DOSE–EFFECT RELATIONSHIPS

2. DOSE–EFFECT RELATIONSHIPS

2.1. The MIC

The major parameter that has been used for several decades as a measure of susceptibility of a microorganism to a drug is the MIC. However, in itself the MIC is not very informative: The MIC is determined at static concentrations, usually in a twofold series of dilutions and is read after 18–24 hr, thus at a spe- cific point in time. The MIC has, however, been shown to be a reasonably reproducible measure of activity of an antimicrobial agent against a micro- organism (EUCAST, 2003), although methods to determine the MIC vary slightly (Andrews, 2001; NCCLS, 2002).

Conversely, in vivo concentrations are not static but decline over time. Furthermore, it is not only the effect of an antimicrobial after 18–24 hr that one is interested in, but primarily the effect of a drug over time in relation to the concentration–time profile of the drug in vivo. As a consequence, some sort of relationship between the MIC as measured in a test tube has to be correlated to the in vivo effect as a function of the concentration–time profile and/or dosing regimen of the antimicrobial.

Impact of Pharmacodynamics on Dosing Schedules 389

2.2. Concentration–time curves and the PK/PD index

The concentration–time curve of a drug possesses two major characteris- tics: the peak concentration (C max ) and the area under the concentration–time curve (AUC) (Figure 1). Both these pharmacokinetic parameters can be related to the MIC of a microorganism by determining the ratio between the two to obtain pharmacokinetic/pharmacodynamic (PK/PD) indices (Mouton et al., 2002a). Thus the AUC/MIC ratio and the Peak/MIC ratio are obtained. A third important PK/PD characteristic of the drug with respect to the microorganism is the time the concentration of the antimicrobial remains above the MIC of the microorganism (T ⬎MIC ). This latter value is usually expressed as a percentage of the dosing interval over 24 hr. By using different dosing regimens in animal models of infection and in in vitro pharmacokinetic models, by varying both the frequency and the dose of the drug it has been shown that there exists a relationship between a PK/PD index and efficacy. The efficacy is usually expressed as either the decrease or increase in the number of bacteria with respect to the initial inoculum (at the start of treatment) as a function of the PK/PD index. It has been shown that this efficacy measure correlates well with survival (Andes and Craig, 2002). In general, two patterns of activity are recognized: Antimicrobials showing a clear relationship between AUC and efficacy and those where efficacy is correlated to the time the concentra- tion remains above the MIC, T ⬎MIC . An example is shown in Figure 2 for levofloxacin and ceftazidime. For levofloxacin there is a clear relationship between AUC and effect while there is virtually no relationship between T ⬎MIC and efficacy, while for ceftazidime the T ⬎MIC is correlated with effect.

PEAK

AUC

MIC TIME > MIC

Figure 1. Diagram of a concentration–time curve showing the pharmacokinetic parameters Peak (or C max ) and AUC. The PK/PD indices are derived by relating the pharmacokinetic parameter to the MIC: AUC/MIC, C max /MIC, and T ⬎MIC .

390 Johan W. Mouton

t 24 hrs ha 6

4 CFU/T hi 2

24-hr AUC/MIC (h)

Peak/MIC

Time Above MIC (%)

10 9 t 24 hrs 8 g ha 7 6 5

CFU/T hi 4 g 10

Time Above MIC (%) Figure 2. Relationship between T ⬎MIC , AUC, and Peak of levofloxacin (upper) and cef-

24-hr AUC/MIC (h)

Peak/MIC

tazidime (lower) in a mouse model of infection with S. pneumoniae as obtained by various dosing regimens and efficacy expressed as cfu (colony forming units). The best relationship is obtained with the AUC for levofloxacin and T ⬎MIC for ceftazidime. Reproduced from Andes and Craig, 2002.

Since the pharmacokinetic parameters describe the concentration–time profile of the drug, and the MIC is a measure of the activity of the drug, another way to look at the PK/PD index is normalizing the relationship between concentration–time profile and effect.

