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Antimicrobial Agents and Chemotherapy, May 1998, p. 1098-1104, Vol. 42, No. 5
0066-4804/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
Levofloxacin Population Pharmacokinetics and Creation of a
Demographic Model for Prediction of Individual Drug Clearance in
Patients with Serious Community-Acquired Infection
Sandra L.
Preston,1,2
George L.
Drusano,1,*
Adam L.
Berman,1
Cynthia L.
Fowler,3
Andrew T.
Chow,3
Bruce
Dornseif,3
Veronica
Reichl,3
Jaya
Natarajan,3
Frankie A.
Wong,3 and
Michael
Corrado3
Division of Clinical Pharmacology,
Departments of Medicine and Pharmacology, Albany Medical
College,1
Department of Pharmacy
Practice, Albany College of Pharmacy,2 Albany,
New York, and
Robert Wood Johnson Pharmaceutical Research
Institute, Raritan New Jersey3
Received 8 July 1997/Returned for modification 31 December
1997/Accepted 10 February 1998
 |
ABSTRACT |
Population pharmacokinetic modeling is a useful approach to
obtaining estimates of both population and individual pharmacokinetic parameter values. The potential for relating pharmacokinetic parameters to pharmacodynamic outcome variables, such as efficacy and toxicity, exists. A logistic regression relationship between the probability of a
successful clinical and microbiological outcome and the peak concentration-to-MIC ratio (and also the area under the plasma concentration-time curve [AUC]/MIC ratio) has previously been developed for levofloxacin; however, levofloxacin assays for
determination of the concentration in plasma are not readily available.
We attempted to derive and validate demographic variable models to
allow prediction of the peak concentration in plasma and clearance (CL)
from plasma for levofloxacin. Two hundred seventy-two patients received
levofloxacin intravenously for the treatment of community-acquired
infection of the respiratory tract, skin or soft tissue, or urinary
tract, and concentrations in plasma, guided by optimal sampling theory, were obtained. Patient data were analyzed by the Non-Parametric Expectation Maximization approach. Maximum a posteriori
probability Bayesian estimation was used to generate individual
parameter values, including CL. Peak concentrations were simulated from these estimates. The first 172 patients were used to produce
demographic models for the prediction of CL and the peak concentration.
The remaining 100 patients served as the validation group for the model. A median bias and median precision were calculated. A
two-compartment model was used for the population pharmacokinetic
analysis. The mean CL and the mean volume of distribution of the
central compartment (V1) were 9.27 liters/h and
0.836 liter/kg, respectively. The mean values for the
intercompartmental rate constants, the rate constant from the central
compartment to the peripheral compartment (Kcp)
and the rate constant from the peripheral compartment to the central
compartment (Kpc), were 0.487 and 0.647 h
1, respectively. The mean peak concentration and the
mean AUC values normalized to a dosage of 500 mg every 24 h were
8.67 µg/ml and 72.53 µg · h/ml, respectively. The variables
included in the final model for the prediction of CL were creatinine
clearance (CLCR), race, and age. The median bias and median
precision were 0.5 and 18.3%, respectively. Peak concentrations were
predicted by using the demographic model-predicted parameters of CL,
V1, Kcp, and Kpc, in the simulation. The median bias and the
median precision were 3.3 and 21.8%, respectively. A population model
of the disposition of levofloxacin has been developed. Population
demographic models for the prediction of peak concentration and CL from
plasma have also been successfully developed. However, the
performance of the model for the prediction of peak concentration was
likely insufficient to be of adequate clinical utility. The model for the prediction of CL was relatively robust, with acceptable bias and
precision, and explained a reasonable amount of the variance in the CL
of levofloxacin from plasma in the population
(r2 = 0.396). Estimated CLCR, age,
and race were the final model covariates, with CLCR
explaining most of the population variance in the CL of levofloxacin
from plasma. This model can potentially optimize the benefit derived
from the pharmacodynamic relationships previously developed for
levofloxacin.
| |
INTRODUCTION |
Population pharmacokinetic modeling
has become a well-accepted method of obtaining information about the
disposition of a drug. Several approaches to such modeling are being
used, including NON-Linear Mixed Effects Modeling (NONMEM), Iterative
Two Stage (IT25) population modeling, Non-Parametric Expectation
Maximization (NPEM2) population modeling, and Non-Parametric Maximum
Likelihood population modeling (NPML) (5, 7, 9, 10).
