• aminoglycosides;
  • population pharmacokinetics;
  • target concentration intervention


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References

Aims  [1] To quantify the random and predictable components of variability for aminoglycoside clearance and volume of distribution [2] To investigate models for predicting aminoglycoside clearance in patients with low serum creatinine concentrations [3] To evaluate the predictive performance of initial dosing strategies for achieving an aminoglycoside target concentration.

Methods  Aminoglycoside demographic, dosing and concentration data were collected from 697 adult patients (>=20 years old) as part of standard clinical care using a target concentration intervention approach for dose individualization. It was assumed that aminoglycoside clearance had a renal and a nonrenal component, with the renal component being linearly related to predicted creatinine clearance.

Results  A two compartment pharmacokinetic model best described the aminoglycoside data. The addition of weight, age, sex and serum creatinine as covariates reduced the random component of between subject variability (BSVR) in clearance (CL) from 94% to 36% of population parameter variability (PPV). The final pharmacokinetic parameter estimates for the model with the best predictive performance were: CL, 4.7 l h–1 70 kg–1; intercompartmental clearance (CLic), 1 l h–1 70 kg–1; volume of central compartment (V1), 19.5 l 70 kg–1; volume of peripheral compartment (V2) 11.2 l 70 kg–1.

Conclusions  Using a fixed dose of aminoglycoside will achieve 35% of typical patients within 80–125% of a required dose. Covariate guided predictions increase this up to 61%. However, because we have shown that random within subject variability (WSVR) in clearance is less than safe and effective variability (SEV), target concentration intervention can potentially achieve safe and effective doses in 90% of patients.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References

The aminoglycosides have been in use for around 50 years and are still widely used in the hospital setting for serious systemic gram-negative bacterial infections [1, 2]. The Target Concentration Intervention (TCI) strategy [3] is commonly employed with the aminoglycosides. The TCI strategy involves firstly selecting the desired target concentration and secondly predicting volume (V) and clearance (CL) for the patient, which can then be used to predict initial doses, required to achieve and maintain the target [4]. TCI then uses information obtained during treatment about doses, concentrations, and clinical effect in an individual and integrates them to estimate pharmacokinetic and pharmacodynamic parameters in that individual [4]. These individually estimated parameters are then used to predict subsequent doses required to achieve the target.

Aminoglycosides are unusual in having at least two target concentrations. For example, using once daily dosing the initial concentration is recommended to be at least 10 mg l–1 to achieve infection cure [1, 5, 6] and subsequent concentrations are targeted to achieve an average steady state concentration of 3 mg l–1 (equivalent to an area under the concentration time curve (AUC) of 72 mg l–1·h over a 24 h dosing interval) to reduce the risk of toxicity [2]. Trough concentrations greater than 0.5 mg l–1 are associated with an increased incidence of nephrotoxicity [7, 8]. The initial concentration is primarily determined by volume of distribution which must rely on patient covariates (typically weight). Subsequent concentration measurements are of no assistance in predicting the dose needed to achieve the initial target concentration but are critical for effective TCI and subsequent dose adjustment. Targets such as average steady state concentration or AUC over a dosing interval depend mainly on clearance, which can be estimated by measuring aminoglycoside concentrations. We examine the quantitative implications of using aminoglycoside pharmacokinetics for initial dose predictions and subsequent dose adjustment aiming for an average steady concentration as an example of a target for TCI.

It is expected that pharmacokinetic parameters can vary widely between individuals, however, they may even differ within an individual during treatment or progression of a disease state. We call the overall parameter variability across all individuals in a defined population the population parameter variability (PPV), which is comprised of between subject variability (BSV) and within subject variability (WSV) [4]. BSV and WSV can be further divided into predictable (BSVP and WSVP) and random (BSVR and WSVR) components. BSVP and WSVP are the variability that can be explained through the use of covariates (e.g. weight, CLCr), while BSVR and WSVR are unpredictable, given the current state of knowledge, and are modelled as if they arise from a random process. WSVR can be approximated by between occasion variability (BOV) [4]. WSVR includes both BOV and stochastic parameter variation within an occasion. For all practical purposes WSVR and BOV can be considered equivalent. We define all variability values (PPV, BSV, WSV, BSVR, WSVR, SEV) as the standard deviation of a log normally distributed random variable with mean zero (e.g. see Temp. Equation 14). They can be considered approximate coefficients of variation.

