Pharmacokinetics of Vancomycin in Elderly Patients Aged over 80 Years

Abstract

Since the 1950s, vancomycin has remained a reference treatment for severe infections caused by Gram-positive bacteria, including methicillin-resistant Staphylococcus aureus. Vancomycin is a nephrotoxic and ototoxic drug mainly eliminated through the kidneys. It has a large interindividual pharmacokinetic variability, which justifies monitoring its plasma concentrations in patients. This is especially important in patients aged over 80 years, who frequently have renal impairment. However, the pharmacokinetics of vancomycin in this population is very poorly described in the literature. The objective of this work was to propose a model able to predict the pharmacokinetics of vancomycin in very elderly people. First, a population pharmacokinetic model was carried out using the algorithm NPAG (nonparametric adaptive grid) on a database of 70 hospitalized patients aged over 80 years and treated with vancomycin. An external validation then was performed on 41 patients, and the predictive capabilities of the model were assessed. The model had two compartments and six parameters. Body weight and creatinine clearance significantly influenced vancomycin volume of distribution and body clearance, respectively. The means (± standard deviations) of vancomycin volume of distribution and clearance were 36.3 ± 15.2 liter and 2.0 ± 0.9 liter/h, respectively. In the validation group, the bias and precision were −0.75 mg/liter and 8.76 mg/liter for population predictions and −0.39 mg/liter and 2.68 mg/liter for individual predictions. In conclusion, a pharmacokinetic model of vancomycin in a very elderly population has been created and validated for predicting plasma concentrations of vancomycin.

INTRODUCTION

Vancomycin is a glycopeptide antibacterial that is widely used for the treatment of serious Gram-positive infections, notably those caused by methicillin-resistant Staphylococcus aureus (MRSA) (1). With the widespread appearance of resistant pathogens such as MRSA, the use of vancomycin has dramatically increased since the early 1980s. The activity of vancomycin is related to an inhibition of the biosynthesis of the bacterial cell wall. The molecule diffuses into the cell wall and binds to the disaccharide pentapeptides, preventing their polymerization and leading to discontinuation of the synthesis of peptidoglycan of the bacterial cell wall.

The concentration-effect relationship of vancomycin has been characterized, and the pharmacokinetic (PK)-pharmacodynamic parameter that best describes the efficacy is the ratio of the area under the serum drug concentration-time curve to the MIC (AUC/MIC) (2, 3). Regarding toxicity, it has been shown that vancomycin nephrotoxicity is dose dependent and linked to vancomycin trough concentration (4). As vancomycin elimination is mainly renal, patients with renal impairment are at risk of overexposure and toxicity. As a consequence, a careful monitoring of vancomycin serum concentrations is recommended (5, 6) to optimize efficacy and prevent toxicity.

Several methods can be used to individualize dosage regimen from the data of therapeutic drug monitoring, such as linear or nonlinear regression analysis, PK nomograms (7), and Bayesian estimation procedures (8). Bayesian techniques make optimal use of information contained in a population model (a priori) combined with information from the patient to propose the most precise dosing regimen for each patient (8). Thus, they are currently considered state-of-the art approaches for vancomycin dose adjustment.

In the geriatric population, there is a large inter-/intraindividual PK variability (9) and a high prevalence of renal impairment. Therefore, elderly patients are considered a population at high risk of toxicity when using vancomycin. At the same time, little is known about the population PK of vancomycin in patients aged 80 years and over.

The objective of this study was to build and validate a vancomycin pharmacokinetic model for patients aged over 80 years that would be usable for therapeutic drug monitoring with Bayesian approaches.

MATERIALS AND METHODS

A population pharmacokinetic study was undertaken using a data set of 111 geriatric patients who were hospitalized in a teaching hospital in France and treated with vancomycin. This study was accepted by the local ethics committee. The collection and use of computerized medical data were conducted after declaration to the Commission Nationale de l'Informatique et des Libertés.

A random sampling method was used to allocate the patient files in two subgroups. First, a pharmacokinetic model was built using 70 patient files. An external validation then was made using the remaining 41 patients of the data set.

