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QUANTITATIVE CLINICAL PHARMACOLOGY |
From the Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden (Dr Viberg, Dr Karlsson, Dr Jönsson), and the Department of Medical Sciences, Infectious Disease, Uppsala University Hospital, Uppsala, Sweden (Dr Cars).
Address for reprints: Anders Viberg, PhD, AstraZeneca R&D Södertälje, Clinical Pharmacology & DMPK, SE-151 85 Södertälje, Sweden.; e-mail: anders.viberg{at}astrazeneca.com.
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: Cefuroxime • dosing strategy • individualization • MIC • risk function
With use of a pharmacokinetic (PK) and pharmacodynamic (PD) model, it is possible to evaluate different dosing schedules by stochastic simulation and, based on a predefined fulfillment criterion, judge which of the different schedules is preferred. However, simulating all possible dosing schedules to find the optimal dosing schedule is not feasible. An alternative approach is to estimate an optimal dosing strategy by minimizing a risk function describing the seriousness of deviations from the target at which the treatment aims. This method has been used when aiming at various PK and PD targets.1-7 Dosing strategies have, to our knowledge, not been estimated for a drug in which the target is dependent on the time the drug exposure is above a threshold concentration. Furthermore, the approach has not been used when target and risk function definitions take into account aspects other than the desired effects and side effects, for example, cost of treatment and amount of drug administered.
Cefuroxime, which is used as a model substance in this study, is a second-generation cephalosporin that has been used worldwide for more than 2 decades against a variety of bacterial infections. In Sweden, it is the most widely used parenteral antibiotic. Following an intravenous dose of cefuroxime, the plasma concentration exhibits 2-compartment pharmacokinetics, with a total volume of distribution ranging from 12 to 30 L and clearance proportional to renal function (fraction excreted unchanged in urine >90%) ranging from 0.8 to 9 L/h.8-14 Cefuroxime shows activity against several pathogens (eg, Escherichia coli and Streptococcus pneumoniae).
Beta-lactam antibiotics, like cefuroxime, show time-dependent killing; that is, the longer time the bacteria are exposed to unbound concentrations above the minimum inhibitory concentration (MIC), the better killing is achieved, and no proportional increase in the killing effect is produced when concentrations are increased greater than 4 to 5 times the MIC of the bacteria.15
However, in vivo as well as in vitro studies indicate that it is not necessary to attain unbound concentrations above MIC for 100% of the dosing interval for full effect; rather, 50% of the dosing interval is suggested to be a breakpoint for full effect during normal dosing.16-18 However, this PD target is not unconditional; for example, when the dosing interval is very long, the time that concentrations stay below the MIC might also become long, and the bacteria may start to regrow. Severe side effects following cefuroxime treatment rarely occur, but a few have been reported, such as skin rashes, sporadic reports of changes in hematological parameters, minor changes in liver transaminases, and reversible encephalopathy.19,20 Use of cephalosporins might also result in disturbances in the gut flora (eg, selection of Clostridium difficile).21 Although the therapeutic interval for cefuroxime appears to be wide, dose individualization is suggested on the basis of renal function.22 The recommended dosing strategy at Uppsala University Hospital involves 4 dosing categories, as given in Table I.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The methodology used for estimation of dosing strategies has been described previously4,5 and involves several foundations: (1) a population PK model and a description of covariate distributions in the target population, (2) the definition of the aim with treatment in terms of target and risk function, (3) the estimation procedures including constraints involved, and (4) an assessment of estimated dosing strategies. This section will describe the issues necessary to consider on an individual basis.
Description of the Target Population
This investigation was aimed at establishing a dosing strategy for an adult population with bacterial infection treated with cefuroxime. A previously developed population PK model based on 97 cefuroxime-treated patients with creatinine clearance ranging from 6.5 to 115 mL/min was used for the description of the PK rate of cefuroxime in the target population.23 In this model, Cystatin C was a covariate for clearance, but for the purpose of this dose estimation, Cystatin C was substituted with creatinine clearance (CLcr) calculated by the Cockcroft and Gault formulae,24 and new parameter estimates were estimated (Table II). Based on empirical covariate distributions (body weight and CLcr) descriptive of the target population and the modified PK model, individual PK estimates for one large population (N = 5000) were simulated to be used during the estimation of dosing strategies. The PK parameters were constrained within ±3 standard deviations of the unexplained interindividual variability about the expected values based on CLcr for CL and WT for V. Data for the empirical covariate distributions of body weight and CLcr were obtained from 110 consecutively registered cefuroxime-treated hospitalized adult patients. The characteristics of the distributions from these patients are described in Table III.