Importantly, WSVR must be relatively small in order for the TCI strategy to be of practical relevance [9]. TCI becomes a practical method of forecasting individual doses when WSVR is smaller than Safe and Effective Variability (SEV). SEV reflects a judgement about the acceptable degree of variability of concentration in the target population, e.g. 90% of concentrations should be within an acceptable percentage of the target concentration [4].

The pharmacokinetics of aminoglycoside antibiotics are well known and they are predominantly excreted unchanged via the renal route [10, 11]. Because of the proposed relationship between renal function and aminoglycoside clearance, many methods have been proposed for predicting aminoglycoside clearance using serum creatinine concentration (SCr) or creatinine clearance (CLCr) [11–13]. These methods rely on empirical models for creatinine production, which are used to predict CLCr and renal function (RF).

Renal function (RF) is a measure of the ability of the kidneys to eliminate a drug or metabolite. It involves several processes including glomerular filtration, tubular secretion, and active and passive reabsorption. An accurate assessment of RF is important in the dose-individualization of drugs with extensive renal elimination. RF is typically predicted from measures of glomerular filtration, for example using creatinine clearance (CLCr). CLCr can be easily predicted from a serum creatinine concentration (SCr) using formulae or nomograms [14]. Measuring CLCr with urine and plasma samples has logistical and patient compliance factors, which can make accurate assessment problematic [15].

Cockcroft and Gault (C & G) developed a formula to predict CLCr from SCr using age, weight and sex. They reviewed the records of 534 patients who had CLCr estimated from two or more 24 h collections of urinary creatinine [14]. Using three previously published formulas [16–18] and a new model for CLCr (Temp. Equation 1 and Equation 2), they predicted the CLCr in ml min–1 for each patient from their SCr. A 15% reduction in Creatinine Production Rate (CPR) for females was based on previous work from other authors [14].

  • image(1)

CPR is predicted by Temp. Equation 2, SCr is the measured serum creatinine concentration in mg/dL, WT is the weight in kg of the patient and age is the age in years.

  • image(2)

Despite being widely studied, there is still no clear consensus as to the best model to predict RF [19, 20]. Most authors use SCr in association with some form of the Cockcroft and Gault (C & G) equation to predict renal clearance [2, 11, 12]. It has been suggested that patients with low SCr concentrations should be dealt with in a different manner. Duffull and colleagues noted that when SCr was low, aminoglycoside clearance was not linearly related to C & G predicted CLCr[12]. It was suggested that low SCr concentrations are due to a low creatinine production rate (CPR) rather than high renal function [12]. An empirical ‘round up’ method was proposed which rounded up SCr concentrations less than 0.06 mmol l–1 to 0.06 mmol l–1. Rosario et al. (1998) [11] and Kirkpatrick et al. (1999) [2] subsequently used this method. Kirkpatrick et al. confirmed that a round up value of 0.06 mmol l–1 provided the best correlation using a linear relationship between SCr and predicted aminoglycoside clearance. Both papers confirmed the lack of linearity with CLCr but did not test the predictive performance, i.e. how well did these models predict individual aminoglycoside clearance based on covariate information alone.

We aim to [1] Quantify the predictable and random components of variability for clearance and volume for the aminoglycosides gentamicin and tobramycin in order to establish quantitative criteria for using TCI with aminoglycosides [2], Examine various methods for dealing with low concentrations because standard approaches appear to overestimate renal function and would be expected to be associated with over-dosing, and [3] Test the performance of models using covariate information alone to predict clearance.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References


Aminoglycoside concentration and dosing data collected between April 1999 and October 2001 was obtained from patient records at Christchurch hospital, Christchurch, New Zealand. Ethical approval was given for the use of de-identified data from the Canterbury Ethics committee. The patient group comprised 697 patients aged 20 years or older, there were 387 males and 272 females with the remainder having sex unrecorded.

