Population pharmacokinetics of netilmicin in short-term prophylactic treatment

Abstract

Aims

To characterize the population pharmacokinetics of netilmicin, an aminoglycoside antibiotic, in adult urology patients and to develop a covariate model for improved dose titration.

Methods

Data from 62 adult patients (55 male, seven female), undergoing urological surgery and treated with netilmicin for short-term prophylaxis, were evaluated retrospectively. The group had (median, range) ages 68, 31–92 years, weights 72, 43–106 kg and heights 167, 148–182 cm. No patient showed renal impairment before netilmicin treatment (serum creatinine ≤1.9 mg dl⁻¹). Netilmicin (100 mg) was administered as a maximum of four successive intravenous infusions of 30 min, at 8-h intervals. A total of five blood samples were collected from each patient. Prior to analysis, the dataset was divided into ‘index’ (n = 44) and ‘validation’ (n = 18) groups at random. The time courses of netilmicin concentrations from all subjects were analysed using a mixed effects, population, nonlinear modelling package (WinNonMix). For covariate model development, a stepwise procedure was used with backward elimination followed by forward inclusion based on age, sex, weight, height, creatinine clearance and type of surgery. The final covariate model parameters from the index group were used to simulate concentrations in the validation group and the bias and precision were compared with the observations.

Results

A bi-compartmental open model with a proportional residual error best described the data. The population parameters for central and peripheral volumes of distribution were (typical population value [interindividual CV%]) V_c = 14.5 l [56%] and V_p = 10.2 l [not estimated], and the systemic and intercompartmental clearances were CL = 3.9 l h⁻¹[42%] and CL_Q = 10.1 l h⁻¹[not estimated], respectively. The final population covariate relationships were based on sex (SEX) and creatinine clearance (CrCL): (V_c, l) = 18.9 − 5.9 × SEX [29%] and (CL, l h⁻¹) = 0.06 × CrCL [33%]. Compared with the observations in the validation group, this model showed a bias (95% confidence interval) of −0.028 (−0.28, 0.25) and precision of 1.22 (0.78, 1.34).

Conclusion

Bi-compartmental pharmacokinetic parameters of netilmicin have been estimated from clinical data in urological surgery patients using a population approach. A given single dose results in large variability in plasma concentrations and thus the population covariate final model can be used for direct estimation of initial dosing in patients.

Introduction

Netilmicin (Schering-Plough, Madrid, Spain) is a semisynthetic aminoglycoside active against a wide range of Gram-negative and some Gram-positive bacteria, including many gentamycin-resistant strains [1, 2]. Aminoglycosides continue to play an important role in the treatment of diverse kinds of infections and are among the most widely used antimicrobial agents for hospitalized patients. Their use can be limited due to potential ototoxicity (mainly irreversible) and nephrotoxicity (reversible), resulting in a narrow therapeutic margin [3, 4]. Furthermore, large inter- and intra-individual variability is observed in the pharmacokinetics (PK) of aminoglycosides [5–8]. Based on these considerations and the knowledge that both therapeutic and toxic responses to netilmicin are closely related to serum concentrations [9, 10], individualized monitoring-based dose titration seems appropriate for optimal therapy. Although once-daily regimens requiring no plasma concentration assessment appeared to reduce toxicity, current experience shows that some monitoring is required [11].

In the past, various dosing aids such as nomograms and basic predictive algorithms based on creatinine clearance, were widely used. However, these methods do not contain measures of variability in clinical response and thus occasionally fail to predict the appropriate therapeutic regimen. Other more accurate approaches based on monitoring plasma concentrations and the implementation of PK models have also been employed [12, 13]. More recently the use of Bayesian methodologies have proven helpful in reducing drug toxicity. Concentration data from limited sampling of individuals, combined with distribution data from a similar patient population, allow individualized predictions, leading to improved dosage adjustment [14, 15].

