A retrospective analysis of pharmacokinetic/pharmacodynamic indices as indicators of the clinical efficacy of ciprofloxacin

María M. Sánchez-Recio, Clara-Isabel Colino and Amparo Sánchez-Navarro*

Department of Pharmacy and Pharmaceutical Technology, Faculty of Pharmacy, University of Salamanca, Spain


    Abstract
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
A retrospective analysis of the relationship between estimated pharmacokinetic/pharmacodynamic indices and the reported efficacy of ciprofloxacin has been carried out using different correlation models. , Tss > MIC, and AUICss were calculated for each clinical case included in the study, from simulated plasma level curves corresponding to the dosage regimen administered. A univariate correlation analysis was performed considering efficacy (%) as the dependent variable and indices as the independent variables according to linear and non-linear pharmacokinetic–pharmacodynamic models (PK-PD models).The results prove that log-transformation of the independent variable improves the data fitting to linear model. The four estimated indices show a log-linear relationship with outcome, Tss > MIC and AUICss being the parameters best correlated with percentage efficacy. The Emax model with intrinsic response is an additional correlation strategy for Tss > MIC, leading to estimated values of Emax and E0 of 100.34 ± 25.09% and 24.40 ± 11.7%, respectively. The wide range of bacteria responsible for the infections considered, including Gram-positive pathogens such as staphylococci, might explain the good correlation between Tss > MIC and percentage efficacy found for ciprofloxacin in this study.


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The dosages and dosing intervals of antimicrobial agents should be designed with reference to pharmacokinetic and pharmacodynamic parameters. Accordingly, a series of so-called efficacy indices or surrogate markers, which take account of both types of information, have been defined and used by different authors to describe the antibacterial activity of various classes of antimicrobial agent.1,2

It is documented that these indices are good outcome predictors for these drugs; several studies have demonstrated that the peak serum concentration/minimum inhibitory concentration ratio () is a good predictor of the antibacterial activity of aminoglycoside agents.3 For ß-lactam antibiotics, the length of time that the serum concentration exceeds the MIC (T > MIC) is the most relevant index affecting bactericidal activity.4 For the quinolones there is not total agreement about the best predictor of efficacy. Like aminoglycosides, these agents show a concentration-dependent bactericidal effect for most bacteria;2 thus the ratio should be the parameter that correlates most closely with efficacy. Indeed, Stein5 reported a value of of eight times the MIC for quinolones to reach a satisfactory outcome. However, other authors2,6 find that the area under the inhibitory curve (AUIC: area under the curve for the time interval that the concentrations are above the MIC divided by the MIC value itself) is the best predictor of efficacy for fluoroquinolones in clinical practice. On the other hand, it has been shown that not just one surrogate marker is related to efficacy, but that the , T > MIC and AUIC are all linked to a positive clinical outcome for fluoroquinolones, aminoglycosides and ß-lactam antibiotics.6,7 Shentag et al.1 support the validity of the AUIC as a universal parameter and attempted to find a breakpoint value for it to predict the efficacy of treatments of most antibacterial agents. However, some criticisms have arisen regarding the usefulness of this efficacy index,8 since the same AUIC value can be obtained with different dosage regimens.

Most studies regarding efficacy indices are prospective studies carried out under very restrictive and controlled conditions including isolation of the pathogen and determination of the MIC value; nevertheless most treatments with antimicrobial agents are initially established empirically from epidemiological data of the specific geographical area, without any specific information about the MIC value in each individual patient.

The aim of the present study was to evaluate the validity of several indices for prediction of the efficacy of antibiotics under non-strictly controlled conditions as happens in daily clinical practice. A retrospective analysis was carried out of the correlation between the calculated efficacy indices and the clinical efficacy of ciprofloxacin reported in literature, using different correlation models.


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Data acquisition

The WINSPIRS (which includes Medline, IPA and Life-Sciences) and IDIS (Iowa Drug Information Service) computer systems were used for the bibliographic search in order to collect information about the clinical efficacy of ciprofloxacin, published in the period 1980–1997. Other biomedical journals not included in these databases were also reviewed.