The goals of TCI were to achieve initial serum aminoglycoside concentrations >10 mg l–1 while attaining a value of area under the concentration-time curve over a 24 h dosing interval between 70 and 100 mg l h–1. TCI was undertaken using the AUC method proposed by Begg et al.[4]. The first sample was taken approximately 0.5 h after the end of the infusion and the second between 6 and 22 h depending upon renal function. Blood sample monitoring was repeated every 2–3 days or more frequently depending on the clinical condition of the patient. The data yielded 2567 serum aminoglycoside concentrations including 46 recorded as below the nominal quantification limit (0.3 mg l–1). A further 17 were less than 0.3 mg l–1 but the measured value was recorded. These values were treated the same way as other concentration measurements. Ninety-seven percent of patients received gentamicin while the remainder received tobramycin. 107 patients [15%] had a SCr on their first occasion of less than 0.06 mmol l–1 while 243 people [35%] had a SCr of less than 0.06 mmol l–1 on some occasion. Table 1 shows a summary of the data obtained. For the purposes of estimating WSVR (BOV) an occasion was defined as each time there was a dose with at least one subsequent aminoglycoside serum concentration measurement before the next dose.

Table 1.  Data Summary
 Median/PatientMean ± SDMinMaxMissing
Number AG Concs3 1 20
Number of Occasions2 1 12
Doses (mg) 385 ± 12280880
Serum Creatinine (mmol l−1)0.07 ± 0.03 0.02  0.9 0.3%
Age (y)  57 ± 1720 94 2%
Weight (kg)  73 ± 173616017%
Sex56% male 5%

Drug assay

Aminoglycoside serum concentrations were analysed at Canterbury Health Laboratories, Christchurch, New Zealand. The Abbott FPIA method (Abbott Laboratories Diagnostics division, Auckland) was used for tobramycin concentrations and the Dade Behring EMIT method (Dade Behring Diagnostics, Auckland) for gentamicin concentrations. The aminoglycoside assay coefficient of variation was 13% at 1.07 mg l–1, 4.2% at 3.13 mg l–1 and 2.5% at 6.32 mg l–1. The lower limit of quantification was defined by the test kit manufacturer for both methodologies as 0.3 mg l–1. Serum creatinine concentration was measured using a Jaffe method creatinine assay with a coefficient of variation of 8% (Abbott Aeroset System; Abbott Laboratories Diagnostics division, Auckland). The lower limit of quantification for creatinine using this assay is 0.0089 mmol l–1.


Population model

 One and two compartment pharmacokinetic models were fitted to the data using subroutines from the NONMEM library (ADVAN1 TRANS2 and ADVAN3 TRANS4, respectively) [21]. The parameters of central (V1) and peripheral (V2) compartment volumes, total body clearance (CL), and intercompartmental clearance (CLic) were estimated for the two compartment pharmacokinetic model.

Group model

 Predictable between subject differences in clearance and volume of distribution were described using covariates to identify a model for patients with a common group of covariates.


An allometric weight model was applied to standardize the pharmacokinetic parameters using a standard weight of 70 kg [22–24]. FWTV and FWTCL are the fractional changes in volume and clearance in a patient with weight WT compared with a standard weight WTSTD.

  • image(3)
  • image(4)


An empirical model was used to describe changes with age. The model was centred on a standard age of 40 years.

  • image(5)

Sex An empirical fractional model was used to describe between subject differences due to sex. The standard parameter value was assumed for males.

