Hollow-Fiber Pharmacodynamic Studies and Mathematical Modeling To Predict the Efficacy of Amoxicillin for Anthrax Postexposure Prophylaxis in Pregnant Women and Children

Abstract

Amoxicillin is considered an option for postexposure prophylaxis of Bacillus anthracis in pregnant and postpartum women who are breastfeeding and in children because of the potential toxicities of ciprofloxacin and doxycycline to the fetus and child. The amoxicillin regimen that effectively kills B. anthracis and prevents resistance is unknown. Fourteen-day dose range and dose fractionation studies were conducted in in vitro pharmacodynamic models to identify the exposure intensity and pharmacodynamic index of amoxicillin that are linked with optimized killing of B. anthracis and resistance prevention. Studies with dicloxacillin, a drug resistant to B. anthracis beta-lactamase, evaluated the role of beta-lactamase production in the pharmacodynamic indices for B. anthracis killing and resistance prevention. Dose fractionation studies showed that trough/MIC and not time above MIC was the index for amoxicillin that was linked to successful outcome through resistance prevention. Failure of amoxicillin regimens was due to inducible or stable high level expression of beta-lactamases. Studies with dicloxacillin demonstrated that a time above MIC of ≥94% was linked with treatment success when B. anthracis beta-lactamase activity was negated. Recursive partitioning analysis showed that amoxicillin regimens that produced peak concentrations of <10.99 μg/ml and troughs of >1.75 μg/ml provided a 100% success rate. Other amoxicillin peak and trough values produced success rates of 28 to 67%. For postpartum and pregnant women and children, Monte Carlo simulations predicted success rates for amoxicillin at 1 g every 8 h (q8h) of 53, 33, and 44% (30 mg/kg q8h), respectively. We conclude that amoxicillin is suboptimal for postexposure prophylaxis of B. anthracis in pregnant and postpartum women and in children.

INTRODUCTION

Bacillus anthracis is the bacterium that causes cutaneous, gastrointestinal, and inhalational anthrax (1). Historically, the mortality for anthrax ranges from <1% for appropriately treated cutaneous anthrax to 89% for inhalational anthrax (2–4). In 2001 anthrax spores were disseminated in envelopes through the U.S. postal system, causing 11 cases of inhalational anthrax and a 45% mortality rate (1). Given the severity of disease caused by B. anthracis, the guidelines published by the Advisory Committee on Immunization Practices (ACIP) recommend ciprofloxacin and doxycycline as first-line antibiotics for postexposure prophylaxis of anthrax for children and for adults who are not allergic to these medications. This includes women who are pregnant and postpartum women who are breastfeeding (5).

When prescribed, these antibiotics are to be administered for 60 days to ensure that inhaled B. anthracis spores residing in the human body are killed as they germinate. However, ciprofloxacin can cause cartilage and joint malformations in immature dogs and may increase the intracranial pressure in animal newborns, and it thus is believed to have the potential to cause similar problems to the human fetus and in children (6, 7). The tetracyclines may retard the normal development of teeth and the growth of the long bones in the fetus and child, although doxycycline may have a lower potential for causing these effects (6–9). Importantly, the safety of long treatment courses of ciprofloxacin and doxycycline for the fetus has not been established (5).

Many strains of B. anthracis are susceptible to amoxicillin. No efficacy or safety data exist for the use of amoxicillin for postexposure prophylaxis of anthrax. However, extensive clinical experience in the treatment of community-associated bacterial infections has shown amoxicillin to be safe to the fetus and child. Hence, the ACIP guidelines recommend switching ciprofloxacin and doxycycline to amoxicillin as postexposure prophylaxis of anthrax in children and pregnant and breastfeeding women if the bacterium is proven to be susceptible to penicillin and the individual is not allergic to this antibiotic class (5).

If used as postexposure prophylaxis for inhalational anthrax, the ACIP guidelines recommend that amoxicillin be administered to pregnant and breastfeeding women at doses of 500 mg every 8 h (q8h). For children who weigh ≥40 kg, the amoxicillin regimen is the same as for adults, while children who weigh <40 kg would be prescribed amoxicillin at 45 mg/kg/day given orally as 3 divided doses (up to 500 mg per dose) (5).