In the last two decades improved mixed effects modelling, using ‘population’ methods, has become applicable to small patient populations of between 10 and 100 individuals. Population analysis packages like NONMEM (nonlinear mixed effect modelling; NONMEM Project Group, University of California at San Francisco, CA, USA [16]) and NPEM (nonparametric expectation maximization, Laboratory of Applied Pharmacokinetics, University of Southern California, Los Angeles, CA, USA [17]), give estimates of structural model parameter distributions, that is the typical population values (a measure of central tendency) and a standard deviation as a measure of interindividual parameter dispersion. Population methods have been successfully applied to aminoglycosides [10, 18, 19] using the above software. Now a particularly user-friendly population analysis package, WinNonMix (Windows nonlinear mixed effects; Pharsight, Cary, NC, USA) has been introduced.

In common with other aminoglycoside antibiotics, the pharmacokinetics of netilmicin are complex [1, 20] and multicompartmental. However, using clinical datasets, the classical PK approaches permit only mono-compartmental models to be used [18, 21], leading to biased estimates of the central volume of distribution [22]. With the population PK approach, parsimony is achieved at a higher level of complexity in the combined PK and statistical models. Thus, more information is extracted from the subject group than with a classical two-stage method. Population PK methods also simultaneously separate the inter- from the intra-individual variabilities. The former arises from subject-specific physiology/pathology-related factors, and the latter from the assay noise and model misspecification error. Population methods can be used to establish individual-specific covariate relationships with the PK parameters, and thus optimal customization can be reached for a priori dosage design. These methods, if used as Bayesian priors, allow improved adjustment in the course of therapy. Although there are several studies of netilmicin population PK in neonates and infants [23–26], there are very few studies in adults [21].

In short-term treatment with netilmicin (e.g. prophylactic utilization before surgery), a standard dose is administered without individualization or plasma concentration monitoring, because it is assumed that the probability of reaching toxic concentrations by accumulation is low [27, 28]. However, in a study of a group of patients undergoing urological surgery and being given a fixed dose of netilmicin, plasma concentrations showed high variability. Analysis of the data using conventional PK methodologies failed to find the sources of this variability [29]. In the present work this dataset is re-examined from a population perspective using WinNonMix. We included explanatory covariates to individualize the parameter estimates. Finally, we evaluated the predictive performance of the developed model using an index/validation dataset procedure.

Methods

Patient data

The study population consisted of a total of 62 patients (55 males and 7 females) suffering from urological disorders and randomly selected among candidates for the following surgical procedures: vesical n = 15; prostatic transurethral resection (TUR) n = 34; nephrectomy n = 6; adenoctomy n = 4; others n = 3 at Galdakao Hospital (Galdakao, Vizcaya, Spain). Ages were between 31 and 92 years (median 68 years). Body weight varied between 43 and 103 kg (72 kg), and the height between 153 and 182 cm (167 cm).

All patients gave informed consent and the project was approved by the hospital ethics committee. Selected subjects (i) were outpatients in the urology ward for a period of 8 months; (ii) were in good general health, without fever on the day of surgery and had normal renal function (serum creatinine ≤ 1.9 mg dl⁻¹); and (iii) received no simultaneous treatment with other antibiotic drugs.

Netilmicin administration and sample collection

A blood sample for serum creatinine measurement was drawn before netilmicin treatment. A standard 30-min infusion of netilmicin (100 mg in 100 ml of saline solution) was administered to each patient at 8-h intervals up to a total of four doses. Between the first and the second dose, surgery was performed. Standard drugs were used during surgery and fluids and analgesics were administered postoperatively, as needed, none of which was reported to interfere with netilmicin analytical determinations.

A total of five blood samples (15 ml each) for netilmicin concentration determination were taken from each subject, amounting to 310 observations in 62 subjects. The first blood sample was taken 1 h after the beginning of the first infusion, except for the first 11 subjects, in which blood was drawn at the end of the first infusion. The second sample was taken 3.5 h after the beginning of the first infusion, and the third sample immediately before the administration of the second infusion. Between the third and fourth infusions, a sample was taken for a second assessment of creatinine plasma concentration. Two additional blood samples were taken 1 h and 8 h after the last dose for netilmicin concentration determination.