Available therapy data were vancomycin dose, date, time, and duration of each infusion. The date and time for each drug concentration were recorded precisely. For each patient, at least two blood samples were collected: a peak-level sample, drawn 15 to 45 min after the end of the infusion, and a trough-level sample, drawn just before the next infusion. The total number of samples per patient was variable, depending on the duration of the therapy. Vancomycin assays were performed by an immunoturbidimetry method on an Abbott Architect C8000 analyzer. In plasma, the lower limit of quantification was 1.1 μg/ml, and the linear range of the assay was 1.1 to 100 μg/ml.

For each patient, the following covariates were available: age, sex, weight, height, and serum creatinine. Variations of weight and serum creatinine during vancomycin therapy were also available. In addition, creatinine clearance was estimated using the Jelliffe formula for patients with unstable renal function (10).

(i) Population pharmacokinetic modeling.

The population pharmacokinetic modeling was based on a nonparametric population approach, including research of the best structural model and appropriate covariates. Models with one and two compartments were successively tested. The influence of some covariates on the pharmacokinetics of vancomycin was explored as linear relationships between the volume of distribution (V; in liters) and body weight (BW; in kilograms) or age (A; in years), linear relationships between the vancomycin elimination rate constant and creatinine clearance or age, or linear combinations of two covariates according to the following equations: V = V₀ + (V₁ × BW) + (V₂ × A) and k_el = k₀ + (V₁ × ClCr) + (V₂ × A). ClCr is creatinine clearance (milliliters per minute), and k_el is elimination rate constant (per hour). V₀ (liters), V₁ (liters per kilogram), V₂ (liters per year), k₀ (per hour), k₁ (minutes per milliliter per hour), and k₂ (per year per hour) were parameters to be estimated during the pharmacokinetic modeling step.

The residual error was modeled as a polynomial function (describing the assay error) multiplied by a parameter (gamma) taking into account uncertainties of the clinical environment: error = gamma × (0.0529 + 0.1352Y − 0.0027Y² + 0.00003Y³), where Y is observed concentration.

The analysis was performed using the NPAG (nonparametric adaptive grid) algorithm, developed by the Laboratory of Applied Pharmacokinetics (LAPK) of the University of Southern California (USC) (11, 12). This algorithm calculates the optimal discrete parameter joint density by successive iterations, with each iteration increasing the likelihood. This algorithm has already shown its usefulness in several pharmacokinetic studies (13–15). Individual pharmacokinetic parameters were determined by Bayesian estimation for each patient.

The Akaike information criterion (AIC) was used to assess the goodness of fit of candidate models (16). This criterion is commonly used in pharmacokinetic studies. The AIC criterion is defined as (2 × k) − 2 × ln(L), where k is the number of parameters and L is likelihood.

When comparing two models, the lowest AIC value indicates the best fit.

(ii) Validation.

The predictive performance of the model was assessed in a set of 41 patient files not included in the modeling step. Parameter distributions obtained in the first step were used as prior distributions to estimate vancomycin concentrations observed in the validation set. Concentrations were estimated using the best parameter combinations observed in the whole population (population prediction) or using a combination of individual parameters for each patient obtained with a Bayesian estimator (Bayesian prediction).

Bias (mean error) and precision (mean squared error and root mean squared error [RMSE]) of predictions were used to measure predictive performance, as recommended by Sheiner and Beal (17). The coefficient of determination between predicted and observed concentrations was also calculated. A graphical analysis between observed and population predicted concentrations (DV versus PRED) and between observed and individual predicted concentrations (DV versus IPRED) was undertaken for both the modeling and the validation step.

RESULTS

Model building.

Anthropometric and physiological characteristics of the study population as well as descriptive statistics of doses administered are shown in Table 1.

TABLE 1.

Anthropometric and physiological characteristics of the population

Parameter	Mean	Median	SD	Minimum	Maximum
Age (yr)	85.63	85.00	4.18	80.00	95.00
Total wt (kg)	61.30	61.60	13.40	27.00	98.30
Height (cm)	162.32	159.99	8.14	147.98	179.98
Creatinine clearance (ml/min)	45.31	46.94	16.35	5.48	82.73
No. of samples per patient	5.53	5	3.51	2	16
No. of doses per patient	21.44	15.5	17.19	2	66
Amt of vancomycin per dose (mg)	590	500	327	125	1,750

The model that showed the lowest Akaike criterion value has two compartments and six parameters, with linear transfer constants between the central and the peripheral compartments, as shown in Table 2. The covariate age did not significantly improve the value of the Akaike criterion, either for the volume of distribution or for the elimination rate constant.

