Population Pharmacokinetics of Amikacin in Critically Ill Patients

ANTIMICROBIAL AGENTS AND CHEMOTHERAPY, July 1996, p. 1682–1689 0066-4804/96/$04.0010 Copyright q 1996, American Society for Microbiology

Vol. 40, No. 7

Population Pharmacokinetics of Amikacin in Critically Ill Patients FRANCOISE BRESSOLLE,1* ANNE GOUBY,2 JEAN-MARIE MARTINEZ,1 PIERRE JOUBERT,3 GILBERT SAISSI,3 ROBERT GUILLAUD,4 AND ROBERTO GOMENI5 Laboratoire de Pharmacocine´tique, Faculte´ de Pharmacie, 34060 Montpellier Cedex 01,1 and Laboratoire de Bacte´riologie,2 Service d’Anesthe´sie Reánimation,3 and Service de Me´decine Pe´diatrique,4 Ho ˆpital G. Doumergue, 30006 Nıˆmes Cedex, France, and Bestfit, L-2210 Luxembourg5 Received 10 October 1995/Returned for modification 12 February 1996/Accepted 1 April 1996

The pharmacokinetic parameters of amikacin were determined in a population of 20 adults and 36 pediatric patients admitted into an intensive care unit. Amikacin was administered by repeated intravenous infusion over 0.5 h (600 to 1,350 mg for adults; 70 to 1,500 mg for children). The number of administrations ranged from 2 to 17, and the number of samples collected from each patient ranged from 2 to 70. The population enrolled in the study had large variabilities in age (0.5 to 85 years), weight (6 to 95 kg), height (72 to 187 cm), creatinine clearance rate (18 to 110 ml/min), blood urea nitrogen concentration (1.5 to 15 mmol/liter), and total protein concentration (30 to 91 g/liter). The mean population parameters and their interindividual variabilities were obtained for an initial group of 44 patients (16 adults and 28 children). A two-compartment model was fitted to the population data by using the computer program P-PHARM. Model selection was guided by evaluation of the minimum objective function and the weighted residuals. The population analysis has been performed with the complete set of the collected data, including the individual serum amikacin concentrations together with the individual estimate of the creatinine clearance values. The potential sources of variability in the population parameters were investigated by using patients’ age, height, weight, creatinine clearance, blood urea nitrogen concentration, and total protein concentration as covariables. A test group of 12 additional patients (4 adults and 8 children) was used to evaluate the predictive performances of the population parameters. The individual pharmacokinetic parameters were computed by a Bayesian fitting procedure. From the resulting individualized values of the parameters, the concentrations of amikacin in the serum of the patients were calculated. To evaluate the performance of the Bayesian estimation, the experimental concentrations were compared with the predicted ones. The Bayesian approach developed in the study accurately predicts amikacin concentrations in serum and allows for the estimation of amikacin pharmacokinetic parameters, minimizing the risk of bias in the prediction. This was demonstrated in patients with both stable and unstable renal functions. individualized optimal dosage regimen should be proposed and initiated as early as possible. Several nomograms and predictive algorithms were proposed to help clinicians in individualizing dosages. Most investigators attempt to correlate aminoglycoside elimination with changes in renal function, as measured by the serum creatinine level or creatinine clearance (CLCR) (13). Unfortunately, such approaches lack accuracy. Other methods that use plasma drug concentrations have been proposed. These methods, often called test dose experiments, based on pharmacokinetic modeling, are more accurate than previous predictive algorithms and allow the clinician to attain and maintain the therapeutic levels (5, 31). A fundamental drawback of these methods is that they require an extended period of initial evaluation to determine individual kinetics; moreover, they assume that the pharmacokinetic parameters for a given patient remain constant throughout the treatment. The Bayesian approach to drug dose individualization has been applied to many drugs, including aminoglycoside antibiotics and vancomycin (20). Recently, methods that use Bayesian forecasting to adjust amikacin doses have been described (1, 3, 13, 19, 20). Dose adjustment by Bayesian forecasting resulted in improvements in the rates of achieving therapeutic drug concentrations and in patient clinical outcomes (2, 12, 15, 20). The aim of the present study was to determine more accurate population pharmacokinetic parameters of amikacin by using a two-compartment open model with a population of

