• CVVH: 10 to 15 mg/kg every 24-48 hours
• CVVHD: 10 to 15 mg/kg every 24 hours or 7.5 mg/kg every 12 hours
• CVVHDF: 7.5 to 10 mg/kg every 12 hours

Will this vancomycin calculator remain free of charge?

Why doesn't this calculator use a volume of distribution (Vd) of 0.7 L/kg? Some pharmacokinetic textbooks use this value.
A value of 0.7 L/kg is a convenient population estimate. Literature demonstrates highly variable values ranging from less than 0.5 L/kg (in morbidly obese patients) to greater than 1 L/kg (in non-obese critically ill patients). By default, this calculator uses Bayesian modeling population estimates to select an appropriate kinetic model based on critical illness and obesity. Users can select a variety of other Vd options, including 0.7 L/kg (Bauer method).

Why did you pick Buelga 2005 as a general hospitalized Bayesian model?
The Buelga model is a commonly selected in vancomycin Bayesian modeling and has been well studied in a variety of patient populations. Although the model was developed in patients with hematological malignancies, it has been validated in a more general cohort of hospitalized patients. Other models do exist that may have less bias and more precision (such as Goti et al. 2018); however, these models utilize a two-comparment approach. A core goal of this calculator is to provide transparency in how a vancomycin dose is calculated -- clinicians (and pharmacokinetic textbooks) utilize one-comparment pharmacokinetics; therefore, only one-comparment Bayesian models are considered for this calculator.

What does it mean if the calculator indicates that Bayesian modeling did not demonstrate a good fit for the patient data?
This error message is generated when the patient data provided cannot produce a model that matches to the patient's vancomycin level. In general, this error is produced in cases of data entry or laboratory error. For example, if a patient with very poor renal function (CrCl 20 mL/min) is given a very large dose (15 mg/kg IV Q8hr), the model would anticipate a very high trough level. Even with optimizing CLvanco and Vd, the model would likely not be able to match to the patient's measured drug level. When the model validates, the sum of squares (SS) would be high, indicating that the model was unable to fit well to the patient data provided.

1. Buelga DS, del Mar Fernandez de Gatta M, Herrera EV, et al. Population pharmacokinetic analysis of vancomycin in patients with hematological malignancies. Antimicrob Agents Chemother. 2005 Dec;49(12):4934-41. PMID 16304155.
2. Adane ED, Herald M, Koura F. Pharmacokinetics of vancomycin in extremely obese patients with suspected or confirmed Staphylococcus aureus infections. Pharmacotherapy. 2015 Feb;35(2):127-39. PMID 25644478.
3. Roberts JA, Taccone FS, Udy AA, et al. Vancomycin dosing in critically ill patients: robust methods for improved continuous-infusion regimens. Antimicrob Agents Chemother. 2011 Jun;55(6):2704-9. PMID 21402850.
4. Masich AM, Kalaria SN, Gonzales JP, et al. Vancomycin Pharmacokinetics in Obese Patients with Sepsis or Septic Shock. Pharmacotherapy. 2020 Mar;40(3):211-220. PMID 31957057.
5. Guo T, van Hest RM, Roggeveen LF, et al. External Evaluation of Population Pharmacokinetic Models of Vancomycin in Large Cohorts of Intensive Care Unit Patients. Antimicrob Agents Chemother. 2019 Apr 25;63(5). PMID 30833424.
6. Broeker A, Nardecchia M, Klinker KP, et al. Towards precision dosing of vancomycin: a systematic evaluation of pharmacometric models for Bayesian forecasting. Clin Microbiol Infect. 2019 Mar 11. pii: S1198-743X(19)30097-7. PMID 30872102.
7. Bauer LA. Applied Clinical Pharmacokinetics. McGraw-Hill/Appleton & Lange; 2001.
8. Matzke GR, McGory RW, Halstenson CE, Keane WF. Pharmacokinetics of vancomycin in patients with various degrees of renal function. Antimicrob Agents Chemother. 1984 Apr;25(4):433-7. PMID 6732213.
9. Rushing TA, Ambrose PJ. Clinical application and evaluation of vancomycin dosing in adults. Journal of Pharmacy Technology. 2001 Mar;17(2):33-8.
10. Dunn RD, Crass RL, Hong J, Pai MP, Krop LC. Vancomycin volume of distribution estimation in adults with class III obesity. Am J Health Syst Pharm. 2019 Dec 2;76(24):2013-2018. PMID 31630155.
11. Bauer LA. The Aminoglycoside Antibiotics. In: Bauer LA. eds. Applied Clinical Pharmacokinetics. 3rd Ed. New York, NY: 2014.
12. Rybak MJ, Le J, Lodise TP, et al. Therapeutic monitoring of vancomycin for serious methicillin-resistant Staphylococcus aureus infections: A revised consensus guideline and review by the American Society of Health-System Pharmacists, the Infectious Diseases Society of America, the Pediatric Infectious Diseases Society, and the Society of Infectious Diseases Pharmacists. Am J Health Syst Pharm. 2020 Mar 19. PMID 32191793.
13. Lewis SJ, Mueller BA. Development of a vancomycin dosing approach for critically ill patients receiving hybrid hemodialysis using Monte Carlo simulation. SAGE Open Med. 2018 May 11;6:2050312118773257. PMID 29780587.
14. Heintz BH, Matzke GR, Dager WE. Antimicrobial dosing concepts and recommendations for critically ill adult patients receiving continuous renal replacement therapy or intermittent hemodialysis. Pharmacotherapy. 2009 May;29(5):562-77. PMID 19397464.