Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

ADR-12616; No of Pages 8

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Advanced Drug Delivery Reviews

j ourna l homepage: www.e lsev ie r .com/ locate /addr

Review

Innovative approaches to optimizing the delivery of vancomycin inindividual patients☆

Manjunath P. Pai a, Michael Neely b,c, Keith A. Rodvold d, Thomas P. Lodise a,⁎a Albany College of Pharmacy and Health Sciences, Albany, NY, USAb University of Southern California, Keck School of Medicine, Los Angeles, CA, USAc Laboratory of Applied Pharmacokinetics and Bioinformatics (LAPKB), Children's Hospital of Los Angeles, Los Angeles, CA, USAd Colleges of Pharmacy and Medicine, University of Illinois at Chicago, Chicago, IL, USA

☆ This review is part of the AdvancedDrug Delivery Reviechallenges of advanced drug delivery in critical illness”.⁎ Corresponding author at: Albany College of Pharma

12208-3492, New York, USA.E-mail address: thomas.lodise@acphs.edu (T.P. Lodise

http://dx.doi.org/10.1016/j.addr.2014.05.0160169-409X/© 2014 Published by Elsevier B.V.

Please cite this article as: M.P. Pai, et al., InnoRev. (2014), http://dx.doi.org/10.1016/j.addr

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 28 May 2014Available online xxxx

Keywords:VancomycinPharmacokineticsBayesianPharmacodynamicsTroughAUC

The delivery of personalized antimicrobial therapy is a critical component in the treatment of patients with inva-sive infections. Vancomycin, the drug of choice for infections due to methicillin-resistant Staphylococcus aureus,requires the use of therapeutic drug monitoring (TDM) for delivery of optimal therapy. Current guidance onvancomycin TDM includes the measurement of a trough concentration as a surrogate for achieving an AUC tominimum inhibitory concentration (MIC) by broth microdilution (AUC/MICBMD) ratio ≥400. Although trough-only monitoring has been widely integrated into clinical practice, there is a high degree of inter-individualvariability between a measured trough concentration and the actual AUC value. The therapeutic discordance be-tween AUC and trough may lead to suboptimal outcomes among patients with infections due to less susceptiblepathogens or unnecessarily increase the probability of acute kidney injury (AKI) in others. Given the potentiallynarrow vancomycin AUC range for optimal effect and minimal AKI, clinicians need a “real-time” system to predictaccurately the AUC with limited pharmacokinetic (PK) sampling. This article reviews two innovative approachesfor calculating the vancomycin AUC in clinical practice based on one or two drug concentrations. One such approachinvolves the use of Bayesian computer software programs to estimate the “true” vancomycin AUC value withminimal PK sampling and provide AUC-guided dosing recommendations at the bedside. An alternative involvesuse of two concentrations (peak and trough) and simple analytic equations to estimateAUCvalues. Both approachesprovide considerable improvements over the current trough-only concentration monitoring method.

© 2014 Published by Elsevier B.V.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02. Pharmacodynamic profile of the “15–20 mg/L” target serum vancomycin concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 03. Mathematical relationship between trough and AUC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04. Concerns of acute kidney injury with trough vancomycin concentrations of 15–20 mg/L . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05. Innovative AUC-guided approaches to individualizing vancomycin delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

5.1. Bayesian approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05.2. Equation-based approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 05.3. Comparison of the equation-based to Bayesian based approach to AUC calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

6. Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 07. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0Conflicts of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

ws theme issue on “Meeting the

cy and Health Sciences, Albany

).

vative approaches to optimiz.2014.05.016

1. Introduction

Vancomycin is the cornerstone of therapy for patients with invasiveinfections due to methicillin-resistant Staphylococcus aureus (MRSA), themost prevalent multi-drug resistant pathogen in the world [1]. The rising

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

2 M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

rates ofMRSAhave coincidedwith a significant increase in the use of van-comycin. In the United States alone, over 20 million days of vancomycinare used annually [2]. Despite its introduction over a half century ago,the optimal dosing strategy for vancomycin remains undefined. Contem-porary vancomycin dosing schemes are designed to achieve an areaunder the curve (AUC) to minimum inhibitory concentration (MIC)(AUC/MIC) ratio≥400 for serious infections due toMRSA [3,4]. AlthoughanAUC/MIC ratio≥400 is the prevailing vancomycin exposure target thatis based on an MIC determined by broth microdilution (AUC/MICBMD),AUCs are not determined routinely in clinical practice due to the per-ceived difficulty in calculating the AUC [3,4]. Historically, a clinician hadto collect multiple pharmacokinetic (PK) samples and apply the linear-trapezoidal rule to determine theAUC in a givenpatient [5]. The perceiveddifficulties associated with determining vancomycin AUC values in “real-time” have led to the expert guideline committee recommendations tomaintain vancomycin trough concentrations between 15 and 20 mg/Las a surrogatemarker of an AUC/MICBMD ratio≥400 for serious infectionsdue toMRSA [3,4]. This recommendation has beenwidely integrated intoclinical practice. However, the clinical benefits ofmaintaining higher van-comycin trough values have not been well described [6–11]. In addition,evidence is mounting that the intensive intermittent dosing vancomycinregimens use to achieve troughs in excess of 15 mg/L may be associatedwith increased acute kidney injury (AKI) rates [12].