TABLE 2.

Effect of compartment number and covariates on goodness of fit

No. of compartments	Covariate linked to V	Covariate linked to kel	Log likelihood	No. of parameters	AIC	ΔAIC
1			−1,139.29	2	2,283
1	wt		−1,125.47	3	2,257	−26
1	wt and age		−1,120.87	4	2,250	−33
1		CrCl	−1,088.34	3	2,183	−100
1	wt	CrCl	−1,084.63	4	2,177	−106
1	wt and age	CrCl	−1,077.89	5	2,166	−117
1		Age and CrCl	−1,088.23	4	2,184	−99
1	wt	Age and CrCl	−1,103.29	5	2,217	−66
1	wt and age	Age and CrCl	−1,080	6	2,172	−111
2			−981.55	4	1,971	−312
2	wt		−975.11	5	1,960	−323
2	wt and age		−969.1	6	1,950	−333
2		CrCl	−948.69	5	1,907	−376
2	wt	CrCl	−937.69	6	1,887	−396
2	wt and age	CrCl	−947.13	7	1,908	−375
2		Age and CrCl	−948.08	6	1,908	−375
2	wt	Age and CrCl	−940.62	7	1,895	−388
2	wt and age	Age and CrCl	−939.67	8	1,895	−388

The elimination parameter was modeled as a combination of a nonrenal elimination and a renal elimination proportional to creatinine clearance, i.e., k_el = k₀ + (k₁ + ClCr), where k₀ and k₁ are intercept and slope parameters, respectively.

The volume of distribution of the central compartment was described with an equation including a constant and a coefficient linked to the weight of the patient: V = V₀ + (V₁ × BW), where V₀ and V₁ are intercept and slope parameters, respectively.

Means and standard deviations of pharmacokinetic parameters are reported in Table 3. A representation of observed and population predicted concentrations (DV versus PRED) and between observed and individual predicted concentrations (DV versus IPRED) is shown in Fig. 1.

TABLE 3.

Means and standard deviations of pharmacokinetic parameters

Parameter	Mean	SD	Percentile
			25	75
k0 (h−1)	0.0229	0.0232	0.00064	0.0309
k1 (min · ml−1 · h−1)	0.00088	0.00057	0.00024	0.00129
V0 (liter)	23.35	12.24	12.01	37.13
V1 (liter · kg−1)	0.211	0.207	0.017	0.318
k12 (h−1)	0.369	0.241	0.0965	0.577
k21 (h−1)	0.207	0.173	0.0468	0.234
kel (h−1)	0.0626	0.0312	0.0397	0.0747
V (liter)	36.28	15.22	24.44	44.48
Clearance (liter · h−1)	2.025	0.934	1.383	2.611

FIG 1.

Observed versus population predicted concentrations (A) and observed versus individual predicted concentrations (B) for the modeling subset of patients.

The distribution of weighted residual errors of individual predicted concentrations is presented in Fig. 2.

FIG 2.

Distribution of weighted residual errors of individual predicted concentrations.

Validation of the model.

Table 4 shows the predictive capabilities of this model in the validation group of patients. Figure 3 shows the graphical representation of observed and population predicted concentrations (DV versus PRED) and between observed and individual predicted concentrations (DV versus IPRED) for the validation subset of patients.

TABLE 4.

Predictive capabilities of the model in the validation group of patients^a

Prediction	Bias (mg/liter; mean error)	Precision (mg2/liter2; mean squared error)	Precision (mg/liter; RMSE)	Coefficient of determination
Population	−0.75	76.75	8.76	0.26
Individual	−0.39	7.16	2.68	0.91

^aThe first row shows the results obtained using the mean population parameters to predict the concentrations. The second row contains the results obtained using the individual parameters, estimated with a Bayesian approach.

FIG 3.

Observed versus population predicted concentrations (A) and observed versus individual predicted concentrations (B) for the validation subset of patients.

DISCUSSION

The pharmacokinetics of vancomycin has a large interindividual variability that is partially explained by differences in renal function, which is frequently impaired in elderly patients. Whereas numerous pharmacokinetic studies were undertaken in adult patients, little is known about the pharmacokinetics of vancomycin in very old patients. To our knowledge, this is the first population PK study of vancomycin performed in patients aged 80 years and over.