Amikacin is one of the most useful aminoglycoside antibiotics for the treatment of severe infections. The drug has a rapid bactericidal effect and has potent in vitro bactericidal activity against many aerobic gram-negative bacilli (especially enteric bacteria) and gram-positive cocci (mainly Staphylococcus aureus) (18). Moreover, its antibacterial activity is highly concentration dependent and does not plateau (23). This drug has a long postantibiotic effect, the duration of which is dependent upon the peak concentration in serum (17). Like the other aminoglycosides, however, amikacin has a very narrow therapeutic index, and the concentrations needed for optimal efficacy are close to those having a high risk of toxicity. The two most frequent toxic manifestations, ototoxicity (which commonly becomes irreversible) and reversible nephrotoxicity, show a positive correlation with conventionally determined high trough concentrations and the area under the concentration-time curve (18). Moreover, large interindividual variations in the concentrations and pharmacokinetic parameters of amikacin in intensive care unit patients were noted (1, 13). Consequently, amikacin is a drug for which therapeutic drug concentration monitoring has an established role, and an

* Corresponding author. Mailing address: Laboratoire de Pharmacocine´tique, Faculte´ de Pharmacie, 34060 Montpellier Cedex 01, France. Phone: 33 67 54 80 75 Fax: 33 67 54 45 26 (work) and 33 67 79 32 92 (home). 1682

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TABLE 1. Demographic and biological data Patients

Age (yrs)

Ht (cm)

Wt (kg)

Serum creatinine concn (mmol/liter)

Total protein concn (g/liter)

Blood urea concn (mmol/liter)

Adults (n 5 20) Children (n 5 36)

52.4 6 19.9 5.66 6 4.27

170.8 6 9.38 109.1 6 29.4

69.4 6 11.0 20.4 6 13.6

73.0 6 26.2 49.1 6 17.5

52.8 6 6.76 68.1 6 10.7

6.69 6 2.17 3.58 6 1.45

patients covering a wide age range (from pediatric patients to aging patients). This model takes into account changes in the drug elimination process when renal function is changed because of individual pathological status and demographic characteristics. The computer program P-PHARM was used to estimate the population pharmacokinetic parameters. To verify the predictive performances of this method, subsequent amikacin concentrations were predicted for an independent group of patients and then compared with the measured concentrations. MATERIALS AND METHODS Patient inclusion and exclusion criteria. Fifty-six patients were included in the study. Twenty adult patients (15 males and 5 females), with ages ranging from 20 to 85 years, admitted into an intensive care unit were evaluated. All patients were mechanically ventilated. Twenty-one bacterial strains were initially isolated. More than one strain was isolated from four patients. Thirty-six pediatric patients (16 boys and 20 girls), with ages ranging from 6 months to 15 years, admitted to the Neonatalogy Department with a presumed bacterial infection were enrolled in the study. From these patients 31 bacterial pathogens were isolated before the initiation of treatment. The blood samples were collected for routine monitoring of the patients. For all patients, anamnestic data, physical examination, and standard laboratory tests which included hematological and biochemical tests (in particular, blood urea nitrogen and total protein) were performed before, during, and at the end of the study. The serum creatinine level was recorded daily or more for all patients. Among these patients, 10 children and 12 adults had various degrees of unstable renal function. Subject demographic data are given in Table 1. The 56 patients included in the study were divided into a model-building set (16 adults and 28 children; population group) and a test data set (4 adults and 8 children; test group). Diagnostic criteria. The diagnosis of infection was based upon both clinical and bacteriological evaluations. Symptomatic, physical, laboratory, and radiographic findings consistent with a specific diagnosis and the isolation of a pathogen from an appropriate source were required to make a definitive diagnosis. A