While trough monitoring is relatively straightforward in mostpractice settings, there is a high degree of inter-individual variability be-tween a measured trough concentration and the actual AUC value [13,14]. Themathematical discordance between the AUC and trough valuesis not surprising and is well-described in the literature [13]. In simpleterms, the AUC is reflective of the cumulative exposure for a definedtime period (e.g., 0–24 h). In contrast, the trough is a single pointexposure measurement at the end of the dosing interval. It is unreason-able to expect a single measurement at the end of the dosing interval tobe representative of the entire concentration-time profile withoutincorporating some covariate(s) and parameter assumptions [13,14].This discrepancy between AUC and trough has clear implications forclinical practice. Trough values of 15–20mg/L do not guarantee optimalAUC/MICBMD exposures in patients with infections due to MRSA withvancomycin MIC values in excess of 1 mg/L. Conversely, a trough of15–20 mg/L may lead to AUC values that have been associated with anincreased risk of AKI.

The therapeutic discordance between vancomycin trough concen-trations and AUCs has renewed our interest in calculating AUCs in prac-tice. Despite the clear advantages associated with AUC vs. trough-onlymonitoring for gauging the probability of efficacy while minimizinglikelihood of AKI, there has been considerable reluctance by cliniciansto move away from trough-only monitoring. Although calculating theAUC by the linear-trapezoidal formula is relatively straightforward [5],it is often too cumbersome to collect multiple levels over one dosing in-terval in the clinical arena. To address this issue, our group recentlyidentified two simplified approaches for estimating AUC values withlow bias and high precision using only one or two antimicrobial concen-trations [14,15]. This article will review the contemporary understand-ing of the pharmacokinetic/pharmacodynamic (PK/PD) profile ofvancomycin and describe two innovative methods for computing theAUC in clinical practice based on one or two samples. We will alsodiscuss the additional information required to improve the delivery ofvancomycin in future patients.

2. Pharmacodynamic profile of the “15–20 mg/L” target serumvancomycin concentration

Our current understanding of the vancomycin PK/PD profile is bestsummarized in the 2009 consensus review by the Infectious DiseasesSociety of America, the Society of Infectious Diseases Pharmacists andthe American Society of Health-Systems Pharmacists [4]. Their statementrepresents the first set of national, evidence-based recommendations for

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

vancomycin dosing andmonitoring.While a variety of PK/PD targets havebeen suggested for vancomycin, they concluded that the AUC/MICBMD

ratio is the optimal predictor of efficacy for vancomycin based on thebest available data [4]. The experts proposed that the data—drawn fromanimal models, in vitro studies, and limited human studies—collectivelysuggests that microbiologic success is optimized when the vancomycinAUC/MICBMD ratio exceeds 400 [3,4,16–19].

Since it is difficult in the clinical setting to obtain multiple serumvancomycin concentrations to determine the AUC and subsequentlycalculate the AUC/MICBMD ratio, the expert guidelines recommendmonitoring trough serum concentrations as a surrogate marker forAUC [3,4]. Their conclusion reads as follows: “Based on the potentialto improve penetration, increase the probability of optimal targetserum vancomycin concentrations, and improve clinical outcomes forcomplicated infections such as bacteremia, endocarditis, osteomyelitis,meningitis, and hospital-acquired pneumonia caused by S. aureus,total trough serum vancomycin concentrations of 15–20 mg/L arerecommended”[3,4].

Despite its subsequent widespread integration in clinical practice,the clinical benefits of maintaining higher vancomycin trough valueshave not been well described. To date, seven published studies of notehave evaluated the relationship between vancomycin trough valuesand clinical outcomes [6–11,20]. No link between clinical success andvancomycin trough values was seen in six of the seven studies that ex-amined this relationship [6–11]. The seventh study by Kullar et al.,showed that vancomycin failure (a composite endpoint including dura-tion of bacteremia, recurrence, and mortality) was higher in patients(58–66%) with vancomycin trough concentrations less than 15 mg/Lcompared to those obtaining trough concentrations between 15 and20 mg/L (40%). However, at the upper end of the trough continuum,treatment failure again increased in patients with vancomycin troughconcentrations N20 mg/L [20].