Plasma concentrations of netilmicin were determined by a fluorescence polarization immunoassay technique (TDx; Abbott Laboratories, Madrid, Spain). The lowest measurable concentration was 0.09 µg ml⁻¹. Assay performance conformed to the specifications per manufacturer's recommendations [30].

Creatinine clearance (CrCL [ml min⁻¹]) was calculated for each patient, from the second creatinine plasma sample, using Mawer's formula [31] included in Koup's methodology [32–34]:

$$\begin{array}{c}\text{CrCL }(\text{men}) = \{Weigh\mathrm{t }\times [29.3 - (0.203 \times Age)]\\ \times [1 - (0.03 \times Pcr)]\}/\\ \left\{\right[14.4 \times Pcr] \times 0.70/IW\}\end{array}$$

$$\begin{array}{c}\text{CrCL }(\text{women}) = \{Weigh\mathrm{t }\times [25.3 - (0.174 \times Age)]\\ \times [1 - (0.03 \times Pcr)]\}/\\ \left\{\right[14.4 \times Pcr] \times 0.70/IW\}\end{array}$$

where Pcr is plasma creatinine concentration and IW is the ideal weight calculated from Peck's formula [35]. CrCL ranged between 26.3 and 104.6 with mean ± s.d. of 63.8 ± 17.5 ml min⁻¹.

Pharmacokinetic analysis

The dataset was split by random selection into an ‘index’ group (n = 44) for development of all models, and a ‘validation’ group (n = 18). WinNonMix (Windows Nonlinear Mixed effects, version 2; Pharsight) was used for analysis.

Step I

We compared mono- and bi-compartmental, structural, PK models together with additive and proportional statistical models for the residual assay error. Lognormal distributions were assumed for the parameters and represented as exponentials of random effects. Model selection was based on the Akaike information criterion (AIC), and the distribution of the weighted residuals when plotted against the predicted variable (nonskewed, random appearance). We define the optimum model from this step as the ‘basic’ model, as it describes the population parameters and their statistical spread without including any covariates.

The model for the j^th concentration measurement in the i^th individual was

$$\text{C}{\text{p}}_{\text{ij}} = \text{f}({\text{p}}_{\text{i}},{\text{t}}_{\text{ij}}) + {\text{ɛ}}_{\text{ij}}$$

where f(p_i, t_ij) is the fitted model, p_i are the model parameters for the i^th individual, t_ij represents the time of the j^th concentration measurement in the i^th individual, and ɛ_ij accounts for the residual or unexplained deviation of model-predicted from observed response, of which intraindividual variability is but one component. ɛ_ij is assumed to be independently and identically distributed with a mean E[ɛ_ij] = 0 and variance Var[ɛ_ij] = σ² in the case of an additive statistical model, or Var[ɛ_ij] = σ² f(p_i, t_ij)^α in the case of a proportional error model, where α would then be a fixed effect. Early in the analysis the variance exponent parameter α was equal to 1.99 and was hence fixed to 2 for all subsequent runs. This error, apart from model misspecification and assay variability, unless specified within f(p_i, t_ij), also includes possible changes in the PK model parameters with time.

The PK parameters for the i^th individual were modelled as

where the overbar represents the population typical values (fixed effect), V_c and V_p are the central and peripheral volume of distribution, respectively, and CL and CL_Q are the central clearance and intercompartmental clearance. η-V_i and η-CL_i are random effects for V and CL for the i^th individual, resulting in measures for the interindividual variability. Their vector, η, is multivariate normally distributed with E[η] = 0 and Var[η] = Ω, a variance-covariance matrix for all the parameters with random effects. Adding interindividual variability to the intercompartmental clearance did not improve the fit. This has also been observed in other netilmicin population studies [23].