If (SEX = Male) then        FSEX = 1 (6)


 FSEX = FFemale


Renal Function  Renal function was defined as the ratio of the predicted creatinine clearance to a standard creatinine clearance of 6 l h–1 70 kg–1. Creatinine clearance was predicted from creatinine production rate (CPR) and serum creatinine (SCr). The creatinine production rate (CPR) model can be expressed as a standard CPR (CPRSTD) with a fractional effect of age (FAGE), weight (FWT) and sex (FSEX). The CPRSTD (0.516 mmol h–1 70 kg–1) was calculated using the CPR formula reported by Cockcroft and Gault for males with an average weight of 72 kg and scaled to 70 kg [14]. Different combinations of these fractional covariate effect factors were applied to the CPR model (Temp. Equation 7) as well as the standard Cockcroft and Gault CPR model in order to determine the contribution of each covariate to the predictable component of between subject variability in clearance (BSVP).

  • image(7)

RF can then be predicted from the CPR model by dividing by SCr and the standard value for CLCr (Temp. Equation 8).

  • image(8)

Low serum creatinine

The low SCr models assume that when SCr is low renal function cannot be predicted accurately using the measured SCr concentrations. We examined 2 methods which used an imputed SCr (SCrIMP) instead of the measured SCr concentration. The round up serum creatinine (RUCR) method [12] assumes a SCrIMP of 0.06 mmol l–1 for all SCr concentrations below 0.06 mmol l–1 (Temp. Equation 9).

  • image(9)

The CrOPT method estimates SCrIMP and also estimates the SCr concentration (SCrOPT) below which measured SCr should be replaced with SCrIMP (Temp. Equation 10).

  • image(10)

An additional method was investigated which does not impute SCr but uses the measured value to estimate creatinine clearance. The FCPR method assumes that patients with low SCr (<0.06 mmol l–1) have lower than predicted CPR, and therefore estimates the fraction of predicted CPR (FCPR) that explains the apparent renal function seen in low SCr patients (Temp. Equation 11).

  • image(11)


It was assumed that clearance had a nonrenal (CLNR) and a renal component (CLR) and that renal clearance was linearly related to RF (Temp. Equation 12).

  • image(12)

Aminoglycoside individual pharmacokinetic model

The individual components of population parameter variability (PPV) can be separated into between subject variability (BSV) and within subject variability (WSV). ηBSV and ηWSV are assumed to be normally distributed random variables with mean 0 and standard deviation BSV and WSV, respectively.

  • image(13)
  • image(14)

ηBSVCLi and ηWSVCLij are ηBSV and ηWSV of CL for the ith patient at the jth occasion, respectively. CLGRP is the covariate predicted group value for CL and CLij is the individual CL for the ith patient at the jth occasion.

The predictable component of BSV (BSVP) was estimated from the difference in BSV with and without covariate predicted group values explaining parameter variability.

Observation model

Residual unidentified variability was described using a combined additive and proportional error model. Where AG is the predicted concentration (without residual error) and Y is the individual prediction including a proportional (CVAG) and additive (SDAG) residual error component. ɛCVAG and ɛSDAG are normally distributed random variables with mean 0 and standard deviations CVAG and SDAG.

  • image(15)

Estimation error

In most cases NONMEM was unable to estimate the asymptotic standard error of the estimates. We used a nonparametric bootstrap [25] method to describe the posterior distribution of the FCPR model parameter estimates. Eight percent of these bootstrap runs were successful at obtaining asymptotic standard errors. The 95% confidence interval for the parameters was obtained from the bootstrap empirical posterior distribution.

Predictive performance

We assessed the predictive performance of using covariates alone to predict the dose rate that would maintain a target average steady state concentration based on information at the first dosing occasion. It was assumed that the best individual estimate of clearance (CLbest) was the maximum a posteriori Bayesian, occasion specific estimate from the population pharmacokinetic model with the final model (Model 5, Table 2). For each model [1–14] occasion specific covariates were used to make a group prediction for CL, which was then compared with CLbest. The bias and imprecision (root mean square error) [26] of predicting CLbest from covariates were expressed as a percentage of the average CLbest.

Table 2.  Model building – model description and objective function value
Model numberSize ModelCPR ModelModel componentsObjΔObjΔNpar
RF ModelLow SCr Model
  1. Δ Obj is the difference in objective function compared to Model 14. ΔNpar is the difference in the number of parameters compared to Model 14. Numbers in parentheses indicate fixed parameters based on literature estimates. CPR Model Std means only SCr was used with CPRSTD to predict CLCr.