From a PK/PD perspective, it is not altogether surprising that there isa paucity of clinical data to support the range of 15–20 mg/L for vanco-mycin serum trough concentrations. The current Clinical LaboratoryStandards Institute (CLSI) and Food andDrug Administration (FDA) sus-ceptibility breakpoint for vancomycin against S. aureus is ≤2 mg/L [21,22]. However, maintaining vancomycin trough concentrations between15 and 20 mg/L only ensures a high likelihood (N90%) of achieving anAUC/MICBMD ratio N400 for S. aureus isolates with vancomycin MICvalues ≤ 1 mg/L [13,23]. Using vancomycin PK data from patientsvarying degrees of renal function, we demonstrated that againstS. aureus isolates withMIC values of 2mg/L, the probability of obtainingan AUC/MICBMD ratio N400 with trough vancomycin concentrations be-tween 15 and 20 mg/was suboptimal and was a function of the totaldaily dose administered (Fig. 1) [13]. In contrast, the probability ofachieving an AUC/MICBMD in excess of 400 was 100% for MIC values≤1 mg/L (Fig. 1). Further study is needed, but these data suggest thatthe current dosing approach ofmaintaining trough vancomycin concen-trations between 15 and 20 mg/L will have a low probability of successfor infections due to MRSA with wild-type MIC values by brothmicrodilution at the upper end of the antibiotic susceptibility range(e.g., 1.5 to 2 mg/L).

3. Mathematical relationship between trough and AUC

As mentioned previously, the trough is a single exposure point esti-mate at the end of the dosing interval. For vancomycin and most drugs,the trough concentration just prior to the next dose is the lowest con-centration observed in the dosing interval. As such, the 24-hour AUCvalue (AUC24) associated with trough values of 15–20mg/L will almostalways lead to an AUC24 in excess of 400 mg∗L/h. As an example, main-taining a vancomycin trough concentration of 17.5 mg/L equates to anAUC24 N 420 mg∗L/h (17.5 mg/L × 24 h). Therefore, the probability ofachieving an AUC/MICBMD ratio ≥400 will always be 100% with vanco-mycin trough values between 15 and 20 mg/L when the MIC value is

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

Fig. 1. Probability of achieving an AUC/MIC ratio≥400 for vancomycin dosing regimens ofvarying intensity when trough vancomycin concentrations are between 15 and 20 mg/L.

3M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

≤1 mg/L. However, while trough concentrations of 15–20 mg/L ensureAUC values of at least 400 mg∗L/h, there is considerable variability inthe upper range of AUC values. This can be shown through a MonteCarlo simulation (n = 5000) of the vancomycin concentration-timeprofile based on the administration of a 1 g every 8 hour regimenusing a well-established population PKmodel [13,24,25].When one ex-amines the relationship between the trough concentration after thethird dose and AUC24 (Fig. 2), a trough concentration will not explainmore than approximately 50% of the inter-individual variability in theAUC (R2= 0.409). Therefore, one cannot rely solely on the vancomycin“15–20 mg/L” trough concentration range to achieve an AUC/MICBMD

ratio ≥400 for S. aureus isolates with MIC values in excess of 1 mg/L.

4. Concerns of acute kidney injury with trough vancomycinconcentrations of 15–20 mg/L

Due to the reluctance to estimate AUC values at the bedside, the lim-ited data in support of the 15–20 mg/L range for vancomycin serumtrough concentrations has raised the question of whether we need tomaintain even higher trough values in clinical practice. There are twothings to consider when evaluating drug therapy. First, the drug mustbe efficacious. Second, the drug must be non-toxic. While maintenance

Fig. 2. Scatter and linear fit plot of vancomycin area under the curve over 24 h (AUC24)versus trough vancomycin concentration from 5000 subject Monte Carlo simulation.

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

of trough concentrations in excess of 20mg/Lwill ensure a higher prob-ability of achieving anAUC/MICBMD ratio N400 for S. aureus isolates withMIC values N1 mg/L, this may not be possible without subjectingpatients to an increased risk of vancomycin-related toxicities, mostnotably AKI [6–9,11,19,20,26–55]. Nephrotoxicity is a long-standing,yet highly debated, adverse effect associatedwith vancomycin adminis-tration [56,57]. To date, 14 studies [6–9,11,20,22,26,27,30,32–34,36,47]of note have comparatively assessed the AKI potential of maintaininghigher vancomycin trough concentrations (N15 mg/L) relative tolower troughs (b15 mg/L) in clinical practice and the results of thesestudies are well summarized in the systematic literature review byVan Hal et al. [12]. Overall, maintaining trough concentrations in excessof 15mg/L was found to substantially increase the risk of a nephrotoxicevent (OR 2.74; 95% CI 1.94–3.88, p b 0.01) relative to trough concentra-tionsb15mg/L. The probability of a nephrotoxic eventwas also found toincrease as a function of treatment duration, with most episodes occur-ring after seven days of therapy [12]. Collectively, these data stronglysuggest that adherence to the recommendations for vancomycinserum trough concentrations in recent expert guidelines [3,4] may re-sult in an elevated risk of vancomycin-induced AKI.