This study showed that the behavior of this drug in this population is not much different from that observed in younger patients. In this cohort of patients over 80, the best structural model was found to be a two-compartment model, as in most of the studies carried out in adults (9, 18–23).

The mean clearance was estimated at 0.034 liter/h/kg, while a range of 0.042 to 0.065 liter/h/kg has been reported in adult patients (22, 23). In a geriatric subgroup of patients, Sánchez et al. (18) found a mean clearance of 0.031 liter/h/kg, very similar to the value determined in this study. Concerning the volume of distribution, we found a mean value of 0.59 liter/kg, very close to those reported by Yamamoto et al. (20), Sánchez et al. (18), Llopis-Salvia and Jiménez-Torres (21), and Tanaka et al. (24).

Published studies on the pharmacokinetics of vancomycin in humans showed that renal function, weight, and age may be predictors of vancomycin clearance and volume of distribution pharmacokinetic parameters (25–27). In our population of very elderly hospitalized patients, creatinine clearance was found to be associated with the vancomycin elimination rate constant, and body weight was associated with the volume of the central compartment. Apart from this relationship between creatinine clearance and elimination rate constant, we did not find any other significant relationships between patient age and pharmacokinetic parameters, contrary to studies carried out in young children (22) or in adult intensive care unit patients (28). This could be explained by the existence of immature processes in young children, such as kidney function (22), and by a larger range of ages in the population studied by Revilla et al. (28), in which patients were between 18 and 85 years.

Interestingly, although the population used during this study was homogeneous in terms of age, we found a large interindividual variability in clearance and volume of distribution: the coefficients of variation of these two parameters were 46% and 42%, respectively. These values were higher than those described by Yamamoto et al. (20) (37.5% and 18.2%, respectively) and Yasuhara et al. (23) (38.5% and 25.4%, respectively) in younger patients. This high variability of pharmacokinetic parameters can be explained in part by the variability of renal function in elderly patients (coefficient of variation of creatinine clearance of 36% in our population). However, the incorporation of covariates such as creatinine clearance and body weight in the model does not explain all the variability observed in this population. Several factors may explain this high interindividual variability. First, the aging process can be considered heterogeneous: as described by Lindeman et al., a decrease in renal function is not observed in one-third of elderly patients (29). The same phenomenon has been described for the elimination process of certain drugs (30). Moreover, nutritional status and concentrations of plasma proteins can be altered in elderly patients and can affect the distribution of vancomycin, which is significantly bounded to plasma proteins (31). Finally, blood flow to the organs may be reduced in elderly patients and may affect the distribution, metabolism, or elimination of drugs (32–36).

The predictive capabilities of the model, determined in a group of patients not included in the model building, were acceptable with low bias (−0.75 mg/liter) and satisfactory accuracy (RMSE of 8.76 mg/liter). After Bayesian estimation of individual pharmacokinetic parameters, predictive capabilities were very good, with bias of −0.39 mg/liter and RMSE of 2.68 mg/liter. The coefficient of determination between observed concentrations and concentrations predicted by the model was 0.91. This model seems to be suitable for the implementation of adaptive control of vancomycin dosing in this population. According to the results obtained in this study, the mean daily dose needed to achieve a target AUC of 400 mg/liter/day in this population should be around 810 mg (standard deviation, 373 mg).

This study has some limitations. First, the modeling was performed using data from clinical activity, so the sampling design was not optimized. Moreover, few clinical or biological variables were available for analysis. For example, the albumin concentration and the nature of the infection or the use of specific drugs (like diuretics, for example) were not known, although they may be useful for pharmacokinetic modeling of vancomycin (9). Such information might have improved the predictive capacity of the model built.

Conclusions.

Vancomycin is a standard treatment for MRSA infections. Because of a risk of accumulation and toxicity, its use in the elderly is difficult. Furthermore, few studies have been undertaken in this particular population. In a study carried out in elderly hospitalized patients over 80 years of age, we found that the pharmacokinetics of this drug is only slightly different in very elderly patients compared to that in younger patients. However, the interindividual variability of pharmacokinetic parameters appears to be larger than that in a younger population. The model built has good predictive capabilities and seems suitable for therapeutic drug monitoring in this population.