The dosages and schedule of administration of amoxicillin that are recommended for pregnant women, postpartum women who are breastfeeding, and children were derived with consideration of the pharmacokinetic (PK) data available for nonpregnant adult and child populations, several published MIC distributions of amoxicillin for B. anthracis, and the conservative but unproven assumption that amoxicillin efficacy and the prevention of emergence of amoxicillin resistance by B. anthracis would be achieved by maintaining the concentration of amoxicillin in the sera of patients at or above the MIC for the infecting bacterium for 75 to 100% of each dosing interval (5, 10).

There are several potential problems with these treatment recommendations. First, the recommended amoxicillin regimen of 500 mg given every 8 h for pregnant women and postpartum women who are breastfeeding did not take into account the differences in absorption, distribution, and elimination of amoxicillin that might be seen in these women compared with nonpregnant adults (11–15). These pharmacokinetic differences often result in a faster elimination of drugs from pregnant and postpartum women than from other adults. Consequently, drug regimens that may be efficacious in nonpregnant adults may fail in pregnant and postpartum women. Second, although the pharmacodynamic (PD) index predictive of efficacy for the penicillin class of antibiotics for infections caused by Staphylococcus aureus, Streptococcus pneumoniae, Pseudomonas aeruginosa, and other pathogens is time above MIC (T>MIC) (16), the pharmacodynamic index for amoxicillin and other beta-lactam antibiotics that is predictive of optimized kill of B. anthracis is unknown. Also, the pharmacodynamic index linked with prevention of emergence of resistance during therapy for amoxicillin has never been determined. It is possible that pharmacodynamic indices other than T>MIC (i.e., area under the curve [AUC]/MIC ratio or peak [maximum concentration {C_max}]/MIC ratio) are predictive of optimized killing of B. anthracis by amoxicillin and with prevention of emergence of resistance. In a previous in vitro hollow-fiber (HF) system study, for example, we showed that the killing of Yersinia pestis (the bacterium that causes plague) with the fluoroquinolone antibiotic moxifloxacin was predicted by the AUC/MIC ratio and prevention of emergence of resistance was linked with the C_max/MIC ratio (17). For B. anthracis, optimized kill of the moxifloxacin-susceptible populations was also predicted by the AUC/MIC ratio. However, prevention of resistance to moxifloxacin for B. anthracis was linked to T>MIC (18). Furthermore, the efficacy of beta-lactam antibiotics against P. aeruginosa is predicted by T>MIC. However, Tam et al. (19) showed that prevention of resistance to the beta-lactam antibiotic meropenem in P. aeruginosa was linked to a trough/MIC ratio of ≥6.2 and not to T>MIC.

If the pharmacodynamic index predictive of the killing of B. anthracis and of prevention of emergence of resistance for amoxicillin is not T>MIC, the dosing strategies for amoxicillin that would optimize the efficacy of postexposure prophylaxis against anthrax may be completely different from those that are currently recommended. Furthermore, even if the pharmacodynamic index linked with optimal killing of the bacterium and with prevention of selection of resistance for amoxicillin was T>MIC, application of Monte Carlo simulations to single-dose pharmacokinetic studies conducted by Andrew et al. (11) suggested that amoxicillin given orally at 500 mg every 4 h and not every 8 h would be necessary to achieve a T>MIC value of 75 to 100% of the dosing interval for pregnant and postpartum women. It would be difficult, if not impossible, for a person to adhere to a 60-day course of a drug that was administered on a 4-hourly basis. If T>MIC did predict amoxicillin efficacy and resistance prevention, this drug would still have potential clinical utility if the maximal drug effect was seen with T>MIC values that were less than 75 to 100% of each dosing interval. For S. aureus, for example, maximal kill is achieved when beta-lactam antibiotic concentrations achieve a T>MIC value of 40 to 50% of the dosing interval (20).

Without specific knowledge of the pharmacodynamic indices and exposure intensities for amoxicillin linked with optimized killing of the susceptible population of B. anthracis and with prevention of emergence of resistance, it is impossible to determine the dosage and frequency of administration of amoxicillin that would offer effective postexposure prophylaxis for anthrax for any patient population.

In this project, an in vitro pharmacodynamic model was used to determine the exposure intensity and pharmacodynamic index for amoxicillin that were linked with optimized killing of B. anthracis and with prevention of emergence of resistance during therapy. Studies with dicloxacillin, a drug that is not hydrolyzed by the type I beta-lactamase that is produced by Bacillus spp. (21, 22), were used to delineate the impact of beta-lactamase production by the bacterium in determining the exposure intensity and pharmacodynamic index of amoxicillin that are linked with the killing of B. anthracis and resistance prevention. Then, by applying Monte Carlo simulations to pharmacokinetic data reported in the literature for amoxicillin in pregnant and postpartum women and in children, the predicted efficacies of commonly prescribed amoxicillin regimens for postexposure prophylaxis of anthrax in these patient populations were assessed.