 1WeightAge, SexAge, SexCrOPT5288.2–569.16
 2WeightAge, SexAgeCrOPT5288.4–568.95
 3WeightAge, SexAgeRUCr5296.7–560.63 (1)
 4WeightC&GC&GRUCr + RFV5304.2–553.11 (5)
 5WeightAge, SexAgeFCPR5306.6–550.74
 8WeightAge, Sex5342.6–514.72
12Std5759.2 –98.10
13Weight5803.2 –54.10
145857.3   00

In order to assess the model performance for dose individualization we used the covariate-based predictions of clearance to predict the initial dose rate required to maintain a target concentration. We then used CLbest to predict the required dose rate for each patient and model and calculated the percentage of patients whose covariate predicted dose was within 80–125% of the required dose.


Model building was performed using NONMEM version V release 1.1 (NONMEM Project Group, University of California, San Francisco, CA, USA) under MS-DOS on a Pentium III 1GHz using Microsoft windows XP and Compaq Visual Fortran version 6.6 A. All model building was performed using the first order conditional estimation (FOCE) method with the interaction estimation option.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References

Model Building

The two compartment pharmacokinetic model described the data better than the one compartment model based on objective function value (Obj) (5857.3 vs. 6123.7). This is a drop of 266.4 units with the addition of 4 parameters, 2 structural and 2 related to parameter variability. The base two-compartment model had a mixed additive and proportional error model and estimated WSVR for CL and V2. Attempts to estimate WSVR for V1 and CLic were unsuccessful.

Table 2 shows by model number a description of the different covariates applied to each of the two compartment pharmacokinetic models and shows a summary of the model building process with respect to the Obj. Model 1 has the lowest Obj while model 14 has the highest. Model 14 represents the base model and uses no covariates. The final model (model 5) was a two compartment PK model with all PK parameters scaled allometrically by weight, it used a mixed additive and proportional error model and estimated BSVP, BSVR for CL, V1, CLic and V2 and WSVR for CL and V2. It included the effects of age, sex and SCr on CPR and age on RF. Low SCr was modelled with FCPR. Attempts to model WSVR for V1 and CLic were unsuccessful. The change in Obj is compared to the widely used model 7 [2, 11, 12], which uses C & G to predict RF and RUCR for low SCr. The model 2 (CrOPT) estimate of SCrOPT was 0.064 mmol l–1 and SCrIMP was 0.069 mmol l–1.

Table 3 shows the predictable and random components of the BSV and WSV as a percentage of PPV. The addition of weight alone (model 13) reduces BSVR of CL from 95% of PPV to 87%, SCr alone (model 12) reduces it to 67% and age alone (model 11) to 64%. The final model (model 5) reduces BSVR to 36% and explains 56% of total CL variability. Figures 1 and 2 show the observed aminoglycoside concentrations plotted against the individual and population predicted concentrations (Model 5).

Table 3.  Predictable and random components of between and within subject variability as a percentage of population parameter variability (PPV from base model 14)
122067147820 3
13 7875 67816
14 0955 08416

Figure 1. Individual predicted concentrations vs. observed concentrations. Dashed line is the line of identity

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Figure 2. Population predicted concentrations vs. observed concentrations. Dashed line is the line of identity

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Bootstrap estimates using Model 5 (FCPR) are shown in Table 5. Twenty-eight percent [28%] of bootstrap runs minimized successfully (converged). There was less than 2% difference in the mean parameter estimates obtained from successful and nonsuccessful runs. Confidence intervals were computed from all bootstrap runs regardless of convergence.

Table 5.  Bootstrap Parameter Estimates for Model 5 (1033 bootstrap runs)
ParameterUnitsAverage95% ConfidenceIntervalAsymptotic prediction error
  1. Asymptotic prediction error = (asymptotic SE/bootstrap SE – 1) * 100; PPVR = sqrt(BSVR2 + WSVR2); BSVP = sqrt(PPV2-PPVR2) where PPV is PPVR for model 14 (no predictable component).