While these programs provide information about the
pharmacokinetics of drugs with regard to the entire
population, it would be useful for one to be able to use the population
pharmacokinetic data to obtain information about the
pharmacokinetics for individual subjects. If pharmacodynamic
relationships linking measures of plasma exposures to measures
of outcome or toxicity were known, one could then use the
individual patient estimates to optimize drug therapy.
Levofloxacin, the optical L isomer of ofloxacin,
is a fluoroquinolone antimicrobial agent for which pharmacodynamic
relationships between both the peak concentration in serum to the MIC
(peak/MIC) ratio and the area under the concentration-time curve
(AUC)/MIC ratio and both clinical and microbiological outcomes have
been developed (8). It would be helpful to be able to use
these relationships to maximize the efficacies of drugs in patients. Unfortunately, assays for the concentrations of fluoroquinolones in
serum must be performed by the high-performance liquid chromatographic (HPLC) method or a microbiologically based assay. Such assays are
labor- and technician time-intensive and HPLC is expensive, making them
impractical for routine performance in the clinical setting. Given
these constraints, it would be desirable to have a model based on
patient demographics to obtain an estimate of the individual
pharmacokinetic parameters. Peak concentrations in serum or AUC
(approximated by the ratio of dose/clearance [CL]) can be estimated
in order to calculate a peak/MIC ratio or AUC/MIC ratio and use the
known pharmacodynamic relationships to achieve maximal benefit for a
particular patient.
Our objective was to produce a population pharmacokinetic model for
levofloxacin using data from an ill, infected, target population,
generate maximum a posteriori probability (MAP) Bayesian estimates of
individual patient parameters, and derive and validate a demographic
variable model which would allow prediction of the peak concentration
in plasma and CL from plasma for levofloxacin without the necessity of
measuring the concentrations in plasma.
| |
MATERIALS AND METHODS |
Patient population.
Two hundred seventy-two patients were
prospectively evaluated for model generation and model validation.
Patients were 18 years of age or older and were being treated for a
community-acquired infection of the skin or skin structure, respiratory
tract, or urinary tract.
Drug dosage and administration.
Patients received
levofloxacin at a dosage of 500 mg every 24 h by a 1-h intravenous
infusion for the treatment of skin or skin structure or respiratory
infection. A dosage of 250 mg intravenously (1-h infusion) every
24 h was used for the treatment of urinary tract infection. At
least three doses of the drug was administered intravenously. After
three doses of levofloxacin had been administered, multiple serum
samples were obtained for determination of drug concentrations. Then,
if clinically appropriate, the patients could be switched to an
equivalent oral dose. For patients who were receiving the 500-mg dose
and who had a calculated creatinine clearance (CLCR) of 20 to 50 ml/min (determined by the method of Cockcroft and Gault
[2]), the dosing interval was extended to every
48 h. No dosage changes were made for patients receiving the
250-mg dose. Patients whose CLCR was <20 ml/min were
excluded from participation in the clinical protocol.
Pharmacokinetic sampling schedule.
Pharmacokinetic parameter
means and standard deviations for the volume of distribution of the
central compartment (V1), CL, and the
intercompartmental transfer rate constants (the rate constant from the
central compartment to the peripheral compartment
[Kcp] and the rate constant from the
peripheral compartment to the central compartment
[Kpc]) were obtained from a phase I clinical
study conducted by the sponsor (6) and were used in
designing the sampling schedule. The mean value and the values of the
mean ± 1 standard deviation were then used to generate a model
ensemble. The model ensemble was generated by using every possible
combination of values for the four parameters (81 possible
combinations; three possible values for each of four parameters). Each
set of four parameter values was entered into the ADAPT II
(4) SAMPLE module to obtain optimal sampling times. The
optimal sampling times generated from the model were weighted by the
probability of occurrence in the population (e.g., the "subject"
whose parameter values were all the mean values for the population
would have a higher probability of occurrence than a subject with
parameter values which all differed by 1 standard deviation from the
mean). The mean ± 1 standard deviation constituted 68.3% of the
population. Each "tail" of the population (>1 standard deviation)
accounted for 15.8% of the population. All calculations were performed
with a D-optimal design criterion, which, when used, minimizes the determinant of the inverse Fisher information matrix (3). A histogram was used to plot the probabilities of information for the
population at various time points. After evaluation of the histogram it
was felt that a six-sample design (samples obtained at the time of the
trough concentration, at the end of infusion, and at 2.0, 6.75, 7.75, and 9.25 h postdosing) represented the best compromise between
limiting sample acquisition in the clinical setting and having enough
data from informative time points to obtain robust individual parameter
estimates in the MAP Bayesian step.