MATERIALS AND METHODS

Antibiotics.

Amoxicillin, the beta-lactamase inhibitor clavulanate, and dicloxacillin were purchased from Sigma-Aldrich, Inc. (St. Louis, MO).

Bacterial strain and suspension preparations.

Stocks of the spore-forming ΔSterne strain of B. anthracis were stored at −80°C. The bacterial suspensions were prepared using two methods.

(i) Direct-suspension method (“standard CLSI method”).

The direct-suspension method was described by the Clinical and Laboratory Standards Institute (CLSI) (23) for susceptibility testing for B. anthracis and other bacteria. Colonies of B. anthracis grown overnight at 35°C on blood agar plates were directly suspended in cation-adjusted Mueller-Hinton broth (MHB). The suspension was vortexed. The optical density at 630 nm (OD₆₃₀) was measured, and the suspension was adjusted to a density of 1 × 10⁶ CFU/ml before it was added at 1:1 (vol/vol) to antibiotic-containing MHB for microdilution broth susceptibility testing and used for agar dilution MIC determinations at 10⁴ CFU/spot. Heat shock studies (with incubation of the suspension at 65°C for 30 min, which kills vegetative bacteria but not spores) (24, 25) showed that 90% of the B. anthracis in suspension were vegetative bacteria and 10% were spores.

(ii) Ciprofloxacin pretreatment method.

In vitro hollow-fiber (HF) pharmacodynamic infection models permit investigators to examine the effect of fluctuating concentrations of drugs on the killing of a microbe (26, 27). In pilot studies, the concentrations of amoxicillin in HF systems inoculated with B. anthracis suspensions prepared using the standard CLSI method progressively declined over time, presumably due to the beta-lactamase produced by the microbe (see Fig. S1A in the supplemental material).

For the current project, bacterial suspensions for inoculation into the HF systems were prepared using colonies of B. anthracis grown on blood agar for 3 days at 35°C (to enhance spore formation) and incubating them for 48 h in MHB supplemented with 20 μg/ml of ciprofloxacin. This procedure killed the vegetative population, resulting in a B. anthracis suspension that consisted primarily of spores. The spore suspension was washed twice with prewarmed medium to remove the ciprofloxacin and preformed beta-lactamase. The OD₆₃₀ of the spore suspension was measured. The suspension was diluted to the desired concentration with medium and was used immediately. Quantitative cultures of the bacterial suspension before and after heat shock demonstrated that the bacteria inoculated into the HF systems were >90% spores. Pretreating the B. anthracis suspensions with ciprofloxacin enabled us to correctly simulate the targeted concentration-time profiles for amoxicillin within the in vitro infection system (see Fig. S1B in the supplemental material).

Pretreatment of the B. anthracis suspension with ciprofloxacin prior to initiation of amoxicillin is consistent with the clinical recommendation proposed by the ACIP that ciprofloxacin (or doxycycline) be used as initial postexposure prophylaxis for anthrax in pregnant and breastfeeding women and in children and switched to amoxicillin after the B. anthracis strain is found to be susceptible to penicillin (5).

Susceptibility testing.

The MICs of amoxicillin, amoxicillin-clavulanate (at a 2:1 ratio), and dicloxacillin for the ΔSterne strain were determined using the microdilution broth technique in MHB specified by CLSI (23) and by an agar dilution method on Mueller-Hinton agar (MHA). The bacterial suspensions were prepared by the “standard CLSI method” and with ciprofloxacin pretreatment. The OD₆₃₀ of the suspensions was measured, and the bacterial concentration was calculated using a standard curve before the suspensions were diluted to the desired concentrations. The final bacterial concentration was 5 × 10⁵ CFU/ml for the broth dilution studies and 10⁴ CFU/spot for the agar dilution experiments. The concentrations of bacteria in the suspensions were confirmed by quantitative cultures.