As noted above, there is a high degree of inter-individual variabilitybetween a measured trough concentration and the actual AUC value[13]. Therefore, it is difficult to estimate the degree of AKI associatedwith a given trough concentration due to the wide range of AUC valuesassociated with it. There have been limited attempts in the literature toquantify the relationship between AUC and the probability of AKI [32,58]. While data are scant, an AUC range of 700–1300 mg h/L has beensuggested to increase the risk of nephrotoxicity [14,32,58,59]. Suzukiet al. [58], compared the mean vancomycin AUC in patients who werenephrotoxic and non-nephrotoxic in a recent case–control study. Mostpatients in the nephrotoxic group had AUC24 values between 600 and800 mg∗h/Lwhile thosewho remained non-nephrotoxic were between400 and 600 mg∗h/L (p= 0.014). Our group also recently examined therelationship between AUC and occurrence of AKI among hospitalizedpatients receiving vancomycin [32]. In contrast to Suzuki et al. [58],we found that the probability of AKI increased 2.5-fold among patientswith AUCs above 1300 mg∗h/L compared with those below (30.8% vs.13.1%, p = 0.02) [32]. Interestingly, although AUC values in excess of1300 mg∗h/L were associated with a substantial increase in AKI, anAUC exposure-response relationship appeared to exist (Fig. 3) [59]. Inparticular, the probability of a nephrotoxic event increased as a functionof the AUC and patient's body weight [59]. Collectively, these limiteddata suggest that vancomycin-induced AKI occurs along a continuumand that certain populations may be at particular risk.

Fig. 3. Probability of nephrotoxicity versus vancomycin area under the curve from time 0to 24 h (AUC0–24) by body weight breakpoint.

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

4 M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

5. Innovative AUC-guided approaches to individualizingvancomycin delivery

The efficacy data, combined with the AKI findings, suggest thattrough-only monitoring is not sufficient to guide vancomycin dosingand that AUC-guided dosing may be warranted [13]. Until recently,AUC determination has required one to collect multiple PK samplesand calculate the AUC by linear-trapezoidal formula. Cognizant of thepractical difficulties associated with this approach, our group hasrecently identified two simplified methods for estimating AUC valuesin practice with low bias and high precision using only one or twoserum antimicrobial concentrations [14,15]. One approach involvesthe use of population modeling and Bayesian software programs tooptimize the delivery of vancomycin based on the collection of onevancomycin trough concentration [14]. The other approach relies onfirst-order pharmacokinetic equations based on the collection of twotimed steady-state serum vancomycin concentrations to estimate theAUC value [15]. Each will be discussed in turn.

5.1. Bayesian approach

The Bayesian dosing approach is based on Bayes' Theorem. In thecontext of PK/PD, his theorem describes quantitatively the importantsequential relationship between: (1) the estimated probability distribu-tion of an individual patient's PK parameter values (e.g. volume orclearance) prior to administering the drug based on the way the drughas behaved in prior patients (Bayesian prior); (2) the measured drugconcentrations that are collected from a patient after administration ofa given drug regimen, and (3) the revised probability distribution of agivenpatient's PK parameter values after dosing and drug concentrationdata is taken into account (Bayesian conditional posterior). With theBayesian conditional posterior, the vancomycin AUC value can beestimated with low bias and subsequent AUC-optimized dosing recom-mendations can be provided in real-time [60–63].

A common analogy that is used to explain a Bayesian approach is asfollows. A person misplaces their mobile phone in their home. A stan-dard approach may be to call the phone number from another lineand hope that the ringtone is loud enough to locate the missingphone. A Bayesian approach recognizes through prior experience (apriori probability) that the person often misplaces their phone in thebedroom. Given this information, the person asks the family memberto place the call when they are closer to the bedroom to maximize theprobability of finding the phone (a posteriori probability). If the phoneis not found in the bedroom, the person moves to the next probablelocation and repeats the step (second iteration). A similar iterative ap-proach can be used to identify an individual PK profilewith limited data.