diagnosis based on clinical findings was made for those patients in whom a pathogen was not identified (seven patients). In the case of respiratory tract infection, expectorated sputum (children) or bronchial brush (adults) specimens were obtained for culture. Respiratory tract infections were classified as pneumonia (with radiographic evidence of infiltrates) or suppurative tracheobronchitis (nine adults and four children). In adults, pneumonia was confirmed by fiber optic bronchoscopy with doublesheathed microbiological brushes (11). Six adult patients developed nosocomial pneumonia defined by its occurrence at least 4 days following admission to the intensive care unit, elevated temperature (.38.58C), leukocytosis (.10 3 109 liter21), purulent sputum at least 3 days before the trial, and lung infiltration on chest X ray. Gastrointestinal disorders were diagnosed in five children after the isolation of pathogens from fecal flora. Abscesses and suppurations were diagnosed in five children. A diagnosis of osteomyelitis (two children) was based upon the presence of fever, an inability to bear weight, gait disturbances, localized pain, focal changes demonstrated by plain radiographs or technetium 99m scans, or both, and an elevated erythrocyte sedimentation rate. Fever, gait disturbances, localized pain, and tenderness in the presence of purulent synovial fluid established the diagnosis of infective arthritis (two children). Urinary tract infections (2 adults and 12 children) were defined as frequency, dysuria, or pyuria accompanied by a cleanvoided urine specimen yielding .105 CFU of a single organism per ml. Fever along with the symptoms of toxicity including tachypnea, tachycardia, and altered mental status in the presence of one or more positive blood cultures obtained from percutaneous punctures of peripheral veins supported a diagnosis of septicemia (two children). One child suffered from meningitis, and one child suffered from mastoiditis. One child was hospitalized for treatment of Fanconi’s anemia, and one child was hospitalized for treatment of Hirschsprung disease. Peritonitis was diagnosed when a culture of peritoneal fluid showed a mixed microbial population or single causative agents (eight adults). Angiocholitis was clinically diagnosed in one adult, and the causative organism was recovered from a culture of blood. The isolated strains and the site of infection are given in Table 2. Measurement of drug concentrations. The concentrations of amikacin in serum were assayed by a fluorescence polarization immunoassay (TDx Abbott Laboratories, Rungis, France). Quality control samples containing 5, 15, and 30 mg of amikacin per liter were assayed each time that samples from study patients

TABLE 2. Isolated strains and clinical response to treatment No. of patients

No. of patients with identifiable pathogens

4 11 5

3 11 4

Sepsis Skin and skin structure

2 5

2 4

Gastrointestinal tract Cerebrospinal fluid Otolaryngological fluid Blood

6 1 1 1

5 1 0 1

9

9

2 8 1

2 6 1

Patients and site of infection

Infants and children (n 5 36) Pulmonary Lower urinary tract Bone and joint

Adults (n 5 20) Pulmonary Lower urinary tract Peritoneum Gallbladder

Pathogen(s) (no. of isolates)

Pseudomonas aeruginosa (2), Moraxella catarrhalis (1) Escherichia coli (10), Klebsiella sp. (1) Staphylococcus aureus (2), Haemophilus influenzae (1), group A beta-hemolytic Streptococcus sp. (1) Klebsiella sp. (1), Staphylococcus aureus (1) Staphylococcus aureus (2), Group A beta-hemolytic Streptococcus spp. (2) Salmonella typhimurium (4), Salmonella enteritidis (1) Enterobacter cloacae (1) Staphylococcus epidermidis (1) Escherichia coli (1), Klebsiella sp. (1), Proteus mirabilis (1), Staphylococcus aureus (5), Pseudomonas aeruginosa (2), Acinetobacter spp. (2) Enterobacter cloacae (1), Escherichia coli (1) Escherichia coli (4), Morganella morganii (2) Klebsiella pneumoniae (1)