CLSI specifies reading the MICs after 16 to 20 h of incubation (23). For susceptibility studies in which the standard CLSI method was used to generate the bacterial suspensions, the broth microdilution MIC values progressively increased from 1 to 32 μg/ml between the 16- and 23-h incubation time points and stabilized thereafter. The broth microdilution and agar dilution MICs did not change between the 16- and 24-h time points when the susceptibility studies were conducted using ciprofloxacin-pretreated bacterial suspensions. Given the instability of the MIC values for amoxicillin between 23 and 26 h of incubation associated with bacterial suspensions prepared using the described “standard CLSI method,” the 24-h MIC values derived using bacterial suspensions prepared by the “ciprofloxacin pretreatment method” were reported for this project for amoxicillin and amoxicillin-clavulanate unless otherwise stated.

Mutation frequency studies.

Mutation frequencies for the ΔSterne strain of B. anthracis in response to 3 times the broth microdilution MIC of amoxicillin were determined on MHA. Three times the broth MIC was chosen because plating a large inoculum of B. anthracis on agar containing 3 times the agar-derived MIC resulted in overgrowth of the culture with wild-type B. anthracis. MIC testing was conducted for colonies of mutants that grew on antibiotic-containing agars.

HF dose-ranging studies for amoxicillin.

The hollow-fiber infection model (HFIM) has been described previously (26, 27). In women in their second and third trimesters of pregnancy and in postpartum women, the mean serum half-lives for amoxicillin were 1.2, 1.3, and 1.6 h, respectively. In healthy volunteers, the mean serum half-lives were 1.0 to 1.6 h, respectively (11, 28–30). The shortest and longest serum half-lives for amoxicillin of 1.0 and 1.6 h were simulated in the HFIMs to characterize the effects of different elimination half-lives on the antimicrobial effects of specific amoxicillin regimens.

For the dose range experiments, 8 to 12 HF cartridges (FiberCell Systems, Inc., Frederick, MD) were inoculated with 15 ml of 10⁷ CFU/ml of ciprofloxacin-pretreated suspensions of B. anthracis. One of the HF arms served as the untreated control. The remaining HF arms were treated with incremental exposures of amoxicillin. The simulated pharmacokinetic profiles were for the free (non-protein-bound) fraction of amoxicillin based on a serum protein binding rate of 20% (29). Amoxicillin was administered on an 8-hourly schedule for 14 days. One of the treatment arms simulated the concentration-time profile for the clinically prescribed regimen of amoxicillin at 500 mg given every 8 h (q8h). Dosages higher and lower than amoxicillin at 500 mg q8h were scaled relative to the free (non-protein-bound) 24-h AUC that was reported in humans who were given amoxicillin at 500 mg q8h (24) (i.e., doubling the dose doubled the free 24-h AUC).

Over the course of the 14-day study, bacterial samples collected from the HF systems were washed twice to prevent drug carryover. The samples were quantitatively cultured on drug-free agar and agar containing 3 times the broth microdilution MIC of amoxicillin to determine the effect of each regimen on total and less susceptible bacterial populations. Three times the broth MIC was used because agar supplemented with 3 times the agar-derived MIC was overgrown with wild-type bacteria due to an inoculum effect.

Over the first 48 h of the experiments, serial samples of broth were collected from the HF systems. The concentrations of amoxicillin in the samples were measured by liquid chromatography-tandem mass spectrometry (LC-MS/MS) to determine the actual concentration-time profiles generated.

The dose range studies were conducted twice for each of the half-lives that were simulated. The doses that were examined in the second study (for each half-life) were selected with consideration of the results of the first experiment.

Assessment of reversible induction and stable overexpression of beta-lactamases by B. anthracis isolates that grew on amoxicillin-supplemented agar plates.

To determine if growth of B. anthracis on amoxicillin-containing agar in the HF studies was due to reversible induction or stable overexpression of beta-lactamases, a portion of individual colonies that grew on amoxicillin-supplemented agar from several of the experiments were passed twice on drug-free agar before the amoxicillin MICs were assessed. The other half of the same colonies that grew on the amoxicillin-supplemented agar were directly passed twice on fresh amoxicillin-containing agar before they were used for susceptibility testing. Reversible induction of beta-lactamase was identified if the portion of a colony that grew on amoxicillin-supplemented agar and passed on antibiotic-free agar had an MIC to amoxicillin that was similar to that of the wild-type isolate while the portion of the same colony that grew on amoxicillin-supplemented agar and was passed on fresh amoxicillin-containing agar had an MIC that was at least 4 times higher than that of the parent strain. If the portions of a bacterial colony that were passed on antibiotic-free agar and on amoxicillin-containing agar had the same MIC (that was at least 4 times higher than that of the wild-type parent strain), that colony was categorized as having stable overexpression of beta-lactamases.