Using richly sampled serum vancomycin concentration-time datafrom three studies comprising 47 adults with varying renal function,our group determined that trough-only data can be used to generate ac-curate and reliable estimates of the daily AUC through the use of aBayesian software program embedded with a PKmodel based on richlysampled vancomycin data as the Bayesian prior (Bayesian estimationtechnique) [14]. Assuming that the AUC estimated from the full data isthe “gold standard”, the Bayesian approach with trough-only datawas associated with 97% (93% - 102%, p = 0.23) accurate AUC estima-tion [14]. In contrast, the traditional trough-only PK approachunderestimated the true AUC by about 25%. Of note, the Bayesianapproach with trough-only data requires the use of a PK model basedon richly sampled PK data as the Bayesian prior. Use of a populationPKmodel that was derived on peak and trough serum vancomycin con-centrations as the Bayesian prior was suboptimal at predicting the trueAUC from vancomycin troughs. We make this distinction since manypublished vancomycin population models are derived from peak andtrough concentration data only [14].

Bayesian dose optimizing software is now readily available and theycan be used at the bedside to identify the optimal vancomycin dosage

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

that achieves the pre-defined AUC target [64]. Bayesian programs offernumerous advantages over the traditional first-order equation ap-proach. Vancomycin concentrations can be obtained at any time, evenover different dosing intervals. The generality of the Bayesian methodallows for application of various pharmacokinetic models (in thiscase a 2-compartment model for vancomycin) and dosing patterns.Additionally, this approach is not limited to trough-only sampling andsamples do not necessarily have to be taken under steady-state condi-tions [61,62].

To estimate the AUC based on dosing history and provide subse-quent AUC-dose optimized recommendations, the Bayesian softwareonly requires four specific components: (1) the structuralmathematicalmodel that best describes the pharmacokinetics of a given agent; (2) adensity file, which contains the parameter estimates and their associat-ed dispersion for the embedded structural PK model (Bayesian prior);(3) a patient file that contains their drug dosing and collected PK data;and (4) a patient “target” file which contains the target exposure profileand initial estimates of future dosing regimens. In short, the dose opti-mization software uses the equations in the structural mathematicalmodel file and the population Bayesian prior in the density file, togetherwith the individual patient's observed drug concentrations in the datafile to calculate a Bayesian posterior parameter value distribution forthat patient. The dose optimization software then calculates the optimaldosing regimen based on the specified exposure profile in the target file[61,62,64]. In simpler terms, it is a step-wise mathematical approachthat increases the probability of finding “the missing cellphone” basedon available information (see analogy above).

The additional advantage of this approach is that it can be modifiedto be an adaptive program [61]. Innovative treatment schemas such asfront-loading doses with a transition to a lower maintenance dosingregimen can be designed to rapidly achieve target concentrations with-in the first 24 to 48 h among critically ill patients. Furthermore,concentration-time information does not need to be collected at“steady-state” (after the 3rd or 4th dose). Dynamic changes in PK pro-files readily occur in patients, especially those in the critical care settingsthat limit the ability of “steady-state” concentration monitoring. Withthe Bayesian approach, vancomycin concentrations can be collectedwithin the first 24 to 48 h, rather than waiting for steady-state condi-tions, and this information can be used to inform subsequent dosing(adaptive feedback control). Furthermore, the Bayesian approach pro-vides the ability to include covariates, such as creatinine clearance, inthe structural PK models (Bayesian prior density file) that account forthe pathophysiological changes that readily occur in critically ill pa-tients. Incorporation of covariates that account for these “dynamic”changes serve as a way to identify dosing schemes that optimize effectand predict future dosing in a patient with an evolving PK profile [61].This requires further study, but it is an approach commonly used inother fields, such as the military for targeting an incoming missile im-pacted by dynamic conditions such as wind speed and direction. Alter-natively, as stated above, amore pragmatic approachwould be frequentobservation and dosage adjustment (adaptive feedback control)performed with minimal delay between observation and adjustment.

5.2. Equation-based approach

As an alternative to using a Bayesian software program, we recentlydemonstrated that use of post-distributional peak (1–2 h post infusion)and trough concentrations can determine the daily AUC value with rea-sonable precision and low bias with simple first-order PK formulas [15,65]. The collection of two PK samples during the same dosing interval,such as a peak and a trough concentration, permits characterization ofthe concentration-time profile for that dosing interval as a simplemono-exponential curve. Simple arithmetic equations can be appliedto calculate the AUC using this approach. Importantly, this approachcould be programmed into the electronic medical system to automati-cally compute the AUC. The major advantage of this approach is that it

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

5M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

relies on fewer assumptions and provides a “real world” snapshot of thepatient-level information for rapid clinical translatability. The majorlimitation of this approach is that it is not adaptive like the Bayesianapproach, and can only provide a snapshot of the AUC for the samplingperiod. This AUC calculation will not be correct if a physiologic changesuch as renal dysfunction occurs during or after the sampling period.