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General model. The dose estimation was performed using the underlying general model
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i is the individual deviation from Target, that is, the deviations that are minimized according to the risk function during the estimation. The risk function describes how serious the deviation (i) from Target is considered, and examples are quadratic risk functions on the linear (RLIN) and log (RLOG) scale described in the second equation. The optimal dosing strategy was defined as the one minimizing the deviations from Target overall according to the defined risk function (ie, the dosing strategy that minimized the risk function).
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Target values. As stated, one part of the target (ie, the aim of treatment from an efficacy point of view) was to expose the individuals to concentrations above MIC for at least 50% of the dosing interval; thus, the target value was set to 50%. To calculate this value, the MIC must be defined and is part of the definition of the target. In this work, the MIC was set to a fixed value during the estimation. The fixed MIC value was chosen in relation to MIC distributions for 2 different species of bacteria representing typically infecting pathogens, E coli and S pneumoniae. The time during which cefuroxime concentrations were above MIC (T>MIC) was calculated for each individual during the minimization, as a function of the individual simulated PK parameters, the fixed MIC value, and the estimated dosing strategy. It was assumed that cefuroxime bound to serum proteins is inactive and that reported MIC values represent unbound concentrations. Therefore, the target concentration was corrected for fraction unbound that was assumed to be 65%.9,25 For each individual, the percentage of the dosing interval with concentrations above MIC (%T>MIC) was calculated as %T>MIC = 100 • T>MIC/estimated dosing interval.
The second part of the target, amount of drug administered, was taken into account when the efficacy target was reached, that is, when the individual prediction of %T>MIC was greater than 50%. In that situation, the target was switched to the relative amount of drug administered in excess to reach %T>MIC = 50% on an individual level (hereafter called drug in excess), and this target was set to the value 0, meaning that administration of a drug amount resulting in %T>MIC = 50% yields no risk. Drug in excess was obtained according to
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Dose,i is the dosing interval resulting in %T>MIC = 50% for each dose size for each individual in the simulated population and is the estimated dosing interval. Accordingly, an estimated dosing interval shorter than Dose,i would result in giving drug in excess.
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50%) were penalized according to a quadratic function on the log scale. When %T>MIC > 50%, predictions with respect to drug in excess were penalized by a quadratic function on a linear scale. The 2 different penalties were weighed so that %T>MIC = 25% gave the same penalty as the administration of 100% drug in excess. The risk function (RF1) is described graphically in Figure 1. An expanded risk function (RF2) was developed for situations in which the target T>MIC = 50% is reached but the estimated dosing interval becomes very long (eg, 48 hours) for the subpopulations of patients with low renal function. This may increase the risk for regrowth of bacteria, as the time the patient is exposed to concentrations below MIC is considerable. Therefore, RF2 was constructed to include an added quadratic penalty on the linear scale when the individual was exposed to a concentration below MIC for longer than 4 hours per dosing interval. This penalty was weighted so that 6 hours below MIC resulted in the same penalty as %T>MIC = 25% (Figure 1).
Estimation of the Dosing Strategy
The dosing strategies estimated for cefuroxime assume intravenous bolus administration and that only a discrete number of dose sizes (250, 750, and 1500 mg) are available. A dosing strategy consists of the dose size(s), the dosing interval(s), and the creatinine clearance cutoff values (CO) at which the dose rate should be increased or decreased. In this study, a series of dosing strategies individualized on the basis of CLcr, composing up to 5 dosing categories, were estimated. In the estimations, the dosing intervals and the COs were the dosing aspects estimated, while the dose sizes were fixed. For each dose size, dosing strategies with 2, 3, and 4 categories were estimated (corresponding to the estimation of 1, 2, and 3 COs). Alternative dosing strategies were used when 2 dose sizes were used in the same estimation. All dosing strategies were estimated using the following fixed MIC values: 0.25, 1, 8, and 16 mg/L. The dose size was fixed to 250 or 750 mg for the 2 lower MIC values and to 750 or 1500 mg for the 2 higher MIC values. The estimation was a stepwise search in which the COs were restricted to take on values that were multiples of 10 mL/min CLcr values, as described previously.5 For each stepwise search, the estimation resulting in the lowest objective function value was considered the best dosing strategy.