The First Order Conditional Estimate method (FOCE), which does not assume a priori that E[η] = 0, was used with a full Ω matrix for estimation of ‘basic’ (no covariates) population PK model parameter distributions. WinNonMix includes a step where these estimates can be used as priors to obtain empirical Bayesian parameters for each individual.

Step II

Patient demographic and pathological characteristics could theoretically explain part of the interindividual variability observed in the basic model. Linear and nonlinear terms containing these explanatory covariates can be regressed against the PK model parameters by expanding (P being any parameter) above to include these additional terms. Covariates considered were bodyweight and height, age, CrCL values, sex and surgery.

A stepwise procedure included backward elimination of terms from the model, followed by forward inclusion, performing successive runs at each step and comparing consecutive WinNonMix least squares objective functions for significance. The difference in −2 times the log-likelihood (−2LLD) objective function between a full and reduced model is asymptotically χ² distributed with degrees of freedom equal to the difference in the number of parameters between the two models. A decrease in more than 7.88 in −2LLD is significant at the P < 0.005 level for one additional parameter. Goodness of fit was also evaluated via the residual plots, standard errors, the correlation matrix of the parameter estimates, the magnitudes of the interindividual variances of the PK parameters, and the residual, intraindividual variability.

The form of the ‘final’, covariate model was

No covariates led to an improvement in V_p and CL_Q.

Validation

The predictive ability of the population model was tested in the validation group (n = 18) by simulating plasma concentrations using the final covariate model for the PK parameters. We compared the predicted concentrations (both Bayesian and population predicted) with the measured concentrations for those 18 patients. The standardized prediction errors or SPE (obtained directly from the analysis output by calculating the difference between observed and predicted concentrations for each sampling time divided by the standard deviation), equivalent in the validation group to the weighted residuals, were computed [36]. As more than one measurement was available for each patient, to account for the correlation of the prediction errors within patients and at the same time to use all the information available in the data, the mean of the standardized prediction error (SMPE) was calculated for each patient in the validation group. Additionally, the mean of the SMPE of all subjects in the validation group was also calculated. Under the assumption of unbiased parameter estimates, the SMPE should have a mean of 0 and a standard deviation of 1. A t-test was then used to determine whether the SMPE was significantly different from 0.

Results

Preliminary analysis of netilmicin concentrations after the first dose (three data points per subject) and those after the last (two data points per subject) with a mono-compartmental PK model showed no differences between either the pre- and post- (V_c) (population mean ± interindividual s.d.) (19.3 ± 5.8 l vs 20.3 ± 5.9 l) or the pre- and post-CL (4.2 ± 1.6 l h⁻¹vs 3.9 ± 1.4 l h⁻¹).

Figure 1 shows the plasma concentration-time data after four doses and the evolution for the typical patient. A bi-compartmental model (in terms of CL, V_c, CL_Q and V_p) was found to describe our data significantly better than a mono-compartmental approach with a difference in −2LLD of 60.8 (P < 0.005 for a χ² distribution).

Figure 1.

Plasma concentration observations (□) (n = 310) from 62 patients at 0.5, 1, 3.5, 8, 24 and 32 h after four 100-mg infusions of netilmicin. The solid curve is the typical population evolution.

Table 1 lists the basic model PK parameters and their distributional characteristics, and Table 2 lists the same for the covariate, final model. The inclusion of two covariates, sex and CrCL, in the regression model resulted in a significant decrease in −2LLD compared with that of the simple model without covariates. The difference in the objective function was 41 (P < 0.005). The interindividual variability in CL and V_c decreased by 21% and 48%, respectively, from the basic to the final model.

Table 1.

Basic parameters estimated from WinNonMix and percentage inter- and intra-individual coefficient of variation with standard errors of the estimate (SEE) for the index group (n = 44).

Parameter	Mean (SEE)
Vc (l)	14.5 (15%)
CL (l h−1)	3.9 (10%)
Vp (l)	10.2 (19%)
CLQ (l h−1)	10.1 (28%)
ω_Vc × 100	56% (114%)
ω_CL × 100	42% (61%)
ω_Vp × 100	–
ω_CLQ × 100	–
Intra-individual variability: 9% (24%)

Table 2.