HF dose fractionation studies.

Hollow-fiber (HF) systems were inoculated with 15 ml of ciprofloxacin-pretreated B. anthracis spore suspensions at 10⁷ CFU/ml. The first arm served as the untreated control. Two or more total daily dosages were chosen for dose fractionation based on the results of the dose-ranging studies. These total daily dosages were delivered to HF arms as 2, 3, or 4 equally divided doses every 12, 8, and 6 h, respectively. In some studies, amoxicillin was also delivered as one-sixth of the total daily dose every 4 h.

Over the course of the 14-day experiments, bacterial suspensions collected from the HF systems were quantitatively cultured onto drug-free agar and agar supplemented with amoxicillin to assess the effect of each treatment regimen on the total and less susceptible bacterial populations. The concentrations of amoxicillin in the media were measured over the first 48 h of the experiments by LC-MS/MS to validate that the targeted PK profiles of the drug were simulated.

The dose fractionation studies were conducted twice for each of the amoxicillin half-lives simulated. The regimens examined in the second trial were based on the results of the first trial.

Continuous-infusion dose range studies with amoxicillin.

Two HF studies using continuous infusions of amoxicillin were conducted to further characterize the intensity and pharmacodynamic index for amoxicillin that were linked with treatment efficacy. The continuous-infusion mode of administration was employed because the dose fractionation studies suggested that high peak concentrations of amoxicillin promoted resistance amplification in B. anthracis. Each HF arm was inoculated with 15 ml of 10⁷ CFU/ml of a ciprofloxacin-pretreated B. anthracis spore suspension. At 0 h, each HF system received a bolus of amoxicillin to bring the concentration of drug to the targeted steady-state concentrations, ranging from 0 to 2.5 μg/ml of drug. These concentrations corresponded to 0 to 10 times the broth-derived MIC value for amoxicillin for suspensions of the wild-type strain that were prepared with ciprofloxacin pretreatment (MIC, 0.25 μg/ml). Over the 14-day experiments, bacterial samples obtained from the HF systems were quantitatively cultured onto drug-free agar and agar supplemented with amoxicillin to enumerate the effect of each antibiotic exposure on the total B. anthracis population and on amplification of resistant mutants. The concentrations of amoxicillin in the media were measured to confirm that the targeted PK profiles were achieved.

Dicloxacillin experiments.

Dicloxacillin has microbiological activity against B. anthracis. It also inactivates the type I beta-lactamase that is produced by Bacillus species (21, 22). To characterize the effect of type I beta-lactamase on outcomes of amoxicillin therapy, the following studies with dicloxacillin were conducted.

(i) Broth and agar dilution susceptibility studies: effect of B. anthracis beta-lactamase on MIC values.

Broth microdilution and agar dilution MICs for dicloxacillin and amoxicillin (both with and without clavulanate) were determined with B. anthracis suspensions prepared using “the standard CLSI method” and with ciprofloxacin pretreatment. The MICs were read after 24 and 48 h of incubation at 35°C.

(ii) Stability of amoxicillin and dicloxacillin to B. anthracis beta-lactamase as determined by differences in the rates of degradation of these drugs in broth cultures and in changes in broth-derived MIC values over 96 h.

Broth macrodilution susceptibility studies were conducted in triplicate for amoxicillin and dicloxacillin using B. anthracis suspensions prepared with ciprofloxacin pretreatment. The MICs of each drug were read at 24, 48, and 96 h of incubation at 35°C. At the times that the MIC values were read, a sample of bacterial suspension taken from one of the triplicate sets of test tubes in the drug dilution series was passed through a 0.2-μm mesh syringe filter to remove the microbe from the medium, and the concentration of amoxicillin or dicloxacillin in the filtrate was measured by LC-MS/MS. Samples collected over the 96-h experiment from test tubes containing dicloxacillin or amoxicillin (but without bacteria) were assayed to quantify the rate of spontaneous degradation of the drugs.

(iii) Combined dose-ranging and dose fractionation studies with dicloxacillin.