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Assessment of Estimated Dosing Strategies
To assess whether an estimated dosing strategy was sufficient and to compare dosing strategies, evaluations related to the target definitions were performed as follows. The distribution of %T>MIC and, when estimated dosing intervals were long, the distribution of the time of drug exposure below MIC were obtained for the simulated population to evaluate the dosing strategies from the efficacy viewpoint. Similarly, the distribution of drug in excess was calculated to judge the nonbeneficial side of cefuroxime treatment. The distributions of these 3 variables were calculated using wild-type MIC distributions for 2 different species of bacteria representing typically infecting pathogens, E coli and S pneumoniae. In the calculations, each individual in the simulated population was randomly assigned 1 MIC value from each of the MIC distributions. The wild-type MIC distributions for E coli and S pneumoniae were obtained from the EUCAST database27 based on 88608 and 25883 reported strains, respectively. The MIC distributions are displayed in Figure 2.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Estimated Dosing Strategies: General Findings
Generally, increasing the fixed MIC value in the dosing strategy estimation resulted in shorter estimated dosing intervals, given the same dose size. Furthermore, the consequence of using the lower dose size compared with the higher dose size was shorter dosing intervals. Dosing strategies involving 2 different dose sizes did in no case result in a significant benefit compared with dosing strategies with only 1 dose size. It was possible to estimate dosing schedules for all tried settings, but it was a clear difference in the assessment of the various strategies depending on the wild-type MIC distribution used. Therefore, the remaining part of the result section is organized with respect to dosing strategies evaluated for each of the 2 distributions used in the assessment of the dosing strategies.
Dosing Strategies Evaluated With Respect to E coli Infections
Using the fixed MIC value 8 mg/L and 750 mg in the estimation resulted in a large proportion of individuals exposed to %T>MIC < 50%. This proportion diminished and the distribution of individuals below target was shrunken toward the target when the number of dosing categories was increased; that is, fewer individuals were exposed to very low %T>MIC with an increasing number of COs (Figure 4). Conversely, the proportion of individuals who were given drug in excess increased when the proportion of individuals below target decreased, that is, with an increase in the number of COs (Figure 4). Using the higher dose size (1500 mg) resulted in an even larger proportion of individuals with %T>MIC < 50% (results not shown).
When the fixed MIC value was increased to 16 mg/L and the 750-mg dose size was used, good target attainment was obtained with respect to %T>MIC < 50%, but the estimated dosing intervals were very short for patients with good renal function (ie, 3 hours, results not shown). Using the 1500-mg dose size resulted also in only a small proportion of the individuals exposed to %T>MIC < 50%, and consequently, a large proportion was exposed to drug in excess (Figure 5). In accordance with the results for MIC 8 mg/L, by increasing the number of COs, the width of the distribution of %T>MIC and drug in excess decreased. For all dosing strategies, and in particular when using 4 dosing categories (3 COs), the dosing interval for the patients with best renal function was short (Table IV) but longer than for the 750-mg dose size.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The estimation of the dosing schedule involves a number of critical definitions. One of them is defining the aim of treatment, which is a prerequisite for any method employed to establish a dosing strategy. In a simple situation, dosing is to be calculated for a single patient with known PK characteristics; settlement of a value of the chosen target (eg, a steady-state concentration of x units) and the appropriate dosing for the individual (given known PK parameters) can be calculated. In the approach presented here, what is needed is not only specifying the value of the target but also defining how seriously to judge a deviation from the target expressed quantitatively in a risk function. From the efficacy perspective, we aimed in our estimations to establish a dosing strategy resulting in %T>MIC = 50%, on the basis that dosing where %T>MIC < 50% results in less effective killing of bacteria and dosing where %T>MIC > 50% does not increase the killing. In the alternative risk function, we added consideration of the duration of continuous time intervals below the MIC. For cefuroxime, concentration-dependent toxicity is limited, and it can be argued that using a high enough dosing strategy resulting in all patients' reaching the efficacy target would be appropriate. However, from both an economical and an ecological/resistance perspective, we also considered minimizing the amount of drug administered in excess to reach the efficacy target. A major difficulty in the construction of the risk function was to weight the aspects against each other. The choices made should preferably have a scientific basis but will also contain value judgments, as exemplified in this study. If dosing drug in excess would have been considered worse than treating below the efficacy target, the risk functions should have been defined accordingly, and dosing strategies with longer dosing intervals and/or lower dose sizes would have been estimated in that situation. The main purpose of this work was to illustrate the approach of estimating optimal dosing strategies based on data-based models and decision-based risk functions.