Final covariate models and parameters with percentage standard errors of the estimate (SEE) from WinNonMix and interindividual coefficient of variation.

Vc = θ1 + θ2 × SEX		CL = θ3 × CrCL
Parameter	Mean (SEE)	Parameter	Mean (SEE)
θ1	18.9 (5%)	θ3	0.06 (11%)
θ2	−5.7 (37%)	–	–
ω_Vc × 100	29% (102%)	ω_CL × 100	33% (71%)
Intra-individual variability (SEE): 11% (30%)

The final population covariate relationships were: (V_c, L) = 18.9-5.9 × SEX (29%) and (CL, l h⁻¹) = 0.06 × CrCL (33%). Male patients were coded as 0 and female as 1.

Figure 2 shows the population-predicted concentrations for all individuals compared with the observation data. The fit appears symmetrical around the unit line and the spread increases with the magnitude of the measurement (proportional error). The same is shown for the final covariate model (Figure 3). The data are less dispersed around the unit line and individualized because of the covariates. Additionally, plots of weighted residuals vs model-predicted concentrations for the base and final model are shown in Figure 4.

Figure 2.

Basic model population plasma (predicted vs observed) concentration (Cp) for 44 patients with the line of identity. The straight clusters are indicative of sample collection times being identical for all individuals. Thus, the population Cp prediction is the same for all individuals at each of the five time-points.

Figure 3.

Final covariate model population (predicted vs observed; Cp). The dispersion around the identity line is reduced and the prediction is individualized through incorporation of covariates.

Figure 4.

Weighted residuals vs model-predicted concentrations for the basic and final models

Results of final model validation

The SMPE based on individual predicted concentrations (Bayesian) was −0.0095 and its standard deviation 0.931, which are close to 0 and 1, respectively. SMPE was not significantly different from 0 (P > 0.05). Similarly, the SMPE based on population-predicted concentrations was −0.013, and its standard deviation was 0.950, which was also not significantly different from 0 (P > 0.05).

Observed concentrations for the patients in the validation group were plotted against concentrations predicted by the final covariate model (Figure 5).

Figure 5.

Observed concentrations (Cp) for 18 patients in the validation group vs the concentrations predicted by the covariate model

Discussion

Inadvertent use of subtherapeutic doses of aminoglycosides has resulted in the emergence of resistant strains of bacteria and the predisposition of patients to breakthrough bacteraemias [3, 6]. Conversely, the use of excessive doses can result in ototoxicity and nephrotoxicity, due to accumulation in the renal or cochlear tissue [3, 5]. The toxicity and efficacy of aminoglycosides, including netilmicin, are known to be related to plasma concentrations [1], which show wide interpatient variability. Accordingly, there is general agreement that the dosing of aminoglycosides should be individualized.

However, questions remain on: (i) the best techniques for optimizing the dosage regimen, (ii) whether trough or peak concentrations are more informative, and how many blood samples should be collected, (iii) the use of simple or more complex pharmacokinetic models, (iv) the possibility of reducing the number of measured aminoglycoside concentrations by using population models, (v) whether monitoring is necessary with once-daily regimens, and (vi) the adequacy of fixed dosing protocols in short-term or prophylactic therapy.

Nomograms are based on estimates of the apparent half-life of aminoglycosides in patients with different degrees of renal impairment assuming a mono-compartmental PK model. Their use has been the subject of controversy for several years, receiving both support and criticism. Using more sophisticated models and simulation techniques it has become clear that use of a fixed dosage regimen, based on half-life and mono-compartmental kinetics, may result either in subtherapeutic serum concentrations at the beginning of treatment or in excessive accumulation after multiple dosing [37]. Such an outcome could be due to a change in half-life without any alteration in creatinine clearance [38] or to the complex pharmacokinetics of these drugs [37, 39]. When aminoglycosides are used once daily, the above must be considered in order to avoid subtherapeutic dosing [40, 41].