Efficacy of treatment

Cured Cured Cured Cured Cured Cured Died Cured Died Cured Cured Cured Cured

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were assayed. Calibration standards for control serum samples were prepared by using concentrations of 3, 10, 20, 35, and 50 mg/liter. Each calibration standard sample was analyzed in duplicate. Coefficients of variation were less than 4% for intra-assay variability and less than 9% for interassay variability. The quantitation limit of the assay, defined as 3 standard deviations above the measured average value for the blank, was 0.5 mg/liter. Drug administration and dose. Amikacin was administered every 24 h as an intravenous infusion over 0.5 h (600 to 1,350 mg for adults; 70 to 1,500 mg for children). Two pediatric patients received the drug twice daily, and two other children received the drug thrice daily. For adults, the amikacin regimens were adjusted to maintain minimum concentrations lower than 5 mg/liter and peak concentrations of 60 6 15 mg/liter (30). For pediatric patients, no published data reported the best drug concentrations to be reached. So, in the present study, the amikacin regimens in these patients were adjusted to maintain minimum concentrations lower than 5 mg/liter and peak concentrations near 50 mg/liter (29). The number of administrations ranged from 2 to 17, according to the patient. Blood sampling. Blood samples were obtained from adults around the time of administration of a regularly scheduled dose every day at the following times: (i) immediately before administration of the dose, (ii) immediately at the end of the infusion, and (iii) two to three times during the treatment between two consecutive dose intakes at the following times: at the end of infusion and at 0.75, 1, 2, 4, 6, 8, 12, 16, 20, and 24 h after the infusion. The number of samples collected from each patient ranged from 25 to 70. The mean duration of treatment was 212.1 6 72.8 h (range 133.5 to 408 h). Blood samples were obtained from children at the following times: (i) immediately before administration of the dose and (ii) immediately at the end of the infusion (one to four times during the treatment). The number of samples collected from each patient ranged from two to eight. The total duration of treatment averaged 94.7 6 54.4 h (range 24 to 336 h). Data analysis. The data analysis was performed by using the P-PHARM computer program (version 1.3) (26). Details about the mathematical presentation of the implemented algorithm have been described previously (14, 22). Preliminary analysis revealed that the data were best fitted by a two-compartment model (on the basis of examination of the Akaike criterion, the objective function, and the distribution of residuals), that the probability density function of the random effect parameters was better approximated by a log-normal rather than a normal distribution, and that the distribution of residuals showed that the error variance was better described by a heteroscedastic (proportional to the estimated values of the predictions) model. The structural model was initially parameterized in terms of the initial volume of distribution (V), total body clearance (CL), and transfer rate constants (k12 and k21). To take into account the considerable inter- and intrasubject variabilities in renal function because of the wide age range of the subjects included in the study (0.5 to 85 years) and the fluctuations in the time of the kidney function (serum creatinine level changes greater than 50%), respectively, CL was modeled as follows (20): CL 5 CLCR 3 a 1 b (equation 1), where a is the slope and b is the intercept. CLCR was assumed to be a linear function of the individual weight, height, age, and sex as defined by a modified Cockcroftt-Gault equation (4, 28), which takes into account children under age 20 years according to the standard procedures used in our hospital. However, this choice was validated by comparing the CLCR values estimated by this formula with the ones obtained by the formula of Dechaux et al. (7). The results of this comparison revealed a very good agreement between these two computational methods. This modeling approach is usually applied to take into account the different degrees of renal dysfunction for drugs which are highly renally excreted (6, 10). On the basis of this assumption the structural model was defined as y 5 y (V, a, b, k12, k21) (equation 2). The population estimation algorithm used in P-PHARM is an EM-type procedure (8). This algorithm computes the maximum likelihood estimates by an iterative procedure, as follows: (i) an expectation step (E step), in which for each individual the individual parameters are estimated (Bayesian estimate) given the current population parameters and the individual data, and (ii) a maximization step (M step), in which the population parameters are estimated by maximum likelihood given the current estimates (E step) of the individual parameters. The E and M steps are iterated up to the convergence of the algorithm. The EM algorithm iterates until the fractional changes of the fixed, random, and residual error variance parameters between two consecutive iterations become less than 0.01. Estimation of population parameters. The two-compartment computer analysis used the entire concentration in serum resulting from all dosings along with estimated CLCR histories and potential explanatory covariables such as patients’ age, height, weight, CLCR, serum urea nitrogen concentration, and total protein concentration. The fixed-effect pharmacokinetic parameters a, b, V, k12, and k21, together with their random-effect parameters, omega(a), omega(b), omega(V), omega(k12), omega(k21), respectively, were computed. Data analysis was performed by the following approach. (i) In step 1, the population parameters together with the individual posterior estimates are computed assuming that no dependency exists between the pharmacokinetic parameters and the covariables. (ii) In step 2, the relationship between the posterior individual estimates and the covariables is investigated by using both the graphical exploratory functions and the multiple linear stepwise algorithm. The stepwise procedure used (9) is an improved version of the forward-selection proce-