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During development of new antibiotics, there is often a limited knowledge of the MIC distribution for the population of pathogens that is intended to be treated. To resemble a drug development situation, we therefore chose to use a fixed MIC value for calculation of %T>MIC and T>MIC, rather than using the available distribution of MIC values in the estimation of the dosing strategies. If the distribution of MIC values is not known at early stages in drug development, it will be necessary to use a fixed MIC value based on the higher values of MIC for the species pathogen that is the target of the antibiotic treatment. Fixing the MIC to a value not representative of the intended MIC population will of course end up in a suboptimal dosing strategy. We employed several MICs for each pathogen of interest and evaluated the dosing strategies with the MIC distributions. Using an MIC of 16 mg/L for E coli can be considered as estimating a highest dose rate required for the population. It is expected that the dosing intervals estimated applying an E coli MIC distribution would be longer compared with using a fixed value of 16 mg/L as the average MIC is lower in the distribution. The estimate will, however, also be dependent on the shape of the MIC distribution.
However, to be able to calculate target attainment, as we have defined it, it is necessary to have a representative distribution of MIC values. In our example, we used the wild-type distribution from EUCAST. The number of reported strains in the database is very high, and it is representative of the sensitivity of bacteria causing infection treated with cefuroxime in Sweden. If treatment is intended for resistant species not within the wild-type MIC distribution, it will be necessary to use another distribution. If a representative MIC distribution does not exist, the target assessment will have to be done according to deviations from the target using the fixed MIC value and the practicality of the dosing strategy.
When comparing different estimated dosing strategies, it will be necessary, once again, to weigh the pros and cons. The risk of suboptimal treatment has to be compared with the risk of side effects and number of dosing categories. A predefined criterion could be chosen to evaluate whether a dosing strategy is successful (ie, no more than X individuals should have %T>MIC = Y%). Instead of using a predefined criterion, we chose to look at the distributions of deviations from target. This makes it possible to evaluate more aspects of the dosing strategy. Not only the total number of individuals below a specific target value but also how the deviations are distributed can be considered. This might occur in a situation in which a small number of extreme deviations have to be weighed against a large number of small deviations from the target. By comparing the different distributions, it is possible to evaluate how much is gained by increasing the number of dosing categories. The fewer dosing categories, the easier in clinical praxis, but still, as many individuals as possible should have optimal treatment. What also needs to be considered is the practicality of the dosing intervals; that is, an integer number of doses should be given on a daily basis.
By using 2 different MIC distributions for assessment of target fulfillment, our results indicate that different dosing schedules could be used depending on the infecting pathogens. If the species of the infecting pathogen is known (and the distribution of MIC values it originates from) or, even better, if the MIC value of the infecting pathogen is known, the dosing could be individualized not only based on renal function but also based on the sensitivity to the drug of the infecting pathogen.
The assessment of the dosing strategies indicates that the recommended dosing of cefuroxime (Table I) might be too low for treatment of infections caused by E coli. The estimated dosing interval considered to be sufficient for the dosing strategy is much shorter than the one presently used. However, reducing the dosing intervals is impractical, and another option would be to consider other antibiotic treatment. For infections caused by S pneumoniae, our results indicate that a dosing strategy comprising only 2 dosing categories with lower dose rates than those used at present (Table I) would be sufficient. In addition, the results indicate that an even lower dose size than 250 mg could possibly be used for infections caused by S pneumoniae and still sufficiently reach the efficacy target as defined in this work.
Financial disclosure: None declared.
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