Selection of data

First, all publications including data about the clinical efficacy of treatments with ciprofloxacin were collected, then the following exclusion criteria were applied to the data acquired: (i) infectious processes caused by more than one pathogen; (ii) infections produced by an unidentified microorganism; (iii) incomplete description of treatment; (iv) paediatric patients; (v) patients with renal impairment, and (vi) fewer than five patients in the study.

After applying these criteria the data were reduced to 67 different clinical cases9–32 corresponding to infections caused by 18 different bacteria, shown in Table IGo.


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Table I. Reported MIC90 values of ciprofloxacin for the pathogens responsible for the infections in the clinical cases considered for correlation analysis
 
Estimation of efficacy indices

According to the methodology previously described,33 the following indices were calculated for each clinical case: (the peak value at steady state divided by the minimum inhibitory concentration), Tss > MIC (the period of time that the plasma drug concentration exceeds the MIC value for 24 h at steady state), (total area under the curve for 24 h at steady state divided by MIC) and (AUICss)24h (area under the curve for the period of time that the concentrations are above the MIC at steady state for a period of 24 h divided by MIC).

A mean MIC value calculated from the literature data was considered to calculate the different indices. Table IGo includes the range of reported MIC values34–37 for the pathogens responsible for the infections in the clinical cases considered. The pharmacokinetic parameter values were obtained from the simulated plasma level curves corresponding to the described dosage regimen of ciprofloxacin administered. A one-compartment model was used for the simulation of drug curves, with the following population pharmacokinetic parameters:38–41 F (absorption fraction) = 0.7; Ka (absorption rate constant) = 2.5/h; Vd (distribution coefficient) = 2.35 L/K and Clp (plasma clearance) = 0.44 L/h/K.

Dosages, dosing intervals and total number of doses given, described in the articles, were considered for simulation of curves. Cmaxss and (Tss)24h > MIC were obtained directly from simulated curves. Additionally, the simulated curves provided the time–concentration data necessary to calculate (AUCss)24h and (AUICss)24h by numerical integration,42 according to the following equations:

where t1 and t2 are the administration times of two sequential doses at equilibrium, C is the simulated concentration and ndd is the number of daily doses. and

For AUIC

Where t3 and t4 are the times when the simulated concentrations are higher than the MIC for an interval dosage at steady state.

Simulation of plasma level curves was carried out using the PKS Pharmacokinetic computer System (Abbot Laboratories Diagnostic Division, North Chicago, IL, USA).

Correlation analysis

In order to establish the influence of the calculated indices on the observed clinical efficacy of ciprofloxacin, a univariate correlation analysis43 was performed considering the percentage of reported efficacy and calculated indices as the dependent and independent variables, respectively. Linear and non-linear conventional response models (PK-PD models),44 were used for the correlation analysis. The equations defining these models are:

Linear model:



Where a and b are the intercept and the slope of the regression straight line, respectively; I represents the calculated index (, (Tss)24h > MIC, or (AUCIss)24h) and E is the observed efficacy expressed as a percentage of clinical or bacteriological response.

Emax model:


Where Emax and E0 represent the maximum and intrinsic responses, respectively, In50 is the value of the parameter for a response of 50% of Emax and n is the Hill coefficient related to the curve profile.

Model fitting was carried out using the PCNonlin 4.2 program (Scientific Consulting, Inc., Apex, NC, USA), which optimizes the model parameters by non-linear regression techniques according to statistical criteria such as the standard deviation of parameters and minimum AIC.45

An ANOVA of the regression43 was performed to establish the statistical significance of the slope for the linear models (P < 0.05).


    Results
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Table IIGo includes the calculated indices together with the corresponding percentage of efficacy reported for ciprofloxacin. In most cases high efficacy is reported and in some cases certain indices take a value equal to zero for a good clinical response.


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Table II. Values of estimated indices and corresponding reported efficacy of ciprofloxacin from clinical studies
 
A wide range of the values calculated for the maximum response was observed: ( = 63.67 ± 100.06); (Tss)24h > MIC = 19.78 ± 7.46 h; = 883.15 ± 1499.90 h; (AUICss)24h = 725.99 ± 1201.75 h). These values are considerably higher than the mean values taken by the indices for the lowest efficacy: ( = 1.48; (Tss)24h > MIC = 2.83 h; ( = 10.8 h; (AUICss)24h =7.95 h).