ANTIMICROB. AGENTS CHEMOTHER. dure which involves the reexamination at every stage of the regression the variables incorporated into the model in previous stages. A variable which may have been the best single variable for entry into the model at an early stage may be superfluous at the later stage because of the relationships between it and the other variables now in the regression. To check this, the partial F criterion (F 5 12 to enter the variable and F 5 12 to remove the variable for an alpha value of 0.01) for each variable in the regression at any stage of calculation is evaluated and compared with a preselected value of F distribution. Any variable which provides a nonsignificant contribution is removed from the model. This process is continued until no more variables can be admitted to the equation and no more are rejected. (iii) In step 3, only the covariables showing a correlation with a pharmacokinetic parameter are retained in the analysis. The population parameters are reestimated considering the relationship with the covariables. During the iterative process, after each E step the program checks the correlation between the posterior individual parameter estimates and the selected covariables. The correlation is assessed on the basis of the F statistical criterion. By default, the program drops the covariables which do not explain significantly the variability in the pharmacokinetic parameters. However, the user can force the EM algorithm to keep selected covariables in the analysis and to restart the EM iterative procedure. The results are compared with those obtained when the influence of covariable factors was not considered. Different evaluation criteria are supplied: the loglikelihood value, the Akaike criterion, the residual plot, and the examination of the change in the remaining interindividual variability in the fixed-effect parameters. Consistency check of the pharmacokinetic parameters estimates. To check the error model assumptions and the distribution on the estimated population pharmacokinetic parameters, P-PHARM estimates the expected concentrations (Cexp) for each individual in the population and computes appropriate statistical tests to evaluate the distribution properties of the differences between the expected and the observed data. For each concentration a standardized concentration prediction error (SCPE) is calculated, as follows: SCPE 5 (Cobs 2 Cexp)/SD(Cexp), where Cobs represents the observed concentrations, and SD(Cexp) represents the estimated standard deviation on the expected values computed by using all sources of random variability including the residual error. To assess the posterior distribution properties of the residuals, the t test was used to compare the mean residuals value to 0; the Kolmogorov-Smirnov test was used to compare the sampled distribution to the expected one (normal with zero mean and unitary variance [N(0,1)]) (27). Performance of Bayesian individual parameter estimates. Data for 12 patients (4 adults and 8 pediatric patients) not included in the calculation of population parameters were used to evaluate the performance of the Bayesian estimation. These patients were enrolled in the study according to the same experimental design (dose, route, and sampling times) as the 44 patients included in the population study. The number of samples ranged from 2 to 6 for the pediatric group and from 33 to 87 for the adult group. The individual data were fitted to a two-compartment linear model, and the individual pharmacokinetic parameters were computed by a Bayesian fitting procedure by using a maximum a posteriori probability (MAP), which uses the prior knowledge of the mean and dispersion of the pharmacokinetic parameters for the population to which the selected individual belongs and the individual concentration(s) in plasma. The MAP-Bayesian procedure does not use the full covariance matrix but uses just the main diagonal of such a matrix. From the resulting individualized pharmacokinetic parameter values, the concentrations of amikacin in the serum of the patient were calculated (predicted concentrations). To evaluate the performance of the Bayesian estimation, the experimental concentrations were compared with the predicted ones. The estimated and observed values for both peak and trough amikacin concentrations were also compared. Reliability of the parameter estimates. To compare the predicted concentrations (CTEST) estimated by the Bayesian approach with the experimental concentrations (CREF), the following criteria were used (24, 25): (i) For bias or mean predictor error:

Bias 5

1 n

O

i5n

@CTEST ~i! 2 CREF ~i!#

(3)

i51

(ii) For precision or root mean square error:

Precision 5

ÎO 1 n

i5n

@CTEST ~i! 2 CREF ~i!#2

(4)

i51

In these expressions, the index i refers to the individual concentration, and n is the total number of values. Confidence intervals for bias and precision were also computed. (iii) Statistical comparisons were performed by the paired t test.

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TABLE 3. Peak and trough concentrations of amikacin Concn (mg/ml [mean 6 SD])a

Group and patients

Population group Adult Pediatric Test group Adult Pediatric a

Peak

Trough

54.1 6 17.3 (n 5 142) 40.7 6 15.8 (n 5 44)

1.44 6 1.53 (n 5 120) 0.97 6 0.66 (n 5 39)

58.3 6 17.0 (n 5 32) 16.0 6 7.19 (n 5 12)

1.02 6 0.88 (n 5 31) 1.40 6 1.39 (n 5 10)

n, number of values; SD, standard deviation.

RESULTS The observed serum amikacin concentrations for both the peak (end of infusion) and the trough (end of the dosing interval) are reported in Table 3. Population characteristics. The population database consisted of 801 amikacin concentrations. The number of measurements available for each patient ranged from 2 to 70. As stated in Materials and Methods, a two-compartment model was used to describe the observed data. The pharmacokinetic parameters for the patient population computed by a threestep approach are given in Table 4. In step 2, the stepwise regression analysis between individual pharmacokinetic parameters and covariables showed a correlation between V and body weight; likewise, the intercept (b) was correlated with height. In step 3, the final pharmacostatistical model retained to fit the population data was as follows: y 5 y (V, a, b, k12, k21) (equation 5), V 5 m 1 n 3 weight (equation 6), and b 5 p 1 q 3 height (equation 7), where m, n, p, and q are the secondstage regression model parameters. The relationship found with the covariables were as follows: V is equal to 1.89 1 0.238 weight (r 5 0.95; (P , 0.001) and b is equal to 21.74 1 0.0317 height (r 5 0.89; P , 0.001). The relationships explained 90.8 and 79.1% of the interindividual variability of the population pharmacokinetic parameters, respectively (Table 4). Examples of the correlation are shown in Fig. 1 for V and weight and in Fig. 2 for b and height. The final computed population parameters are reported in Table 4. The maximum likelihood and Akaike criterion, as well as the remaining interindividual variabilities in the parameters, were lower in step 3 than in step 1. The standard log-likelihood ratio test based on chi-square statistics shows a significant improvement on the maximum likelihood (P , 0.001) after the inclusion of the second-stage regression model, which relates weight and height to V and b, respectively. Check of consistency of pharmacokinetic parameter estimates. Under the assumption of a correct regression model and unbiased parameter estimates, in all cases the mean value of SCPE was not significantly different from zero (Student t test), and the Kolmogorov-Smirnov test showed that the SCPE distributions were not significantly different from a normal distribution [N(0,1)]. The goodness of fit is shown by the anal-

