JBUR-4077; No. of Pages 8

Amikacin population pharmacokinetics amongpaediatric burn patients

Catherine M.T. Sherwin a,*, Stephanie Wead b, Chris Stockmann a,Daniel Healy b,d, Michael G. Spigarelli a, Alice Neely c,d, Richard Kagan c,d

aDivision of Clinical Pharmacology, Department of Paediatrics, University of Utah School of Medicine, Salt Lake City,

Utah, United Statesb James L. Winkle College of Pharmacy, University of Cincinnati, Cincinnati, Ohio, United StatescDepartment of Surgery, University of Cincinnati, Cincinnati, Ohio, United StatesdThe Shriners Hospitals for Children1, Cincinnati, Ohio, United States

b u r n s x x x ( 2 0 1 3 ) x x x – x x x

a r t i c l e i n f o

Article history:

Accepted 14 June 2013

Keywords:

Amikacin

Pharmacokinetics

Paediatric burns

a b s t r a c t

Introduction: The objectives of this study were to (1) determine the pharmacokinetics of

amikacin among children with severe burn and (2) identify influential covariates.

Methods: Population-based pharmacokinetic modelling was performed in NONMEM 7.2 for

hospitalized children who received amikacin at 10–20 mg/kg divided two, three, or four

times per day as part of early empiric treatment of presumed burn-related sepsis.

Results: The analysis included data from 70 patients (6 months to 17 years) with 282

amikacin serum concentrations. Amikacin’s mean Cmax was 33.2 � 9.4 mg/mL and the mean

Cmin was 3.8 � 4.6 mg/mL. The final covariate model estimated clearance as 5.98 L/h/70 kg

(4.97–6.99, 95% CI), the volume of distribution in the central compartment as 16.7 L/70 kg

(14.0–19.4, 95% CI), the volume of distribution in the peripheral compartment as 40.1 L/70 kg

(15.0–80.4, 95% CI), and the inter-compartmental clearance as 3.38 L/h/70 kg (2.44–4.32, 95% CI).

In multivariate analyses, current weight (P < 0.001) was a significant covariate, while age, sex,

height, serum creatinine, C-reactive protein, platelet count, the extent and type of burn, and

concomitant vancomycin administration did not influence amikacin pharmacokinetics.

Discussion: Children with burn featured elevated amikacin clearance when compared to

healthy adult volunteers. However, peak amikacin concentrations are comparable to those

attained in other critically-ill children, suggesting that elevated amikacin clearance may not

result in sub-therapeutic antibacterial effects. In this study, we found that amikacin dis-

plays two-compartment pharmacokinetics, with weight exerting a strong effect upon

amikacin clearance. Further pharmacodynamic studies are needed to establish the optimal

dosing regimen for amikacin in paediatric burn patients.

# 2013 Elsevier Ltd and ISBI. All rights reserved.

Available online at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/burns

1. Introduction

The aminoglycoside antibiotic amikacin is a mainstay of

treatment for gram-negative sepsis among critically-ill burn

* Corresponding author at: University of Utah Health Sciences Center, 2United States. Tel.: +1 801 587 7404; fax: +1 801 585 9410.

E-mail address: Catherine.Sherwin@hsc.utah.edu (Catherine M.T.

Please cite this article in press as: Sherwin CMT, et al. Amikacin populathttp://dx.doi.org/10.1016/j.burns.2013.06.015

0305-4179/$36.00 # 2013 Elsevier Ltd and ISBI. All rights reserved.http://dx.doi.org/10.1016/j.burns.2013.06.015

patients [1,2]. The pathophysiology of burn can result in

substantially altered aminoglycoside pharmacokinetics, in-

cluding heightened renal clearance, increased volume of

distribution, and altered protein binding [3–6]. As a conse-

quence of these pharmacokinetic changes, previous reports

95 Chipeta Way, Clinical Pharmacology, Salt Lake City, Utah 84108,

Sherwin).

ion pharmacokinetics among paediatric burn patients. Burns (2013),

b u r n s x x x ( 2 0 1 3 ) x x x – x x x2

JBUR-4077; No. of Pages 8

have recommended higher aminoglycoside doses and/or more

frequent administration [1,7]. However, aminoglycosides may

adversely affect auditory, vestibular, and renal function,

adding further complexity to dosing in this patient population

[8]. Investigation of amikacin pharmacokinetic parameters is

essential for defining factors that contribute to variability in

drug disposition and in determining an optimal dosing

regimen for paediatric burn patients.