The results of the univariate correlation analysis corresponding to the log-linear and Emax models, selected as best choices of indices–response relationship for ciprofloxacin, are shown in Tables III and IVGoGo, respectively; the estimated model parameters and standard deviation, as well as the statistical significance of the slope and AIC values, are also included in these tables.


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Table III. Parameters defining the log-linear relationship between the reported efficacy and estimated indices of ciprofloxacin
 

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Table IV. Parameters defining the non-linear relationship between the reported efficacy and estimated indices of ciprofloxacin
 
Analysis of the estimated parameters and statistical criteria corresponding to the log-linear model (Table IIIGo), revealed that (Tss)24h > MIC and (AUICss)24h were the parameters best correlated with efficacy, showing the highest correlation coefficients together with the lowest AIC values. For (Tss)24h > MIC, the slope takes a value of 31.90 ± 6.60, which was significantly higher than the values of this parameter for the rest of the indices.

Regarding the Emax model, which corresponds to the asymptotic model defined by the corresponding equation previously defined with n = 1 (Table IVGo), it was observed that by the statistical criterion of goodness of fit, the (Tss)24h > MIC together with the AUIC were the parameters that correlated best with efficacy (showing the lowest AIC value as well as the highest accuracy for estimated parameters). Emax and E0 showed the clinically most meaningful values for (Tss)24h > MIC in comparison with the rest of the indices estimated. A calculated value of 100.34 ± 25.09% for Emax was the expected value with an acceptable accuracy; on the other hand an E0 value of 24.40 ± 11.7% may have been associated with the inherent response of individuals to infectious processes. Nevertheless, for the other indices, the accuracy of Emax was much lower and the values taken by E0 were too high (76.06 ± 28.1%, 76.02 ± 30.3% and 73.60 ± 32.0%) to be acceptable from a clinical point of view.


    Discussion
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
This retrospective study carried out with ciprofloxacin pharmacokinetic and pharmacodynamic data, first revealed a wide variability in the estimated values of the indices for the maximum response (reported efficacy of 100%) which, as shown in Table IIGo, can even take a value of zero in some cases. Scrutiny of those cases shows that such variability is due to a high MIC value used to calculate the efficacy indices. This suggests low sensitivity of the pathogen and leads to the contradictory situation of low sensitivity and high efficacy. Notice that the mean of the reported values of MIC was used to calculate the indices and that mean values can differ strongly from the actual MIC value when a wide literature MIC range for the pathogen is found. The high variability in MIC values for several pathogens has already been discussed by other authors46 who found a 64- or even 128-fold range in the MICs for the pathogens for which antimicrobial agents are intended for empirical use. The Alexander Project and International Commissions such as EUCAST (European Committee on Susceptibility Testing) aim to standardize the methodology and criteria relating to the microbiological parameters defining resistance or susceptibility to antimicrobial agents. Consensus in this field would be very helpful and it should facilitate the application of dual individualization principles in antimicrobial therapy. Such a practice involves the use of the quantitative susceptibility of the infecting bacteria together with pharmacokinetic optimization of the antibiotic in an attempt to predict the time of bacterial eradication and consequently to optimize the dosage schedule.

The mean reported MIC values were assumed to be representative of the susceptibility of the pathogen, except for the few cases leading to zero values of the estimated indices. Analysis and comparison of the index values showed a large variability in this type of parameter, as well as a relevant difference between the mean values for 100% efficacy and the values for the lowest reported efficacy. The greatest difference was seen in (AUICss)24h, followed by (, and finally (Tss)24h > MIC. This conclusion would be in reasonable agreement with results from other authors suggesting AUIC or as the best predictor of outcome for fluoroquinolones.

In order to establish the relationship between clinical outcome and pharmacodynamic/-kinetic parameters, a correlation analysis was performed. For the linear model, log-transformation of the indices led to a significant decrease in the standard deviation of the parameters and the Akaike information criterion (AIC) values, together with an increase in Pearson's correlation coefficient (r) for the four indices considered. Therefore, the log-linear model would be the better choice of the two linear approaches.