In our patients, treated with a fixed dose established from simple PK models [42], we observed a large variability in netilmicin concentrations. It is possible that fluids administered during and after surgery could have changed the pharmacokinetic parameters, but this was rejected after comparing mono-compartmental parameter estimates before and after the operation.

One way to explain variability has been to establish population models that include covariates. Optimum dosing can then be instituted at the beginning of treatment for each patient. However, in most cases not all the variability can be explained by the covariates. Thus, during long-term treatment, monitoring serum concentration is still recommended to minimize toxicity [19, 37].

In this study, using a population approach we have fitted a bi-compartmental model to the experimental data, which is in agreement with earlier reports [18–21]. However, mono- and even tri-compartmental models have been proposed for netilmicin pharmacokinetics [15, 17, 39]. The use of population methods that require only a few measurements per patient allows the study of the pharmacokinetics in a patient group during routine prophylaxis with the drug. Here, the interindividual variability in the pharmacokinetic parameters for netilmicin was decreased markedly by the inclusion of CrCL and sex.

The aminoglycosides are polar polycationic molecules, minimally bound to plasma proteins and are eliminated almost solely by glomerular filtration [3, 5, 25]. Therefore, it is reasonable to expect that CrCL should make a significant positive contribution to the regression equation for netilmicin clearance, and this was found to be the case. Regression analysis of our data from 44 patients who received netilmicin therapy showed that estimated CrCL was a significant determinant of netilmicin clearance. Our results are consistent with earlier reports [22] in adults and also in neonates using a nonparametric population method [25]. In some studies creatinine clearance could not be used to predict netilmicin pharmacokinetics because patients were neonates, most in their first week of life. At this stage, the pharmacokinetic parameters reflect the serum concentrations of the mother rather than the renal function of the neonate [23]. Additionally, the clearance value estimated in the present study is similar to those obtained by others using nonpopulation approaches, which also showed considerable variability (CL = 55.4 ± 18 ml min⁻¹, range 25.6–97.2 [21], and CL = 90.9 ± 13.9 ml min⁻¹[39]).

Some studies have reported a statistically significant but weak inverse correlation between volume of distribution and creatinine clearance [43]. Other investigators have not found an effect of renal function on the rate of elimination of netilmicin, which is reasonable considering that the elimination constant is a mixed parameter depending on the variabilities of both volume of distribution and clearance [19, 23, 25, 29, 44].

In the present study a significant relationship between volume of distribution and sex was seen. Others have also found that the apparent volume of distribution of netilmicin is affected by sex, among other factors [25]. According to the final equation described in Results, V_c will be smaller in females than in males, which could be due to sex-related differences in extracellular fluid volume. Because of its limited binding to plasma proteins, netilmicin distributes readily throughout the extracellular fluid. However, the polar, polycationic nature of its structure prevents netilmicin from readily crossing cell membranes into the intracellular fluid. Therefore, the apparent volume of distribution of netilmicin corresponds approximately to the extracellular fluid volume [25]. Thus, sex-related changes in body water could affect directly the volume of distribution of netilmicin, since sex, among other factors, is a predictor of extracellular fluid volume [45]. The inclusion of sex in the regression model reduced the interindividual variance of the volume by 48%. We found that age, bodyweight, height or type of surgery did not influence netilmicin pharmacokinetics significantly. Body mass index also showed no relationship with the studied model parameters.

The final model, described in the present study, may be applied clinically by incorporating creatinine clearance for the estimation of CL, and 0 = male, 1 =female for the estimation of V_c.

The availability of pharmacokinetic parameter distributions and covariate models for specific patient populations is essential for dose individualization. Population-specific pharmacostatistical models, such as the one developed and validated here, could lead to better prediction of drug concentrations among individuals, with the concomitant decrease in the risk of not achieving therapeutic concentrations or of exceeding toxic concentrations.