The equations to compute AUC from two samples are based in parton an original approach proposed by Begg, Barclay, and Duffull for ami-noglycosides [66] and modified by Pai and Rodvold [15]. This approachhas recently been validated for computation of daptomycin AUC [65].However, these previous investigations are based on the assumptionthat these agents are administered using a once-daily approach. This isoften not the case for vancomycin because twice daily and thrice dailydosing in patients with good kidney function is common. The AUCcomputation may be modified based on two concentrations as follows.

Fig. 4 reflects the concentration-timeprofile of vancomycin based onthe administration of 1000 mg every 8 h (1-hour infusion) and focuseson theprofilewhere TDM is often employed (around the3rd or 4th dose[at 24 h to 32 h time points of therapy]). As illustrated, the “true” vanco-mycin concentration follows at least a bi-exponential decline (2-compartment model). It is not possible to accurately characterize theinitial (α-phase) concentration-time profile without measurement ofa concentration between the end of infusion and the moment in thecurve that occurs 2–3 h from the start of infusion. Because two concen-trations may be measured during the same phase (β-phase) of theconcentration–time decline, it is possible to fit a mono-exponentialdecline function to characterize this profile from the start of infusion(artificial time) to the end of the dosing interval. This fit is also illustratedin Fig. 4.

The Sawchuk–Zaske method [67] can be used for this mono-exponential fit by computing the elimination rate constant (Ke) usingthe following equation.

Ke ¼Ln

C1C2

� �

tð1Þ

where, C1 is thefirst concentration after the dose thatmay be referred toas the “peak” concentration, C2 is the second concentration collectedtoward the end of the dosing interval or “trough” concentration, and tis the difference in time between these two concentrations. Once theKe is computed, this information can be used to compute theoreticalconcentrations through back-extrapolation (end of infusion or start of

Fig. 4. Expected concentration-time profile after administration of the 4th dose of a 1000mg every 8 hour regimen of vancomycin with a peak and trough concentration fit with amono-exponential decline function.

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

infusion value). This method can also be used to forward-extrapolateconcentrations to the “true” trough concentration (Ct) at the end ofthe dosing interval. This may be necessary because it is often not clini-cally possible to measure the trough concentration exactly at the endof the dosing interval.

Once the theoretical (i.e., notmeasured) concentrations at the end ofinfusion (Ceoi), start of infusion (Csoi), and Ct are known, AUC can becalculated using arithmetic functions. In the first scenario (Fig. 5), theend of infusion concentration is estimated. The start of infusion andtrough concentration can be assumed to be the same because they areat near-steady state (Fig. 4), which permits superposition. Alternatively,samples may be collected prior to the dose (trough) and after the dose(peak) to expedite AUC calculation (instead of waiting until the end ofthe dosing interval).

The area between the start (same as Ct) and theoretical end ofinfusion (Ceoi′) for a given infusion time (t′) can be related as the areaof a trapezoid:

AUCt0−t1 ¼ Ceoi 0 þ Ct� �� 0:5� t0 ð2Þ

The area under a mono-exponential curve from the time of the endof infusion (t1) to the time of the end of the dosing interval (t2) is:

AUCt1−t2 ¼Z infinity

t1Ceoi0 � e−Ke� tð Þdt−

Z infinity

t2Ct � e−Ke� tð Þdt

AUCt1−t2 ¼ Ceoi0− CtKe

:

ð3Þ

So the area under scenario 1 can be simplified to

AUCt0−t2 ¼ t0 � Ceoi 0 þ Ct� �

2þ Ceoi 0−Ct

Ke: ð4Þ

As shown by Fig. 5, this approach captures a majority of the area butwill under-predict the true AUC as the rise in concentration to the end ofinfusion is not entirely linear and theα-phase is ignored by thismethod.An alternative to overcome this limitationwould be to back-extrapolatethe concentration to the theoretical start of infusion (Csoi′). Under thissecond scenario (Fig. 6), the equation can be simplified to:

AUCt0−t2 ¼Z infinity

t0Csoi0 � e−Ke� tð Þdt−

Z infinity

t2Ct � e−Ke� tð Þdt

AUCt0−t2 ¼ Csoi 0− CtKe

ð5Þ

Fig. 5. Expected area under the curve captured using Eq. (4) based on an expected vanco-mycin concentration time profile.

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

Fig. 6. Expected area under the curve captured using Eq. (5) based on an expected vanco-mycin concentration time profile.