FIG. 1. Scatter plot of individual V (Bayesian estimates) versus weight.

ysis of the scatter plot of the posterior predicted values versus the individual observed concentrations (Fig. 3) and by the frequency distribution histogram of the normalized residuals, which reveals a distribution very close to the expected one. Typical posterior individual fittings are displayed in Fig. 4. Extreme values for the parameters V, k12, k21, a, and b after posterior individual fitting are 2.96 to 24.2 liters, 0.0527 to 0.254 h21, 0.0229 to 0.327 h21, 0.1 to 0.48, and 0.427 to 5.48 liters/h, respectively. Evaluation of the Bayesian pharmacokinetic parameter prediction. For the patients in the test group, individual pharmacokinetic parameters were calculated by using the population characteristics. From these parameters, individual concentrations in serum were estimated. Estimated and observed amikacin concentrations were compared. No significant differences were found between the predicted and observed peak (49.2 6 22.9 and 46.8 6 24.2 mg/ml, respectively) and trough (1.24 6 1.03 and 1.16 6 1.03 mg/ml, respectively) amikacin concentrations. Likewise, during the whole treatment, all of the other concentrations were well estimated. The data in Table 5 describe the performance of the Bayesian estimation as expressed by bias and precision. Bias was not statistically different from zero (t test), and the 95% confidence interval included the zero value. We also noted that precision on the concentration prediction remains lower than the interindividual standard deviation (Table 5). Because of differences in the number of blood samples from the adult and pediatric groups, an independent evaluation of the Bayesian pharmacokinetic prediction error was done separately with the pediatric population (Table 5). This additional analysis was performed to avoid possible bias in the overall evaluation because of the large number of blood samples from the adult group. DISCUSSION It is now admitted that monitoring of aminoglycoside concentrations in blood should be individualized to improve the

TABLE 4. Population pharmacokinetic parameters for amikacina Step

1 3 a

a

0.384 (68.3) 0.30 (46.7)

b (liters/h) d

1.84 (115.4) 2.42 (39.7)

V (liters)

9.28 (30.1) 10.7 (8.08)

The sigma value is for all parameters. ML, maximum likelihood. c AIC, Akaike criterion. d Values are means (percent coefficient of variation). b

k12 (h21)

0.175 (40.2) 0.133 (27.4)

k21 (h21)

0.130 (45.3) 0.112 (40.0)

Sigmaa

MLb 22

9.12 3 10 9.04 3 1022

22,053.2 22,145.3

AICc

22.55 22.67

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FIG. 2. Scatter plot of individual b (Bayesian estimates) versus height.

clinical efficacy of treatment and to prevent oto- and nephrotoxicities. The direct dependence of the excretion of such drugs on renal function has led some investigators to develop nomograms for dosage individualization. More recently, efficient methods based on the Bayesian feedback approach have been introduced. Population pharmacokinetic values serve as the starting point, and they are then adjusted to estimate individual parameters suitable to predict an individualized dosage regimen. The performance of such a method depends on good estimates of the distribution of the population parameters (mean and variance). Unfortunately, mean population parameters estimated by using the standard compartmental model are not suitable for describing a complex kinetic process that varies over time, such as the one characterizing drug kinetics in critically ill patients. Indeed, in such a population, fluid and blood administrations are frequent, some patients present with hemodynamic instability, and deterioration in renal function attributed to the underlying disease process can occur during the treatment. The intersubject variability of the CL of amikacin in our population of patients is presented in Fig. 5, which displays the changes in CL as a function of changes in age and individual weight. The intrasubject variability is mainly evidenced in Fig. 6, which displays the changes in amikacin CL as a function of CLCR and age. For these reasons, with the present population it was not possible to use a model with a constant CL value because this parameter has been shown to be strongly related to the pathological and demographic charFIG. 4. Typical posterior individual fittings.