Amikacin features concentration-dependent bactericidal

activity and a substantial post-antibiotic effect [9–11]. Howev-

er, similar to other aminoglycoside antibiotics, adaptive

resistance to amikacin is enhanced by continued presence

of the drug [12]. Previous reports have suggested that the

development of adaptive resistance may be minimized during

once-daily dosing [13–15]. Additionally, amikacin toxicity may

occur with sustained drug concentrations [16]. Nephrotoxicity

occurs as a consequence of amikacin accumulation in the

proximal renal tubules [17]. However, Williams et al. demon-

strated that once proximal tubular cells have been saturated

with amikacin, increasing concentrations are not likely to

result in increased intracellular amikacin accumulation

[18,19]. Amikacin use has also been associated with loss of

cochlear and vestibular hair cells, leading to hearing loss and

disequilibrium [20]. The risk of ototoxicity has been strongly

associated with high trough concentrations [21]. In an attempt

to enhance efficacy and reduce the risk of nephrotoxicity and

ototoxicity once-daily dosing of amikacin has become com-

mon practice among non-burn patients [22,23]. However,

limited pharmacologic and clinical evidence exists to aid in

the determination of an optimal, individualized amikacin

dosing regimen for severely-burned paediatric patients.

The primary objective of this study was to evaluate the

pharmacokinetic parameters of amikacin among critically-ill

children with severe burn. As a secondary aim, covariates

which influence amikacin pharmacokinetic parameters were

evaluated. We hypothesized that burned children would more

rapidly clear amikacin than healthy volunteers, which could

potentially result in sub-therapeutic antibacterial activity.

Ultimately, improved understanding of amikacin pharmaco-

kinetics in this population offers the opportunity to develop

optimal dosing regimens and aid in the design of future

studies conducted among paediatric burn patients.

2. Methods

2.1. Subjects

This study involved 73 paediatric burn patients who were

hospitalized in the dedicated burn unit at the Cincinnati

Shriners Hospital for Children, Cincinnati, Ohio. All patients

received amikacin as part of an empiric regimen with

piperacillin/tazobactam and vancomycin for presumed or

proven burn wound sepsis. Patient demographics, including:

age, sex, weight, height, per cent total body surface area burn,

and serum creatinine were recorded.

This study was reviewed and approved by the University of

Cincinnati Institutional Review Board. Parental permission

and informed assent (when appropriate) were obtained prior

to the performance of any study-related procedures.

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2.2. Drug administration

Amikacin was infused over 30 min using a syringe pump at a

daily dose of 10–20 mg/kg divided two (13% of patients), three

(45%), or four (42%) times. Dosing adjustments (e.g., decreased/

increased dose or shorten/lengthen dosing interval) were

made to target peak concentrations from 25 to 30 mg/mL and

trough concentrations of 4–8 mg/mL.

2.3. Sample collection

Blood samples were obtained for routine therapeutic drug

monitoring for medical care. Samples were drawn within

30 min before the dose (trough concentration) and 1 h after the

end of the intravenous infusion (peak concentration). The

duration of treatment was determined on the basis of the

child’s clinical status and results of microbiologic testing.

2.4. Analytical assay

Amikacin serum concentrations were measured using an

automated fluorescence polarization immunoassay (Abbott

TDx, Abbott Park, IL) [24]. The assay was linear from 0.8–

50.0 mg/mL with reported within-day and between-day coeffi-

cients of variation <7.6% for low (5 mg/mL), medium (15 mg/

mL), and high (30 mg/mL) quality control specimens that were

run with each batch of patient unknowns.