The higher value of the slope obtained for (Tss)24h > MIC means that the response is more sensitive to changes in this index than to any other parameter estimated, since the slope is a measure of the sensitivity of the dependent variable (efficacy) to changes in the independent variable (log I). Consequently, the time that the plasma concentration exceeds the MIC value for 24 h at steady state may be considered even better correlated with the percentage efficacy than the AUIC in this study, in which a broad range of different clinical conditions are included. This finding is not expected for fluoroquinolones for which the ratio is expected to be the most relevant predictor, according to the concentration-dependent bactericidal effect reported for these drugs. Nevertheless, many authors 1,2,6 find not the ratio but the AUIC to be the best predictor of efficacy in clinical practice. Considering that AUIC depends not only on the maximum concentration achieved but also on the persistence of plasma concentrations, the best correlation of AUIC with outcome proves the influence of time on clinical efficacy for these agents.

According to our results the four estimated indices, (AUICss)24h, (Tss)24h > MIC, and , were linearly correlated with the efficacy of ciprofloxacin. Log-transformation of the independent variable (estimated index) improved the linear correlation. Statistical criteria selected the (AUICss)24h and the (Tss)24h > MIC as the parameters with the strongest linear correlation with efficacy. The highest value of the slope obtained for (Tss)24h > MIC, and the best Emax model fitting for this index point to this parameter as the best, correlated with the percentage efficacy for ciprofloxacin.

Although (Tss)24h > MIC is not considered to be the most relevant predictor for quinolones it has to be taken into account that the data analysed comprise infections caused by 18 different bacteria including several species of Staphylococcus (Table IGo). Our findings might be a consequence of the fact that some quinolones behave like time-dependent antibiotics with staphylococci.47

Our results do not contradict the previous information about ciprofloxacin but extend it, showing that many factors may influence the potential usefulness of antimicrobial agents when used in clinical practice. It should be noted that if no correlation analysis is performed, and a comparison of the values of the indices for the highest and lowest efficacies is carried out, (AUICss)24h and show more relevance that (Tss)24h > MIC. However, when correlation analysis is performed taking into account different percentages of efficacy, the (Tss)24h > MIC is the index selected. This fact might imply that very high values of the former indices guarantee maximum efficacy but below a fixed value these indices are less correlated with the percentage efficacy than the (Tss)24h > MIC, at least for our study conditions, which included Gram-positive bacteria. On the other hand, the discriminative analysis of the different correlation models performed in our study selects the log-linear model, as well as the Emax model with intrinsic response, as being more suitable for this purpose than the linear model.

The different correlation models used by other authors may account for the differences in the results, which are not incompatible but are instead based on different correlation strategies. Accordingly, Deziel-Evans et al.,48 using the point-biserial correlation coefficient, found a strong correlation between T > MIC and efficacy for aminoglycosides. This is despite aminoglycosides having a concentration-dependent bactericidal activity and most authors suggesting the ratio as the efficacy parameter for predicting outcome with these drugs.

Our study indicates that pharmacokinetic/pharmacodynamic ratios are useful predictors of the potential efficacy of antibacterial therapy and that the higher these parameters the greater the efficacy of treatment. Nevertheless, the particular efficacy parameter that is best correlated with outcome will depend on clinical circumstances and the correlation model used. We suggest that indices– efficacy relationships should be determined for each clinical circumstance, using different correlation strategies, in order to select the best choice in each case. Simulation techniques, as described in Materials and methods, provide an easy method for estimating these different indices, whose values can be correlated with the observed efficacy. Population kinetic studies on most antibacterial agents would be of great benefit for the application of dual dosage principles to optimization of antimicrobial therapy. Consensus about the microbiological criteria defining resistance or sensitivity of bacteria to antimicrobial agents would also contribute to the improvement and extension of these predictions.


    Notes
 
* Correspondence address. Departamento de Farmacia y Tecnología Farmaceútica, Facultad de Farmacia, Universidad de Salamanca, Avda del Campo Charro S. N., 37007 Salamanca, España. Tel: +34-923-294536; Fax: +34-923-294515; E-mail: asn{at}gugu.usal.es Back


    References
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
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Received 4 June 1999; returned 22 September 1999; revised 25 October 1999; accepted 23 November 1999