To characterize the impact of beta-lactamase production on the results of the earlier amoxicillin dose-ranging and dose fractionation studies, two combined dose-ranging and dose fractionation HF studies were conducted in which the concentration-time profiles for the amoxicillin regimens evaluated in the dose fractionation studies described above were simulated using dicloxacillin in place of amoxicillin. In two additional arms, dicloxacillin was administered simulating the free (non-protein-bound) serum concentration-time profiles for the clinical regimens of dicloxacillin at 500 mg q6h and dicloxacillin at 500 mg q4h. For simulation of the clinical regimens of dicloxacillin, a human serum protein binding rate of 95% was used.

Over the course of the 14-day experiment, samples of bacterial suspensions obtained from the HF systems were quantitatively cultured onto drug-free agar and agar supplemented with 3 times the broth microdilution MIC for dicloxacillin to evaluate the effect of each regimen on the total and less drug-susceptible B. anthracis populations. The concentrations of dicloxacillin in the media were measured to confirm that the targeted concentration-time profiles were achieved. These experiments were conducted twice.

Mathematical modeling of the amoxicillin HF study results.

The dose fractionation and dose-ranging hollow-fiber (HF) studies with amoxicillin were conducted to identify the amoxicillin dose intensities and frequencies of administration that were predicted to optimize the killing of B. anthracis and to prevent emergence of resistance to amoxicillin during therapy. The HF studies simulated the longest and shortest half-lives for amoxicillin that were described in the literature among women in the second and third trimesters of pregnancy, women who are 3 months postpartum, nonpregnant adults, and children. The in vitro experiments did not account for the distribution of amoxicillin clearances within these human populations and did not examine the effect on treatment outcomes of the different clearances of amoxicillin in 3 of the 5 patient populations. The HF experiments also did not account for the different volumes of distributions of amoxicillin among the patient populations.

Mathematical models were applied to the data generated from the HF studies to predict the dose-response relationships for the patient populations that had serum half-lives for amoxicillin that fell between the two extremes of amoxicillin serum half-lives and to account for the distribution of clearances and volumes of distributions of amoxicillin that would be found in different patient populations. The PK data for women in their second and third trimesters of pregnancy and for women who were 3 months postpartum were obtained from the clinical PK study conducted by the Women's Health Initiative (11). The PK data for the other populations were obtained from another report (31). The point estimates of mean system volumes were taken into account, producing different peak concentrations. Andrew et al. reported that the populations examined had quite similar system volumes, differing mainly in the variance observed (11). These volumes were larger than those observed in nonpregnant adults.

(i) Population PK analysis.

Population parameter values (traditional two stage) were employed for simulation as presented in the publication by Andrew et al. (11).

(ii) Monte Carlo simulations and target attainment analysis.

The PK parameter values from the study by Andrew et al. (11) and from others for children (31) were employed to perform Monte Carlo simulations. The PK exposure targets for optimized bacterial kill and resistance suppression were identified from the HF studies. The mean parameter vectors and major diagonal covariance matrices from the studies were employed for the simulations. The ADAPT II package of programs of D'Argenio and Schumitzky (32) was employed for the simulations. Both normal and log normal distributions were evaluated. The choice was made depending upon the fidelity with which the mean parameter vector and its variances were recreated by the simulation for each distribution. There were 9,999 subjects simulated for each physiological state and dose examined. Target attainment was calculated as the fraction of simulated subjects for whom non-protein-bound amoxicillin fell within the optimal range as determined from the HF studies.

In order to identify targets for evaluation with the Monte Carlo simulations, the results from each of 60 experimental arms from the dose range and dose fractionation HF studies with amoxicillin were scored as having succeeded (no resistance with progressive bacterial kill) or failed (resistance emerged). We then explored whether the peak/MIC ratio, trough/MIC ratio, or a combination of both was important to identifying regimens that were successful, using a recursive partitioning algorithm, as implemented in SYSTAT for Windows v11 (SYSTAT Software, Chicago, IL). The factors best describing success with their attendant breakpoints were then employed as targets in the Monte Carlo simulation analysis.

The relationship between covariates and the likelihood of regimen failure (resistance emergence) was also explored by employing logistic regression analysis. Covariates were examined univariately. Any covariate having a P value of 0.15 or less was acceptable for exploration as part of a final multicovariate model. Model identification was by the likelihood ratio test (i.e., twice the likelihood difference between the base and the expanded model evaluated against a χ² distribution with the appropriate number of degrees of freedom). The base model was the covariate with the most significant P value. All statistical tests were done with SYSTAT for Windows, v. 11.0, (SYSTAT Software, Chicago, IL).

RESULTS

Amoxicillin susceptibility test results.