2.5. Pharmacokinetic analysis

For a detailed description of the pharmacokinetic modelling

methods please refer to the Appendix. Briefly, amikacin

pharmacokinetics were evaluated in NONMEM 7.2 (non-linear

mixed effects modelling; ICON Development Solutions, Ellicott

City, MD). Non-linear mixed effects models were used to

describe the amikacin concentration-time response for this

population of burned children. Population estimates of

amikacin clearance (CL) and volume of distribution (Vd) were

calculated based upon the dose and time of administration for

each patient.

Model variability and random effects were classified as

belonging to one of two types of error: (1) between-subject

variability (BSV) and (2) residual unexplained variability (RUV).

BSV is the inherent variability between individual subjects.

RUV reflects the difference between the model prediction for

the individual and the measured concentration. This includes

errors in the time of measurement, errors in the drug dose,

error in the assay, etc. [25]. Estimates of these errors were

calculated using additive, proportional, and combined error

models.

Patient age, sex, weight, height, per cent total body surface

area burn, and serum creatinine were evaluated for their effect

upon amikacin pharmacokinetic parameters. Initially, rela-

tionships between potential covariates and amikacin phar-

macokinetics were assessed in generalized additive models.

Further covariate selection was performed by the stepwise

addition of covariates that significantly improved the model’s

fit (P < 0.05). Covariates were then eliminated in a backward

stepwise procedure if they did not result in a highly significant

improvement to the model’s fit (P < 0.01). The final covariate

ion pharmacokinetics among paediatric burn patients. Burns (2013),

Table 1 – Demographic characteristics among severely-burned children who received amikacin for proven orpresumed gram-negative infections.

Characteristic Number (%)(n = 70)

Age (years)

Median 4.5

Range 0.6–17

Sex

Boys 45 (64)

Girls 25 (36)

Race/Ethnicity

White 37 (53)

Black 13 (19)

Hispanic 16 (23)

Asian/Pacific Islander 2 (3)

Other 2 (3)

Weight (kg)

Median 20

Range 8–90

Concomitant vancomycin use

Yes 62 (89)

No 8 (11)

Type of burn

Flame 47 (67)

Scald 18 (26)

Electrical 5 (7)

Inhalation injury

Yes 13 (19)

No 57 (81)

Per cent total body surface area burned

Median 43

Range 11–98

Fig. 1 – Diagnostic plot comparing weight versus age.

(regression line shown as a dashed line.).

b u r n s x x x ( 2 0 1 3 ) x x x – x x x 3

JBUR-4077; No. of Pages 8

model was used to estimate amikacin’s pharmacokinetic

parameters in this population of severely burned children.

3. Results

3.1. Subjects and pharmacokinetics

Three patients were excluded from the pharmacokinetic

analysis due to missing data. From the remaining 70 patients,

there were 282 amikacin concentrations within the dataset.

Patients were dosed at 10 to 20 mg/kg/day divided 2, 3, or 4

times (actual dosages ranged from 4.9 to 22.3 mg/kg; mean

16.4 � 3.9 mg/kg). Amikacin’s mean peak concentration (Cmax)

was determined to be 33.2 � 9.4 mg/mL. The mean trough

concentration (Cmin) was 3.8 � 4.6 mg/mL.

The median age of the children included in this study was

4.5 (range: 0.6–17) years. A majority of subjects were boys (64%)

and white (53%). The median body weight of the patients was

20 (range: 8–90) kg (Table 1). Flame injuries were the most

common (67%) type of burn. A minority of children (19%)

suffered inhalation injuries. The median per cent total body

surface area burned was 43% (range: 11–98%).

3.2. Population pharmacokinetic models

Multiple structural models were explored to determine the

model that best fit the amikacin concentration data.

Please cite this article in press as: Sherwin CMT, et al. Amikacin populathttp://dx.doi.org/10.1016/j.burns.2013.06.015

One-compartment and two-compartment structural models

were assessed. A combined residual error model resulted in

the greatest improvement in the model fit.