2.3. The sigmoid dose–response curve

As can be observed from Figure 2, the relationship between PK/PD index and effect can be described by a sigmoid curve. The model most often used to

Impact of Pharmacodynamics on Dosing Schedules 391 describe this relationship is the E max model with variable slope or Hill equa-

tion, where the effect E ⫽ E ⫻ EI g /(EI g ⫹I max g 50 50 ). The EI 50 is the PK/PD index necessary to obtain 50% of the maximum effect, I is the PK/PD index value, and g is the slope factor. Focusing on quinolones, this relationship has now been demonstrated in numerous studies. Observations in vitro (Lacy et al., 1999; Lister, 2002; Lister and Sanders, 1999a, b; Madaras-Kelly et al., 1996), animals (Andes and Craig, 1998; Bedos et al., 1998a, b; Croisier et al., 2002; Drusano et al., 1993; Ernst et al., 2002; Fernandez et al., 1999; Mattoes et al., 2001; Ng et al., 1999; Onyeji et al., 1999; Scaglione et al., 1999) and clinical studies (Ambrose et al., 2001; Forrest et al., 1993, 1997; Highet et al., 1999; Preston et al., 1998) have shown a clear relationship between AUC/MIC ratio and effect and the results are fairly consistent. Importantly, the AUC/MIC values needed to obtain a certain outcome is similar for the various quinolones. It has to be emphasized here that this is true for the free fraction of the drug, that is, non-protein bound fraction, only (Cars, 1990; Liu et al., 2002).

Figure 3 shows five characteristics of the sigmoid relationship in relation to the efficacy parameter often used to characterize the potency of the drug. Apart from the minimum (or no) effect and the maximum effect, these are the static effect, the 50% effect and the 90% of E max values. The PK/PD index

values correlating with these effects are the EI s , EI 50 , and EI 90 , respectively. The static effect is where the number of bacteria remaining after treatment is equal to the initial inoculum. Both the static effect and the EI 90 are applied as an effect measure—for various practical purposes the 100% effect is not suitable to use. The EI 50 is, since it is in the steepest part of the curve, most sensitive to changes and is often employed to show differences between treat- ment effects.

10 8 no effect

static effect (inoculum) 6 50% E max

log cfu 4 90% E max 2 100% E max

log (auc) levofloxacin

Figure 3. Diagram showing various characteristic effect levels of a sigmoid dose–response relationship, in this example levofloxacin based on data from Scaglione et al., 1999.

392 Johan W. Mouton

2.4. Determination of clinical breakpoints for susceptibility testing using the PK/PD index

The relationship between PK/PD index value and effects can be used to determine clinical breakpoints, presuming that these distinguish between bac- teria that can likely be treated with a commonly used dosing regimen and those that can not. If the dosing regimen commonly used is known, the AUC and other pharmacokinetic parameters can easily be estimated for the average patient from pharmacokinetic studies available. From the PK/PD index–effect

relationship, the EI s , EI 50 , and EI 90 are identified and the only unknown para- meter in the equation is (taking the EI 90 as an example) the MIC; EI 90 ⫽ AUC/MIC or, to put it differently, MIC ⫽ AUC/EI 90 . This MIC would be

a reasonable estimate of the clinical breakpoint. Higher MICs than this break- point would result in lower AUC/MIC ratios and thus have a lower probability of successful treatment (resistant) while infections with microorganisms with lower MIC values would have a higher chance of successful treatment (susceptible).

The debate that ensues, is whether to apply the EI s or the EI 90 as a parame- ter to settle on the S breakpoint. Both have their advantages and disadvantages. The argument to use the EI 90 is that, since the objective of treating patients is to treat them optimally, one should always aim for an EI 90 . On the other hand, in non-immunocompromised patients and/or non severe infections, the EI s is probably as good as the EI 90 . Whichever of these two is used, what is clear and obvious is that this relationship can be used to determine breakpoints and that this also provides a method or system where the different quinolones are treated equally in the sense that their breakpoints are consistent with each other (Mouton, 2002; Turnidge, 1999). The same argument, of course also applies to other classes.