6 M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

As shown, this approachwill lead to the computation of a larger AUCand will substitute for the AUC not captured by Eq. (4). However, as il-lustrated, this approach will slightly over-predict the true vancomycinAUC. Under all these scenarios, the AUC24 will be a function of the num-ber of identical doses administered during that interval. Thus, in thespecific example presented, the computation will lead to AUC estima-tion over an 8 hour interval (AUC8). The AUC24 can be calculated bymultiplying this estimate by 3 (AUC8 × 3).

5.3. Comparison of the equation-based to Bayesian based approach to AUCcalculation

We have previously described the dataset used to validate thesingle-measurement based Bayesian AUC calculation using data fromthemanuscript fromour recent group [14]. Concentrations collected be-tween 1.5 and 3 h from the start of infusionwere used as the Cp and theconcentration close to the end of the dosing interval was selected as Ct.Vancomycin AUC was calculated separately using Eqs. (4) and (5). Theequation-calculated AUC was compared to the Bayesian AUC using thefull concentration-time profile (AUCf) and a value based on a trough-only measurement (AUCt). Table 1 summarizes the median [5th and95th] percentile AUC values and the ratio of the trough only or peakand trough based AUC calculation to the reference standard (AUCf). Asshown in Table 1, the proposed methods accurately (low bias andhigh precision) reflect the reference AUCf value. As expected from de-scriptions of Eqs. (4) and (5), (4) tends to under-predict AUCf whileEq. (5) tends to over-predict AUCf. However the median error is ≤2%by these methods, which is not clinically significant.

A key issue to consider when applying the equation-based approachis the optimal sampling window for collection of the peak concentra-tion. A sample collected too early for example may be in the α-phaseand lead to an erroneous Ke estimate. Given that it is not practical to col-lect multiple samples after the end of infusion to identify the optimal

Table 1Median [5th, 95th percentile] area under the curve (AUC) values, ratio of computed to referenmethods for AUC estimation.

AUC estimation method Number of samples AUC (mg∗h/L

Bayesian All 250 [84.1, 688Bayesian Trough only 259 [82.9, 573Eq. (4) Peak and trough 239 [90.6, 662Eq. (5) Peak and trough 247 [100, 675

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

peak sampling time-point, we used a population simulation to addressthis question. We simulated 5000 concentration-time profiles basedon the administration of three 1500 mg (1.5 h infusion) vancomycindoses. We tested 45 Cp–Ct pairs that included 9 Cp values between 1 hand 3 h from the endof infusion (15 minute increments) and 5 Ct valuesin 15 minute incrementswithin anhour before the end of the dosing in-terval. This simulation revealed that the mean percent error in the AUCcalculation using Eqs. (4) or (5) is b2% when the Cp value is collected1.75 h to 3 h after the end of infusion.

6. Future directions

Several things should be noted when interpreting and applying thefindings from this review. Contemporary vancomycin dosing focuseson achieving an AUC/MICBMD ratio ≥400. Although the AUC/MICBMD

≥400 PK/PD target for vancomycin is the prevailing PK/PD target [3,4,16–19], data in support of this target is largely derived fromneutropenicmouse thigh infectionmodel data [16] and there are limited clinical datato support this target [3,4,18,47,68]. Furthermore, most clinical evalua-tions performed to date that identified AUC/MICBMD≥400 as the criticalPK/PD target for vancomycin used a simple formula based on dailyvancomycin dose and estimated renal function to estimate AUC values[18,47,68]. In most cases, they used the Cockcroft–Gault creatinineclearance formula [69]. As highlighted throughout this manuscript,there is considerable inter-patient variability in vancomycin exposureprofiles in clinical practice and it is difficult to generate valid estimatesof exposure variables in a given individual based on glomerularfiltration estimation formulas alone [9–11].

Using the validated Bayesianmethod discussed in thismanuscript toestimate the vancomycin exposure profile with limited vancomycinblood concentration data [14], our group determined that AUC/MICBMD

is the pharmacodynamic indexmost closely linked to outcomes for van-comycin among adult patients with MRSA bloodstream infections [70].In contrast to the reported AUC/MICBMD ratio of 400 [18,47,68], the crit-ical day 1 and day 2 AUC/MICBMD ratio values identified by classificationand regression tree (CART) analysis were AUC0–24h/MICBMD ≥521 andAUC0–24h/MICBMD ≥650. Achievement of both day 1 and day 2 AUC/MICBMD values in excess of the CART-derived AUC/MICBMD breakpointswere associated with success rates of 80–85%, consistent with the nearmaximal effect expected for patients with MRSA BSIs; failure to achievethe CART-derived AUC/MIC exposure thresholds was associated withsuccess rates below60%. Collectively, these findings establish the criticalimportance of individualized estimates of the daily AUC/MICBMD ratioduring the first two days of vancomycin therapy [70]. As this was a ret-rospective study, these data also provide justification to support a larger-scale, multi-centered clinical trial to prospectively validate the findingsand determine the vancomycin pharmacokinetic/pharmacodynamic(PK/PD) profile associated with maximal effect. For any drug, a clear un-derstanding of the PK/PD target associatedwithmaximal effect is neededto optimally dose it in clinical practice.