Assays for concentrations in plasma.
Plasma samples were
analyzed by a validated reversed-phase HPLC method with UV (330 nm)
detection (1). Briefly, the procedure used a single-step
liquid-liquid extraction with methyl t-butyl ether. A
reversed-phase C18 column was used to separate levofloxacin and the internal standard (ciprofloxacin). Elution was accomplished isocratically with a mobile phase consisting of 0.005 M copper (II)
sulfate pentahydrate in 0.01 M isoleucine-methanol (87.5:12.5 [vol/vol]) at a flow rate of 1.0 ml/min. The interassay precision values (as percent coefficient of variation) were less than 10%. The
quantification range in plasma was 0.08 to 5.12 µg/ml.
Population pharmacokinetic analysis.
Patient data were
analyzed by the NPEM2 approach with a one- and a two-compartment open
model with first-order elimination from the central compartment and a
zero-order intravenous infusion. Akaike's information criterion
(11) was used to discriminate among models. Population
pharmacokinetic parameters including CL (in liters per hour),
V1 (in liters per kilogram), and
Kcp and Kpc (in
hours1) were estimated. The assay variance was estimated
by regression modeling on the basis of the observed variance at four
different points throughout the range. The inverse of the estimated
assay variance was used as the weighting in the pharmacokinetic model. By this approach, total observation variance is approximated by the
assay variance. A change of less than 0.001% in the likelihood function was taken as the convergence criterion for NPEM2.
MAP Bayesian estimation was used to generate Bayesian posterior
parameter values by using the population of one utility in the NPEM2
package of programs. The individual patient parameter estimates were
then used in the simulation module of ADAPT II to obtain estimates of
peak concentrations in plasma.
Demographic model generation.
Data for the first 172 patients were arbitrarily set aside, and these data were used to
generate demographic models for prediction of pharmacokinetic parameter
values. The general linear model module of SYSTAT (Evanston, Ill.) was
used to develop the relationship, with peak concentration, CL,
V1, Kcp, and
Kpc serving as the dependent variables and site
of infection, gender, race, age, body weight, serum creatinine level,
inverse serum creatinine level, and CLCR serving as the
independent variables (CLCR was estimated by the method of
Cockcroft and Gault [2]). Of these, site of infection, gender, and
race were treated as categorical variables, with the others being
treated as continuous variables. All analyses were performed by a
stepwise backward procedure. Criteria for model inclusion and removal
were significance levels of 0.05 and 0.10, respectively. For the peak
concentration analysis, Bayesian posterior estimated peak
concentrations were normalized to a dose of 500 mg and a dosing
interval of every 24 h. The covariates included in the final model
were then used to predict parameter values and peak concentrations in
the remaining 100 patients (an example of the method is presented in
the Appendix). The bias and precision of these estimates were
calculated for the predicted values for the 100 patients by using the
values predicted by the model and the actual values obtained from MAP
Bayesian estimation. Bias was calculated as percent error:
{[observed parameter value (obs) 
predicted parameter value
(pred)]/obs value} × 100. Precision was calculated as percent
absolute error: [(|obs pred|)/obs] × 100. Median values of
bias and precision are presented to describe the performance of the
model with the 100-patient validation sample.
| |
RESULTS |
Pharmacokinetic analysis.
The two-compartment model was chosen
as most appropriate on the basis of Akaike's information criterion and
visual inspection of the population scatter plots (data not shown) for
one- and two-compartment models. The population pharmacokinetic
parameter values obtained from the NPEM2 analysis are listed in Table
1. Mean peak concentration and AUC
normalized to a dose of 500 mg and a dosing interval of every 24 h
were 8.67 ± 3.99 µg/ml and 72.53 ± 51.17 µg · h/ml, respectively.