From these arguments, it is obvious that the breakpoint is dependent on the dosing regimen given. If a certain PK/PD index value is desired to obtain a cer- tain effect, this is dependent on both the PK part and the MIC part of the ratio. Since for the same strain the MIC is a constant, the clinical breakpoint is entirely dependent on the dosing regimen. An example is provided in Figure 4 for amoxicillin/clavulanic acid. The per cent of T ⬎MIC of amoxicillin over

24 hr is depicted here as a function of the MIC for four different dosing regimens (Mouton and Punt, 2001). The value needed for efficacy in this example is taken as 40%. Thus, drawing a horizontal line at the 40% level, the crossing point with the T ⬎MIC function indicates the clinical breakpoint for that specific dosing regimen. It is clear from this figure, that the breakpoint value obtained is dependent of the dosing regimen and this is one of the reasons breakpoints differ between countries (there are other reasons, these are discussed below).

Impact of Pharmacodynamics on Dosing Schedules 393

MIC mg/L

Figure 4. Diagram showing the relationship between T ⬎MIC and MIC of amoxicillin for four different dosing regimens of amoxicillin–clavulanic acid to demonstrate that the clinical breakpoint is dependent on the dosing regimen. Assuming that 40% T ⬎MIC is the time of the dosing regimen needed for effect, the breakpoint for the 875 mg q12 h is 2 mg/L while for the dosing regimen of 500 mg q6 h it is 8 mg/L. Based on Mouton and Punt, 2001.

2.5. Monte Carlo simulations

In the discussion above, the AUC/MIC or T ⬎MIC was used as a reference value to determine tentative PK/PD breakpoints. However, the values used to calculate the breakpoint were mean values of the population. Thus, approxi- mately half the population will maintain a PK/PD index lower than this value (for instance because of a higher than average clearance) and the other half will have a higher value. However, when PK/PD indices are being used as a value for the determination of breakpoints that are used to predict the proba- bility of success of treatment as discussed above, this should be true not only for the population mean, but also for each individual within the population, also that part of the population with a higher elimination. An example is given in Figure 5. The figure shows the proportion of the population reaching a certain concentration of ceftazidime after a 1 g dose. It is apparent that there are individuals with a T ⬎MIC of 50%, while others have, with the same dosing regimen, a T ⬎MIC of more than 80%. It is, in particular, those individuals who have lower values than average that one should be concerned about, since if they have infection with a microorganism with an MIC at the breakpoint level, it may be reported as susceptible, while the PK/PD index value for those par- ticular individuals is less than optimal. Thus, when using the relationship between PK/PD index and efficacy, the breakpoint chosen should take this interindividual variation into account. To that end, Drusano et al. suggested an

integrated approach of population pharmacokinetics and microbiological susceptibility information (Drusano et al., 2000, 2001) by applying Monte Carlo simulations. This is a method which takes the variability in the input variables into consideration in the simulations (Bonate, 2001) and thereby gen- erates slightly different pharmacokinetic parameters concordant to the varia- tion in the population. Thus, PK/PD index values are generated not only for the population mean, but for every possible individual in the population. This is subsequently used to determine the breakpoints, not using the mean PK/PD index of the population but also taking into account the distribution. This approach has been used now by several authors (Ambrose and Grasela, 2000; Drusano et al., 2001; Montgomery et al., 2001; Mouton et al., 2002b; Nicolau and Ambrose, 2001). An extensive discussion on this subject can be found in Mouton (2003); it is mentioned here because it may affect breakpoint values in some cases.

From the discussion above, two important conclusions have to be drawn. The first is, as discussed in the last section, that the clinical breakpoint value is dependent on the dosing regimen. The second one is that, when different

394 Johan W. Mouton

Figure 5. Simulation of ceftazidime after a 1 g dose using data from (Mouton et al., 1990). The greyscale indicates the probability of presence of a certain concentration. Due to inter- individual variability, some individuals in the population will have a T ⬎MIC 50%, while others will have a value of 80%. The population mean is in the middle of the black area. Reproduced from Mouton, 2003.

Impact of Pharmacodynamics on Dosing Schedules 395 agents within a class show more or less similar dose–effect relationships, the

breakpoints of these agents relative to each other should be consistent.