One-compartment models with first-order elimination

were explored. However, a two-compartment combined error

model better described the disposition of amikacin in these

severely-burned children. Using a two-compartment model,

the base model estimated CL at 2.48 L/h (2.12–2.84 95% CI); the

volume of distribution in the central compartment (VC) was

2.71 L (2.05–3.37 95% CI) and the volume of distribution in the

peripheral compartment (VP) was 8.53 L (3.13–13.9 95% CI).

The inter-compartmental clearance Q was estimated as

1.13 L/h (0.79–1.47 95% CI). Estimates of the BSV in CL and

VC were 52.5% and 42.9%, respectively. The BSV in Q was fixed

at 10%. The RUV coefficient of variation was estimated at

23.9%.

3.3. Covariate models

Using univariate analyses, weight (P < 0.001), age (P < 0.05),

and concomitant vancomycin administration (P < 0.05) were

identified as having a significant influence upon amikacin

pharmacokinetics. However, in multivariate analyses ac-

counting for weight, age and vancomycin use did not

significantly influence the volume of distribution (Fig. 1).

The final covariate model was chosen as it produced the

best model fit, reduced the BSV, and decreased the RUV (Figs. 2

and 3). The parameter estimates derived from the final

covariate model are featured in Table 2.

3.4. Model evaluation

Diagnostic plots were generated for observed amikacin

concentrations versus population predicted and individual

predicted values (Figs. 2 and 3). Plots of residuals and

conditional weighted residuals versus time after dose and

population predicted amikacin concentrations were also

examined (Fig. 4).

Mean estimates from the 1000 bootstrap runs were similar

to the population estimates derived from the final covariate

model. Bootstraps were successfully generated 100% of the

time. The final covariate model generated reasonably stable

ion pharmacokinetics among paediatric burn patients. Burns (2013),

Fig. 2 – Diagnostic plots of the observed versus population predicted amikacin concentrations for the (A) base two-

compartment model and(B) final two-compartment covariate model. (Regression lines are shown as dashed lines.).

b u r n s x x x ( 2 0 1 3 ) x x x – x x x4

JBUR-4077; No. of Pages 8

and accurate estimates of the fixed and random effects.

Simulations from the observed amikacin data are presented in

Fig. 5 using a visual predictive check (VPC), with the median

simulated value compared to the 5th, 10th, 90th, and 95th

quantiles. Of 58,590 simulated observations 94.6% fell within

the 90% confidence interval, demonstrating model stability

and reasonable agreement between the observed and simu-

lated amikacin concentration data.

4. Discussion

This study examined amikacin’s disposition in paediatric burn

patients and identified patient characteristics, specifically

weight, that influence the pharmacokinetics of amikacin.

Although the pharmacokinetics of amikacin have been well

described among healthy adult volunteers [26–28], few studies

have examined amikacin’s disposition in patients with severe

burns [7,29]. Moreover, several previous studies have assumed

a one-compartment model [29,30], although this study found

that a two-compartment model was superior for patients with

burns. Peak serum concentrations were comparable to

previous reports from paediatric burn patients and other

critically-ill children (29.4 � 4.2 mg/mL reported by Zaske et al.

vs. 33.2 � 9.4 reported here) [1,31]. However, the original Zaske

study included data from 3 children and 7 adults, whereas this

study examined the pharmacokinetics of amikacin in children

Fig. 3 – Diagnostic plots of the observed versus individual pred

compartment model and (B) final two-compartment covariate m

Please cite this article in press as: Sherwin CMT, et al. Amikacin populathttp://dx.doi.org/10.1016/j.burns.2013.06.015

only. Bressolle et al. evaluated the population pharmacoki-

netics of amikacin in a population of critically-ill children

without burns injuries; however, their population model could

not be used to establish a constant CL value, as CL was strongly

influenced by demographic and pathological characteristics of

their study cohort [32]. In this study, we applied allometric

scaling and estimated CL as 5.98 L/h/70 kg, which is compara-

ble to the range of CL values reported by Bressolle et al.

Additionally, this study corroborates earlier reports by

identifying current body weight as a significant covariate that

influences amikacin’s volume of distribution [32–34].