Approximate marginal density plots depicting the probability of
occurrence of a value for a particular parameter in the population
are
displayed in Fig.
1A to D. The
probability distributions of
CL and
V1 tend to
follow a Gaussian pattern, while the distributions
of the
intercompartmental transfer rate constants
Kcp
and
Kpc are flatter with clearance.
Three-dimensional joint density plots
for all the parameters are
illustrated in Fig.
2A to C. These
plots
demonstrate how two parameters covary with each other. The
performance
of the MAP Bayesian estimation step is displayed in
the plot of the
observed versus predicted concentration in plasma
in Fig.
3. The Bayesian step used the median
values for each parameter
as the measure of central tendency. This has
been found to improve
predictive performance (
9a). The
coefficient of determination
(
r2) for the line
of best fit was 0.966. The slope was not significantly
different from
1.0, and the intercept was not significantly different
from 0.0.
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FIG. 1.
Probability distributions of pharmacokinetic parameters
in the population. The marginal distributions, which indicate the
probability of occurrence of pharmacokinetic parameter values in the
population, are displayed. (A) Slope of V1 to
body weight (VS; in liters/kilogram). (B) CL (in liters/hour). (C and
D) Kcp (KCP) and Kpc
(KPC), (in hours1), respectively.
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FIG. 2.
Three-dimensional probability distributions of
pharmacokinetic parameters. (A to C) Three-dimensional probability
distribution plots of the population for pharmacokinetic parameters.
Parameters and units are as described in the legend to Fig. 1.
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FIG. 3.
Observed versus MAP Bayesian-predicted concentrations in
272 patients. A scatter plot of observed versus MAP Bayesian-predicted
concentrations based on pharmacokinetic parameter medians is shown. The
slope and the intercept of the line are 1.01 and 0.0054, respectively.
The slope is not significantly different from 1.0, and the intercept is
not significantly different from 0.0. The r2
value is 0.966.
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|
Demographic model data.
The descriptive statistics for the
total group (n = 272), the model generation group
(n = 172), and the validation group (n = 100) are listed in Table 2. The
covariates included in the final model for the prediction of the peak
concentration by a stepwise backward approach were gender, weight, and
age, with a coefficient of determination of 0.105. The covariates
included in the final model for the prediction of CL were age, race,
and CLCR (r2 = 0.396) (Table
3). The covariates included in the
stepwise backward analysis for the prediction of
V1 included age, gender, and race, with an
r2 value of 0.132 (Table
4). Prediction of
Kpc included age and site
(r2 = 0.087) (Table
5). Prediction of
Kcp included weight and race (r2 = 0.065) (Table
6). By using data for all 272 patients,
we generated for CL a stepwise backward model which yielded the same
covariates in the final model as the covariates for the group of 172 patients (age, race, and CLCR).
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TABLE 2.
Descriptive statistics for total group and subgroups used
for demographic model generation and validation
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|
By using the developed models for the prediction of peak concentrations
for the validation group of 100 patients, the median
bias and median
precision were
17.1 and 28.9%, respectively.
The median bias and the
median precision for the prediction of
CL were 0.5 and 18.3%,
respectively; those for the prediction
of
V1
were
4.6 and 31.5%, respectively; those for the prediction
of
Kcp were
6.6 and 48.9%, respectively; and
those for the prediction
of
Kpc were 4.6 and
44.2%, respectively.
Because of the relatively poor bias and precision for the prediction of
peak concentration, the four predicted model parameters
(CL,
V1,
Kpc, and
Kcp) were used to simulate predicted peak
concentrations
by using ADAPT II for each patient. The median bias and
the median
precision were 3.3 and 21.8%, respectively. For the
prediction
of AUC, the median bias and the median precision were
1.0
and
19.5%, respectively.
The coefficients of determination for all models except CL were low
(
r2 = 0.396). A scattergram of measured versus
predicted (from the
demographics model) CL of levofloxacin from plasma
for the validation
population is presented in Fig.
4.
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FIG. 4.
Measured versus predicted CL obtained with the
demographic model. The measured versus predicted CL for the validation
group (n = 100) obtained with the demographic model
developed in this study is shown. Note that when the measured CL
reaches approximately 13 liters/h, the predictive performance decreases
(the model underpredicts CL).