CLl h−1 70 kg−1  4.70  4.54  4.90 
VssL/70 kg−1 30.8 28.2 33.5 
CLNRl h−1 70 kg−1  1.12  0.74  1.55 10%
CLRl h−1 70 kg−1  3.56  3.16  3.94 –2%
V1L/70 kg−1 19.5 19.10 19.9–10%
CLicl h−1 70 kg−1  1.020.85  1.20 –8%
V2L/70 kg−1 11.39.02  14.1 –8%
PPVRCL 0.320.300.35 
BSVPCL 0.360.340.38 
BSVRCL 0.300.270.33 83%
BSVRV1 64%
PPVRCLic 0.820.680.94 
BSVPCLic 2.672.642.70 
BSVRCLic 0.820.680.94 79%
PPVRV2 0.790.590.96 
BSVPV2 1.601.511.69 
BSVRV2 1.170.801.54 17%
WSVRV2 0.750.540.92 43%
CVAG –3%
SDAGmg/L0.140.100.19  3%
RCL,V1 0.550.460.65 
RCLic,V2 0.900.751.00 
KAGECR 112102122 
FSEXCR   0.82  0.77  0.88 
KAGERF 119107133 
FCPR   0.70  0.66  0.76 

Equations for prediction of aminoglycoside clearance are shown in Figure 3 (Model 3, RUCR) and Figure 4 (Model 5, FCPR). Model 3 (RUCR) is shown because this is directly comparable to the model proposed by Duffull et al.[12] and Model 5 (FCPR) is shown because it is our preferred final model.


Figure 3. RUCR Prediction of Clearance. Age in years, SCr in mmol l−1 and WT in kg. (Model 3) Fsex = 0.85 for females

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Figure 4. FCPR Prediction of Clearance. Age in years, SCr in mmol l−1 and WT in kg. (Model 5) Fsex = 0.82 for females

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Predictive performance

The models without bias significantly different from zero were models 5, 8 and 9. An acceptable dose range was chosen as the criterion for successful dosing. If the predicted dose rate was within 80–125% of the optimal dose rate then the prediction was considered successful. Models 1–11 had greater than 50% of patients within the 80–125% acceptable dose range [Table 4].

Table 4.  Bias and imprecision of group model prediction of clearance (occasion 1) and success rate for achieving safe and effective concentrations within 80–125% of the dose predicted from CLbest (based on Model 5) to reach a target average steady state concentration
ModelBias%SigRMSE%Dose <80%Dose >125%In Range%
  1. Sig = Bias significantly different from zero. *  = P < 0.05, **  = P < 0.01, ***  = P < 0.001, NS = P > 0.05.



  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References

Several studies on the population pharmacokinetics of aminoglycosides have been undertaken over the last 30 years, however, there is still no consensus as to the best pharmacokinetic model, with many authors using one compartment models [2, 12] while others use two [11, 27]. The use of a two compartment pharmacokinetic model seems reasonable as it provided a better fit to our concentration data as determined by improvement in the Obj. However, sampling was sparse and it is difficult to conclude that a two-compartment model is a better description on the basis of individual profiles.

Rosario et al.[11] collected data from patients with cancer who were given gentamicin and also found a two compartment pharmacokinetic model significantly improved the objective function value. Table 6 summarizes the results of the base model without covariates applied to the Christchurch data and the base model applied to the Glasgow data. These data show that the Christchurch data is more variable than that from Glasgow, with the PPV being considerable larger especially for V2. The reason for the greater variability could be due to the wider range of conditions for which patients included in the current analysis were being treated. However, the base model CL and VSS estimates do compare reasonably well.