Effective and safe aminoglycoside dosing among children

with severe burn is challenging due to their shorter half-life,

faster CL, and larger volume of distribution when compared

with healthy volunteers [35,36]. In a non-compartmental

analysis of amikacin’s pharmacokinetics among 38 paediatric

burn patients performed over 20 years ago at our institution,

Kopcha et al. found that the volume of distribution varied

widely and decreased with increasing age [7]. On the basis of

these findings, the authors concluded that doses above the

manufacturer’s recommendations are required to achieve

therapeutic concentrations in children with severe burns. The

present study applied a two-compartment model and found

that VP varied substantially, while VC was relatively stable.

Moreover, in multivariate analyses age did not significantly

influence amikacin pharmacokinetics; however, current

weight was correlated with the volume of distribution in

icted amikacin concentrations for the (A) base two-

odel. (Regression lines are shown as dashed lines.).

ion pharmacokinetics among paediatric burn patients. Burns (2013),

Table 2 – Amikacin pharmacokinetic parameter estimates and bootstrap estimates from the final two-compartmentcovariate model.

Parameters Parameterestimates

% RSEa % CVb 95% CIc Bootstrapmean (n = 1000)

95% CIc

Pharmacokinetic parameters

Clearance (CL), L/h/70 kg 5.98 8.6 – 4.97–6.99 5.57 4.0–6.18

Volume of distribution in the

central compartment (VC), L/70 kg

16.7 8.14 – 14.0–19.4 15.8 2.58–19.1

Intercompartmental clearance (Q), L/h/70 kg 3.38 14.2 – 2.44–4.32 3.96 2.95–6.56

Volume of distribution in the peripheral

compartment (VP), L/70 kg

40.1 34.3 – 15.8–80.4 57.1 8.1–101.0

Between subject variability (BSV)

BSV (v)–Clearance (CL) 0.0874 26.4 29.6 0.0421–0.133 0.087 0.003–0.12

BSV (v)–Volume of distribution in the

central compartment (VC)

0.06 9.6 24.2 �0.00442 to 0.121d 0.26 0.00002–2.2

BSV (v)–Intercompartmental clearance

(Q), Fixed

0.01 – – – 0.003 –

Residual unexplained variability (RUV)

RUV (s)–Standard deviation (mg/mL) 1.81 45.14 1.35 0.211–3.41 1.183 0.29–4.34

RUV (s)–Coefficient of variation (%) 0.0385 33.24 19.6 0.0134–0.0636 0.049 0.056–0.09

a Per cent root mean square error.b Per cent coefficient of variance.c Ninety-five per cent confidence interval.d 95% CI includes zero.

b u r n s x x x ( 2 0 1 3 ) x x x – x x x 5

JBUR-4077; No. of Pages 8

the central compartment. Previous studies in neonates have

also identified current weight as an important determinant of

amikacin volume of distribution [34].

Although increased amikacin clearance has been frequent-

ly reported among burn patients [30], the pharmacokinetic

mechanism for this is not completely understood. As

amikacin is almost exclusively eliminated via glomerular

filtration, an increase in the glomerular filtration rate (as

estimated by creatinine clearance) may contribute to height-

ened amikacin clearance [37]. Conil et al. identified a strong

correlation between amikacin elimination and creatinine

clearance among a cohort of 38 adults with severe burn [30].

However, additional studies have also suggested that tubular

secretion may play a role in the elimination of amikacin

[38,39]. In aggregate, these studies suggest that amikacin’s

heightened clearance in burn patients may reflect some

combination of both increased glomerular filtration rate and

increased tubular secretion.

Fig. 4 – Diagnostic plots of the conditional weighted residual vers

base two-compartment model and (B) final two-compartment c

lines.).