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| |
DISCUSSION |
Determination of the pharmacokinetic profile of a drug in the
population of interest is of particular importance for the evaluation of a new agent. The limited ability of ill patients to undergo the
rigors of a classical pharmacokinetic study has resulted in the
availability of few data on the dispositions of agents in such
populations.
The advent of optimal sampling theory and population pharmacokinetic
analysis has had a positive effect in this area. In this study, we have
combined optimal sampling theory and population pharmacokinetic
analysis, as implemented in the ADAPT II program of D'Argenio and
Schumitzky (3), as well as the NPEM2 package of programs of
Schumitzky and Jelliffe (9a), to allow the study of the
disposition of the new fluoroquinolone antimicrobial agent levofloxacin
in a phase II multicenter clinical trial.
Our pharmacokinetic findings were highly consistent with those of
earlier studies of levofloxacin (7). The
V1 value of 0.836 liter/kg and the CL from
plasma of 9.27 liters/h are quite close to the mean values determined
for levofloxacin in earlier trials, especially when corrected for the
older age of the patient population studied in our analysis. This is
understandable, because the population that we studied had a mean age
of 46.8 years and the clinical study protocol accepted patients with
serum creatinine levels of as high as 3.4 mg/dl. For a drug like
levofloxacin, which is mainly cleared renally, the older age and the
slightly higher average serum creatinine level could reflect glomerular filtration rates which are lower than those seen in healthy volunteers, causing a decreased level of CL by the kidneys and therefore total CL
of levofloxacin.
One conclusion which can be drawn is that a relatively sparse sampling
strategy, driven by optimal sampling theory, can be implemented in a
medium-sized (circa 300-patient) multicenter clinical trial and, when
analyzed by population modeling techniques, can provide excellent point
estimates of the mean values and their dispersions for important
pharmacokinetic parameter values.
Examination of the marginal density plots for the pharmacokinetic
parameter values is also of interest. V1 and the
CL of levofloxacin from plasma are approximately normal in
distribution, while Kcp and
Kpc are flatter in their distributions. The
Gaussian nature of V1 and CL imply that they
conform to our distributional expectations for a predictive model. The
relative flatness of the distributions for Kcp
and Kpc may be an artifact related to model
misspecification. That is, the overall structural model choice for a
population analysis may not apply to some patients, who may have a drug
disposition profile which differs in nature from that required for a
two-compartment model. For the case of a two-compartment model being
forced onto a patient's data which are one compartment in nature, the
estimator will, by definition, give more probability of a very low
Kcp and a high Kpc.
The three-dimensional joint density plots which are a standard part of
the NPEM2 output also provide useful insight into the data.
V1 and CL are poorly correlated, as can be seen
by examining Fig. 2A. This is to be expected, given the physiologic
independence of V1 and CL. The marginal density
plots and the joint density plots are also of interest as a way of
identifying outlier subpopulations (e.g., rapid acetylators for
isoniazid). When examined with this purpose in mind, it is clear that
levofloxacin is a very well behaved drug with respect to
V1 and CL, with no substantial outlier subpopulations.
A central reason for undertaking this study was to develop a
demographic information-based population model which would allow estimates of the peak concentration and the CL of levofloxacin from
plasma to be obtained for individual patients if basic demographic patient information is available without having to directly measure the
concentrations in plasma. Peak concentration and CL from plasma were
chosen because peak concentration and AUC, when placed in a ratio to
the MIC for the patient's infecting pathogen (peak/MIC or AUC/MIC
ratio), could be directly linked to the probability of a successful
clinical or microbiological outcome in a logistic regression model
(8). We also felt it important that we have an independent
measure of the predictive performance of the population pharmacokinetic
relationship that we developed.
To attain both these ends, we used the data for the first 172 patients
in our data set to develop our demographic model, and for the
subsequent 100 patients the peak concentrations and AUCs were predicted
from our relationships and the bias and precision of estimation
determined against the measured values.
For peak concentration estimation, the general linear modeling
procedure resulted in a model which produced relatively biased and
imprecise predicted peak concentrations. Because of this finding, we
attempted to predict the peak concentration by predicting all four
model parameters and simulating a peak from those values. Much more
acceptable results were obtained, with a median bias of 3.3% and a
median precision of 21.8%. However, even this attempt did not explain
an acceptable amount of the variance in peak concentrations seen in the
population. Consequently, we doubt its utility for optimizing therapy.