Table 6.  Comparison of population pharmacokinetic models without use of covariates to explain PPV
 ChristchurchGlasgow (11)
CL l h−1 70 kg−14.04.4
PPV CL %4934
VSS L/70 kg−130.627.3
PPV V %V1 = 26 V2 = 170V1 = 16 V2 = ‘low’

Aminoglycosides have a molecular weight of 477.6, are highly polar molecules with negligible plasma protein binding and are expected to cross cell membranes slowly. Renal clearance is therefore expected to be similar to the glomerular filtration rate. Our estimate of renal clearance (CLR, Table 5) is 40% lower than the predicted CLCr which implies either that aminoglycosides are re-absorbed after filtration or that CLCr is an over-prediction of glomerular filtration. Wright et al.[28] have estimated that the C & G method underestimates filtration estimated by 31Cr-EDTA by 12%, which would make the latter explanation unlikely. Even if the estimate of nonrenal clearance was assumed to be zero the clearance of aminoglycosides is still 22% lower than CLCr. This provides indirect evidence for renal re-absorption of aminoglycosides and confirms directly measured values. Contrepois et al.[29] observed a mean aminoglycoside renal clearance of 5.25 l h–1 70 kg–1 in 12 males aged 21–28 y. The CLR was 82% of simultaneous inulin clearance measurement. Regamey et al.[30] measured CLR of gentamicin and tobramycin of 6.7 l h–1 per 1.73 m2 which was 94% of the estimated total clearance (2 healthy subjects). Measured CLCr and gentamicin CLR in critically ill patients are poorly correlated with CLNR estimates of 1.8 l h–1[13].

Based on the expected poor ability to cross cell membranes the apparent volume of distribution of aminoglycosides is expected to be close to extracellular fluid volume. The estimate of V1 of 19.5 l/70 kg–1 is compatible with this assumption. However Vss of 30.8 l/70 kg–1 implies tissue uptake or binding. Aminoglycosides are known to be taken-up into certain tissues by active transport mechanisms [31–34], which may account for some of the additional apparent volume beyond extracellular fluid. However, it would seem unlikely that accumulation of aminoglycosides in the ear and kidneys would account totally for this observed difference. This might indicate the uptake into other tissue sites.

Quantification of pharmacokinetic variability

To the best of our knowledge this is the first study that has tried to quantify the WSVR in aminoglycosides. Table 3 shows that the WSVR is relatively small for CL, approximately 8% of PPV, and around 19% of PPV for V2. Attempts to quantify the size of the WSVR for CLic and V1 were unsuccessful for numerical reasons and probably reflect the sparse sampling design and limitations of the software.

Prediction of renal function with low serum creatinine

Our results confirm [2, 11, 12] that having a cut-off value below which all concentrations should be replaced with some other higher value improves the overall fit. None of the low serum creatinine models markedly changed the predictable component of between subject variability for either CL or V. The FCPR method incorporates the speculation [12] that the reason for over prediction of CLCr was due to low CPR rather than high renal function. In addition, unlike the simple round up method [12], it does not discard information about renal function that might be reflected by changes in SCr less than 0.06 mmol l–1. Despite these potential advantages it does not seem to offer any additional benefit to the predictive performance of the model. Nevertheless, we suggest the FCPR method [Figure 4] be considered as an alternative to the method [Figure 3] proposed by Duffull et al.[12]. We found no evidence that sex is an independent predictor of renal function (Model 1). This observation is quite different from the well-understood association of a lower CPR in females presumably reflecting different body composition compared to males.

The importance of within subject variability

The target concentration strategy used by Christchurch hospital [5], assumes that the information in measured concentrations can be used to predict future doses to achieve a target concentration. Implicit in this assumption is that pharmacokinetic parameters estimated from measured concentrations will not vary importantly when the subsequent predicted dose is given. A quantitative description of the extent of this variability is provided by WSVR. We have been able to estimate the WSVR in CL and V2. The WSVR in CL is more important because it will determine the dose-to-dose variability in AUC especially with once a day dosing when the half-life is short relative to the dosing interval.