FIG. 3. Scatter plot of predicted concentrations (Bayesian estimates) versus observed concentrations.

acteristics of the individuals. To take into account these different sources of variability, the CL parameter was defined in terms of equation 1 in the model used to fit the data. In addition, the variability in the other population parameters was partially explained by additional covariables. In contrast to previously published studies on amikacin (1, 19), in the present study, a two-compartment open model was used to accurately describe amikacin pharmacokinetics. This also provides information about the average level of drug accumulation in tissue and thereby allows one to identify patients with abnormal levels of drug accumulation earlier than could be done with a one-compartment model. Moreover, opposite the Bayesian approach developed by Garraffo et al. (13), covariables were included in the present model to explain part of the interindividual variabilities in the population pharmacokinetic parameters.

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TABLE 5. Statistical analysis after Bayesian estimationa Patients and parameter

Predicted concn (mg/ml)

Biasb

Precision

Adults and children Total concn (n 5 218) Peak level (n 5 44) Trough level (n 5 41)

20.5 6 31.1 49.2 6 22.9 1.24 6 1.03

1.08 (20.12,2.27)c 1.26 (20.7,3.22) 0.0759 (20.027,0.18)

7.0 (27.5,21.5) 6.68 (210.5,23.9) 0.323 (0.245,0.401)

Children Peak level (n 5 12) Trough level (n 5 10)

16.2 6 5.84 1.45 6 1.43

0.20 (21.55,2.05) 0.069 (20.12,0.26)

2.05 (20.46,7.08) 0.27 (0.073,0.47)

a Reference concentrations for adults and children were as follows: total, 18.6 6 29.5 mg/ml; peak, 46.8 6 24.2 mg/ml; and trough, 1.16 6 1.03 mg/ml. Reference concentrations for children were as follows: peak, 16.0 6 7.19 mg/ml, and trough, 1.40 6 1.39 mg/ml. b Not statistically different from 0. c The values in parentheses represent the 95% confidence intervals.

The initial V normalized to body weight computed after posterior individual fitting of data for adult patients entering the population group (0.255 6 0.0411 liter/kg) was larger than that reported for healthy volunteers and non-critically ill patients (30). Localized edema (e.g., ascites, pleural effusions, and dependent edema) or generalized edema (e.g., adult respiratory distress syndrome and multiple organ failure) could account for the larger V of amikacin in the critically ill patients in the present study. This V was larger for children younger than age 3 years (0.403 6 0.0716 liter/kg) compared with that for the adult patients. This would be anticipated if one takes into account the increased interstitial and total body water of patients under age 3 years. Similar findings have been reported by Marik et al. (21). The Bayesian approach developed in the present study accurately predicts amikacin concentrations in serum. This was demonstrated for patients with both stable and unstable renal functions. For both peak and trough levels, bias was not significantly different from zero. Around the predicted peak and

trough levels, for the whole group, precisions were 6.68 and 0.323, respectively (the corresponding coefficients of variation were 13.6 and 26%). For the pediatric group, precisions around the predicted peak and trough levels were 2.05 and 0.27, respectively (the corresponding coefficients of variation were 12.7 and 18.6%). All patients in the present study were critically ill, and for some of them, important variations in hemodynamic status occurred during treatment. Such variations induced outlier amikacin concentrations which can reasonably explain the observed precision. Similar findings have been reported previously (12). This Bayesian approach allows for the estimation of amikacin pharmacokinetic parameters, minimizing the risk of bias in the prediction. At variance with previously reported data (1, 13, 19), the population enrolled in the present study was affected by a large variability in age (0.5 to 85 years), weight (6 to 95 kg), height (72 to 187 cm), CLCR (18 to 110 ml/min), blood urea concentration (1.5 to 15 mmol/ liter), and total protein concentration (30 to 91 g/liter). By using the present population pharmacokinetic parame-

FIG. 5. Changes in amikacin CL (in liters per hour) as a function of the changes in age and individual weight.

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FIG. 6. Changes in amikacin CL as a function of CLCR and age.

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