For V1 estimation, the model included the
covariates of age, race, and gender. An increased
V1 was noted for females, but V1 decreased with age.
For the model for estimation of CL from plasma, stepwise backward
analyses indicated that CL was influenced by CLCR, age, and
race. This relationship was better than that for estimation of the peak
concentration, with an r2 value of 0.396. Certainly, the direct correlation of the CLCR estimate with
CL from plasma is understandable for a drug which is mainly cleared
renally. Also, patients of younger ages would tend to have better CL
processes and therefore a higher total CL. The influence of race,
however, is difficult for us to understand. We can give no
physiological explanation for this finding. It is noteworthy, however,
that the race category of "other" included only two patients and
the coefficient generated may not be a valid reflection of this
particular patient subpopulation.
For the prediction of CL, the median bias was 0.5% and the median
precision was 18.3%. Only this relationship predicting CL explains
enough of the variance to warrant its use clinically. Of note, when
examining the plot of measured CL versus predicted CL (Fig. 4), it
appears that the predictive ability of the model decreases above a
measured CL of approximately 13 liters/h. This would imply that if the
predicted CL was greater than 12 liters/h, there is a reasonably high
possibility that it could indeed be an underestimation of the measured
CL. This has therapeutic implications in that patients with higher CLs
will have a lower peak and a lower AUC and, hence, lower peak/MIC and
AUC/MIC ratios, with a consequence lower probability of the successful
outcome that the clinician would be expecting on the basis of the
predicted CL.
The ability to reasonably estimate CL without the necessity of
measuring concentrations in plasma is important. As we have developed
pharmacodynamic relationships linking the peak/MIC ratio or the AUC/MIC
ratio to the probability that levofloxacin will produce a successful
clinical or microbiological outcome, the clinician can now obtain
guidance as to the expectation of successful therapy with this agent in
the empirical setting (using an MIC for the most resistant pathogen
that they are willing to treat) or after the sensitivity result returns
from the clinical microbiology laboratory. The predicted result, if it
is felt to be potentially suboptimal, could lead to dose escalation,
the addition of a second agent, or a switch to a more appropriate
agent.
This also has potential economic impact. Patients experiencing
therapeutic failure use more hospital resources (longer stays, residence in an intensive care unit, etc.). Optimizing outcome could
potentially lead to substantial cost savings as well as the obvious and
most important benefit of improved patient care. Whether or not the
optimization of therapy can affect length of stay is an interesting
question which needs to be addressed in a prospective trial.
In summary, we have developed a population model of the disposition of
levofloxacin in a target population for the use of this drug. We have
further developed a population demographic model for the prediction of
CL from plasma. This relationship was developed to allow patients to
directly benefit from the pharmacodynamic relationships that we have
developed for this agent. It will be important to validate
prospectively the use of this relationship along with our
pharmacodynamic relationships with a similar patient population and
document the impact (if any) on patient outcome and the expenditure of
hospital resources.
| |
APPENDIX |
An example of the mathematical prediction of levofloxacin
parameters for a 50-year-old Caucasian male weighing 70 kg with a skin
structure infection and a CLCR of 75 ml/min is as
follows: CL = constant + race + (age
· 0.032) + (CLCR · 0.070) CL = 5.945 1.486 1.6 + 5.25 CL = 8.12 liters/h V1 = constant + gender + race + (age · 0.332) V1 = 72.096 + 6.482 + 10.027 16.6 V1 = 88.60 liters
| |
ACKNOWLEDGMENT |
This work was supported in part by a grant from R. W. Johnson Pharmaceutical Research Institute.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Division
of Clinical Pharmacology, Departments of Medicine and Pharmacology
A-142, Albany Medical College, 47 New Scotland Ave., Albany, NY 12208. Phone: (518) 262-6330. Fax: (518) 263-6333. E-mail:
GLDRUSANO{at}AOL.COM.
| |
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Antimicrobial Agents and Chemotherapy, May 1998, p. 1098-1104, Vol. 42, No. 5
0066-4804/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
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Abstract
Introduction