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Adult patients with severe burn have also been reported to

feature altered amikacin pharmacokinetics [30,38]. Conil et al.

found that conventional once-daily dosing did not consistent-

ly achieve peak concentration targets that have been shown to

be predictive of clinical efficacy [30]. Rong-hua et al. evaluated

amikacin pharmacokinetics in the sub-eschar fluid of patients

with early stage burn [38]. They reported half-lives of amikacin

in the sub-eschar fluid that were 25–40-fold longer than those

found in healthy volunteers. Additionally, amikacin concen-

trations remained above the minimum inhibitory concentra-

tion (MIC) of many common pathogenic bacteria at 24 h after a

single dose infusion. This suggests that amikacin can easily

diffuse into the sub-eschar and intra-eschar tissue and may

provide effective inhibitory concentrations for a sustained

period of time among severely burned patients, despite

seemingly low serum concentrations.

Elevated amikacin clearance, as seen in burn, is often

accompanied by renal failure in critically-ill patients. Akers

us population predicted amikacin concentrations for the (A)

ovariate model. (Regression lines are shown as dashed

ion pharmacokinetics among paediatric burn patients. Burns (2013),

Fig. 5 – Visual predictive check for final covariate model,

amikacin observed data compared with the 95th, 50th and

5th percentiles for 100 simulated data sets. Observed data

for 36 h. Comparison of median (dashed line) and 5th–95th

percentile interval (solid black lines). 50th quantiles ( );

10th–90th quantiles ( ); 5th–95th quantiles ( ).

b u r n s x x x ( 2 0 1 3 ) x x x – x x x6

JBUR-4077; No. of Pages 8

et al. evaluated amikacin pharmacokinetics among 60 burn

patients, 12 of whom were treated with continuous venove-

nous hemofiltration [29]. Among all patients, only 8.5%

achieved the preferred amikacin pharmacodynamic target

of a maximum concentration to MIC ratio � 10. Although

mortality and burn size were higher among patients receiving

renal replacement therapy, amikacin clearance was not

significantly affected. The authors suggest that higher

amikacin MICs and suboptimal dosing are the primary

determinants of low pharmacodynamic target attainment,

as opposed to increased CL related to renal replacement

therapy. In another pharmacokinetic study conducted among

patients receiving high-dose chemotherapy, Davis et al.

observed higher amikacin volume of distribution, CL and

elimination half-life when compared to healthy volunteers

[40].

This study is subject to several limitations. These data were

collected during routine therapeutic drug monitoring and a

limited number of observations were available for each

patient. Additionally, this study was not designed to correlate

amikacin pharmacokinetics with clinical efficacy, although

several earlier studies have suggested that high peak

concentrations and the speed with which peak concentrations

are achieved are positively correlated with improved clinical

outcomes [41–43]. More recent studies have clearly established

the influence of appropriate early antibiotic therapy on

survival [44,45]. This includes appropriate serum concentra-

tions with an antibiotic that provides targeted coverage for the

pathogenic organism.

In conclusion, children with burn feature elevated amika-

cin clearance when compared to healthy adult volunteers.

However, peak amikacin concentrations are comparable to

those attained in other critically-ill children, suggesting that

elevated amikacin clearance may not result in sub-therapeutic

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antibacterial effects. In this study, we found that amikacin

displays two-compartment pharmacokinetics, with weight

exerting a strong effect upon amikacin clearance. The extent

of burn, serum creatinine, and inflammatory biomarkers did

not significantly influence amikacin pharmacokinetics. Fur-

ther research is warranted to determine if dosage adjustments

optimize the safety and efficacy of amikacin for paediatric

burn patients.

5. Conflicts of interest

All authors have completed and submitted the ICMJE Form for

Disclosure of Potential Conflicts of Interest. Dr. Kagan serves

as a consultant for Johnson & Bell, Ltd. and Rosselot Law Firm

and has grants pending from the Shriners Hospitals for

Children. The authors declare: [DH, RK, AN, SW] had support

from [Shriners Hospitals for Children] for the submitted work;

no financial relationships with any organisations that might

have an interest in the submitted work in the previous 3 years;

no other relationships or activities that could appear to have

influenced the submitted.

Funding

Shriners Hospitals for Children (grant #70011, DPH).

Role of the sponsor

The funding sponsor had no part in the design and conduct of

the study; collection, management, analysis and interpreta-

tion of the data; and preparation, review, or approval of the

manuscript. The sponsor had no access to the data and did not

perform any of the study analyses.