WSVR alone is not sufficient to decide if TCI is necessary or will succeed. The extent of variability that is safe and effective (Safe and Effective Variability; SEV [4]) around the target concentration defines the need and potential for success. If SEV is large then there is a wide margin for acceptable dosing but if it is small then dose adjustments based only on covariate model predictions (fixed effects) may be inadequate to individualize dose because covariates can only reduce the predictable component of BSV. The random component of BSV can be decreased using TCI to estimate the average individual pharmacokinetic parameter of interest, e.g. clearance. The limiting imprecision of dosing is then determined by random WSV. If we propose that variation of 80–125% around the target concentration, e.g. average steady state concentration, is likely to produce safe and effective aminoglycoside therapy if achieved in 90% of patients then, assuming a lognormal distribution, 90% of concentrations will be > = 80 and < = 125% of the target with SEV = 0.135. This can be compared to the slightly lower bootstrap estimate of WSVR for clearance of 0.13. Clearance is the key parameter determining average steady state concentration. Using covariate based predictions we estimated that 65% of BSV in clearance is predictable. However, because BSVR of 0.29 is substantially more than the proposed SEV of 0.135 we can predict that covariate guided predictions based on weight and renal function will be inadequate for safe and effective aminoglycoside therapy. Because WSVR is smaller than SEV this means that target concentration intervention should be capable of helping to achieve safe and effective therapy by reducing uncertainty in individual CL to a limiting value approaching WSVR. It should be noted that the efficiency of using measured concentrations to reduce BSV will depend on the residual error in the measurement but given enough measurements this source of random noise will average out to zero. Methods that use weight, SCr, and age for initial dosing and nomograms for TCI, e.g [35], have been shown to be better than nothing [36] but are still unable to reliably achieve target concentrations in clinical use [37]. Bayesian TCI approaches are more effective for TCI [12].

Predictive performance of covariate models

An improved correlation of predicted CLCr (using C & G) with a Bayesian estimate of gentamicin clearance along with a closer fit to a linear relationship between these variables [2, 11, 12], a lower bias in the predicted mid-dose concentration [12] and a lower objective function [11] were the basis for the use of the round up method advocated by others. However, none of these studies evaluated how well the round up method helped to predict the dose needed to reach the target concentration.

The performance of group models for predicting clearance from covariates is shown in Table 4. We have evaluated performance in terms of the ability to achieve initially predicted doses within 80%–125% of target. If everyone got the same dose we would expect 35% of patients to receive safe and effective therapy (Table 4; Model 14). Covariate guided dose predictions at best can increase this to only 61% of patients. Weight, SCr and age individually contribute less than half of the benefit (Models 11–13; Table 3). However, with weight, SCr and age in combination, at least half of a population similar to the one we studied would get adequate treatment. There are relatively minor differences between the models, which use weight, age, sex and serum creatinine to predict clearance.

Safe and effective variability and rational dose individualization

We are unable to provide anything other than a plausible suggestion for SEV based on a goal of achieving 90% of concentrations within 80–125% of the target. Aminoglycoside target concentrations are only murkily defined and it is even harder to know what degree of imprecision (SEV) in hitting these targets is clinically acceptable. One approach we have tried is to ask experienced clinicians what range of concentrations they think are safe and effective. We have illustrated how SEV might be derived from such a concentration range by assuming the range is a 90% prediction interval and the variability in average steady state concentration is log normally distributed.

Our results support a paradigm for rational choices for dose selection [4]. If SEV is larger than overall variability (PPV) then a standard dose based on an average patient will be adequate. If SEV is less than random BSV, but larger than WSVR, then covariate-guided dose prediction can achieve adequate therapy. Finally, if SEV is less than random BSV but larger than WSVR, then target-concentration intervention may be able to help ensure safe and effective treatment.

Based on these criteria we conclude that covariates alone cannot be used to guide aminoglycoside dosing because, at best, only 61% of patients will get initial doses within 80–125% of the required dose. We predict that individual concentration feedback using TCI can achieve upto 90% of concentrations within 80%–125% of an average steady state target concentration. Our analysis gives quantitative support to using TCI in order to achieve the target concentrations required to maximize the clinical benefit of aminoglycosides.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
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