Similar to the “efficacy” exposure-response data, our understandingof the relationship between vancomycin exposure and probability ofAKI is limited. Most studies performed to date have examined therelationship between vancomycin trough concentration and AKI atpre-defined thresholds [12]. The more quantitative analyses indicate

ce AUC values, and coefficient of determination (R2) for the Bayesian and equation based

) Ratio of computed AUC to reference AUC R2

] Reference Reference] 1.0 [0.74, 1.28] 0.948] 0.99 [0.83, 1.16] 0.971] 1.02 [0.85, 1.22] 0.987

ing the delivery of vancomycin in individual patients, Adv. Drug Deliv.

7M.P. Pai et al. / Advanced Drug Delivery Reviews xxx (2014) xxx–xxx

that vancomycin-induced AKI occurs along a continuum and its likeli-hood varies by patient population [32,58,59]. However, the findingshave varied. To truly optimize the dosing of vancomycin, a firmerunderstanding of the PK/PD targets associated with maximal effectand minimal AKI are required. No model can be proven but ratheronly disproven. So, additional work is always needed to ensure general-izability of any AUC/MIC target to broader patient populations.

Given that vancomycin TDM occurs routinely in clinical practice,clinicians involved in improving optimal dose delivery must have toolsto accomplish this goal. The state-of-the-art approach that will be adap-tive to dynamic patient conditions is the Bayesian approach [14,60–62].Several software programs and trainingmodules exist to empower clini-cians to adopt this approach for vancomycin in clinical practice [64]. Animportant future direction is for clinicians who perform vancomycinTDM to learn this tool for dose optimization if they wish to only relyon a single point measurement (vancomycin serum trough concentra-tion). We have clearly laid out the fallacies of a single-point measure-ment when it is not coupled with this software tool.

An alternative (but less ideal solution) would be to apply anapproach that is currently applied with aminoglycoside dosing that in-cludes peak and trough concentrations [15,65,71]. Instead of treatingthese two values as independent terms, they can be integrated by ananalytic solution to derive a reasonable estimate of vancomycin AUC.This estimate of AUC will be a static representation of information forthe specific sampling period but is a step above trough-only or peak-only concentration interpretation. The increasing use of electronic med-ical systems including technologies that scan the exact (or close to)times that doses are administered and samples collected provides an op-portunity for automation of this calculation. An important future direc-tion could be automation of vancomycin AUC output value if peak andtrough concentrations are measured in clinical practice using Eqs. (1),(4) or (5).

7. Conclusions

We live in an age where personalized medicine and individualizedtherapies are recognized modalities to improve the safety and efficacyof medications. A one-size-fits-all approach to drug dose delivery is nolonger reasonable. Dose delivery optimization requires measurement,and in the case of vancomycin that currently includes measurement ofa trough concentration. Interpretation of a trough concentration as anindependent value ignores the true concentration–time profile in agiven patient. A Bayesian approach can overcome this major limitationby using prior probabilistic information to fit the trough-only measure-ment to a more realistic profile. This approach requires a Bayesian priorgenerated from the rich data repository that exists for vancomycin.Alternatively, a lesser solution that could more easily be automatedfor clinical use includes the application of an analytic solution but it re-quires peak and trough concentration measurement. While there willalways be barriers to implementation of these approaches, these are“largely logistic and educational, but not technological” [14]. Clinicianswho routinely use vancomycin TDM must ultimately decide upon thebest solution for their clinical practice. We believe that the best solutionis the Bayesian approach, but offer an alternative for centers that do notyet have the expertise to implement this approach.

Conflicts of interest

M.N. is a founder of Applied Pharmacometrics, Inc., which isdeveloping the BestDose software for commercial distribution. M.N.provides scientific advice to the company, but does not receive anyfinancial compensation. M.N. is also the Principal Investigator for theLaboratory of Applied Pharmacokinetics and Bioinformatics, which pro-duces Pmetrics as a free research tool and developed the algorithmspowering BestDose (both available at http://www.lapk.org).

No conflicts exist for M.P., K.R., and T.L.

Please cite this article as: M.P. Pai, et al., Innovative approaches to optimizRev. (2014), http://dx.doi.org/10.1016/j.addr.2014.05.016

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