Acknowledgements

We would like to acknowledge Mary Rieman, RN clinical

research coordinator and the other clinical research staff as

well as the Departments of Microbiology and Laboratory

Medicine at SHC-Cincinnati for facilitating data collection. We

would also like to thank our summer student Patrick Muvunyi

for cleaning and formatting the dataset.

Appendix

Population pharmacokinetic analysis

Amikacin’s pharmacokinetic parameters were derived using

NONMEM 7.2 (non-linear mixed effects modelling; ICON

Development Solutions, Ellicott City, MD). One- and two-

compartment structural models were fitted to the data. The

one-compartment model enabled the estimation of amikacin

clearance (CL) and the volume of distribution (Vd). The two-

compartment model was parameterized to give estimates of

amikacin CL, central compartment volume of distribution (VC),

ion pharmacokinetics among paediatric burn patients. Burns (2013),

b u r n s x x x ( 2 0 1 3 ) x x x – x x x 7

JBUR-4077; No. of Pages 8

peripheral compartment volume of distribution (VP), and

inter-compartmental clearance (Q).

Between subject variability (BSV) was assumed to be log-

normally distributed and was assessed using an exponential

equation of the form:

Pi ¼ upop � expðhrÞ; (1)

where Pi is the value of the pharmacokinetic parameters for

the ith individual, upop is the population mean for P, and h

represents the between subject random effect with a mean of

zero and a variance of v2.

During model development, residual unexplained variabil-

ity (RUV) was evaluated using additive, proportional, and

combined error models. The combined error model followed

the form of:

Yi j ¼ Ymi jð1 þ ei jÞ þ ei j; (2)

where Yij is the observed concentration for the ith individual at

time j, Ymij is the model prediction, and eij is a normally-

distributed random error with a mean of zero and a variance

of s2.

Covariate analysis

Plots were generated to perform exploratory analyses and

assess the relationships between parameter estimates and

potential covariates. Age, weight, height, C-reactive protein

(CRP), platelet count, serum creatinine, and concomitant

vancomycin administration were included in the covariate

analysis. All pharmacokinetic parameters were scaled accord-

ing to standard allometric equations (Eq. (3)) in which

parameter estimates determined for this paediatric popula-

tion were standardized to values reported for a typical, 70 kg

adult.

CLi ¼ CLpop �BW70

� �u;allo !

� expðhCLÞ; (3)

where CLi is the individual clearance in the ith individual,

CLpop is the estimate of the population clearance, hCL is the

random between subject variability, u,allo is a fixed allometric

power parameter that was assigned a value of 0.75 to describe

the systematic dependence of clearance on individual body

weight and a value of 1 for the volume of distribution, and BW

is the body weight of the ith individual.

Additionally, the type of burn (e.g., flame, scald, and

electrical burns), the per cent of total body surface area

burned, and the per cent full-thickness and partial-thickness

burns were included as potential covariates. Each covariate

was assessed separately in univariate analyses. Covariates

which were significant in univariate analyses were then

included in multivariate analyses through a backward and

forward stepwise selection process.

Models were compared by examining residual plots, the

precision of parameter estimates, measures of variability, and

the objective function value (OFV). Residual plots were used to

discriminate between different weightings and the F-test was

used to compare the weighted sum of squared residuals

(WRSS) among identically weighted one- and two-compart-

ment models. Model fit was based on minimization of the OFV.

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A reduction of more than 3.84 (-2 log likelihood difference) was

considered statistically significant with P < 0.05 and one

degree of freedom.

Model evaluation

To assess uncertainty in parameter estimates nonparametric

bootstrapping techniques were applied to the final pharma-

cokinetic models [46]. PDx-Pop was used to derive 1000

bootstrap runs by randomly sampling with replacement from

the original dataset. Standard errors were assessed for both

the estimated population parameters and random effects

error models. Bootstrap techniques, goodness-of-fit plots, and

visual predictive checks were used to evaluate model fit.

r e f e r e n c e s

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