In three trials, the 24-h broth microdilution MICs of amoxicillin for the ΔSterne B. anthracis strain were 16 μg/ml for bacterial suspensions prepared using the standard CLSI method and 0.25 μg/ml when the bacterial suspension was prepared with ciprofloxacin pretreatment (see Table S1 in the supplemental material). Over the course of this project, the broth microdilution MICs of amoxicillin for the wild-type B. anthracis strain that were conducted as part of each HF experiment varied significantly (range, 0.125 to >256 μg/ml) for bacterial suspensions prepared using the standard CLSI method. With bacterial suspensions prepared with ciprofloxacin pretreatment, the MICs of amoxicillin were 0.125 to 0.25 μg/ml. Greater than 90% of the MIC values were 0.25 μg/ml. Notably, the 24-h agar MIC of amoxicillin was 0.06 μg/ml, independent of the method used to prepare the bacterial suspension.

Clavulanate decreased the MICs of amoxicillin 32-fold for bacterial suspensions that were prepared using the standard CLSI method (see Table S1 in the supplemental material) but had no effect on the broth microdilution MIC values when the bacterial suspension was prepared with ciprofloxacin pretreatment. The agar dilution MICs for amoxicillin did not change when MIC determinations were conducted alone and together with clavulanate (see Table S1 in the supplemental material).

Mutation frequency determinations.

Mutation frequencies for the parent B. anthracis strain in response to 3 times the broth-derived MIC value of 0.25 μg/ml of amoxicillin ranged from −3.52 to −5.63 log CFU. Mutation frequencies could not be determined with agar supplemented with 3 times the agar-derived MIC of 0.06 μg/ml because the wild-type bacterium overgrew the entire surface of the antibiotic-supplemented agar plate. The use of the higher drug concentration in the plate made the estimate of the mutational frequency conservative.

Results of the two dose range studies in which a 1-h serum half-life of amoxicillin was simulated.

The targeted PK-PD values associated with the simulated free serum concentration-time profiles for amoxicillin at 250 to 2000 mg given every 8 h (q8h) are shown in Table 1. In addition to the standard PD values, the trough/MIC values for individual regimens were calculated.

Table 1.

Targeted PK-PD parameters in the two dose-ranging studies for amoxicillin in which a 1-h half-life was simulated^a

Treatment arm	Total daily dose (mg)	Target half-life (h)	Free AUC/MIC ratio	Free Cmax/MIC ratio	Free trough/MIC ratio	Free T>MIC (%)	Dose-ranging study resultb
							First study	Second study
ΔSterne control	0	NA	0	0	0	0	NA	NA
Amoxicillin (mg) q8h
250	750	1	108.51	13.6	0.21	68.7	Failure	ND
500	1,500	1	165.97	20.8	0.33	81.0	Failure	Success
875	2,625	1	352.35	44.2	0.69	93.7	Failure	Success
1,000	3,000	1	389.38	48.8	0.76	95.8	Failure	Failure
1,250	3,750	1	478.73	60.0	0.94	98	ND	Success
1,500	4,500	1	584.05	73.2	1.14	100	Success	Failurec
2,000	6,000	1	778.74	97.6	1.53	100	Success	ND

^aAmoxicillin was administered on a q8h schedule. The broth microdilution-derived MIC in MHB using a ciprofloxacin pretreated B. anthracis suspension was 0.25 μg/ml. NA, not applicable; ND, not done.

^bFailure was defined as regrowth for the treatment regimen.

^cThe simulated concentration-time profile provided a T>MIC of approximately 21h (or 88% of a dosing interval) for the experimental arm in the second trial.

The targeted concentration-time profiles were well achieved within the HF systems (data not shown). In the first dose range study in which the half-life of 1 h was simulated, amoxicillin regimens with dosages of ≤1,000 mg q8h failed (Fig. 1A and second-to-last column of Table 1) due to amplification of a B. anthracis subpopulation with decreased susceptibility to the treatment antibiotic (Fig. 2). Simulated dosages for amoxicillin of 1,500 and 2,000 mg q8h were successful. However, in the second dose range study, amoxicillin regimens of 500 to 1,250 mg q8h were successful, while 1,000 mg q8h and the highest amoxicillin dosage (1,500 mg q8h) failed (Fig. 1B and last column of Table 1).

Fig 1.

Effect on the total population of amoxicillin regimens examined in two dose-ranging studies in which the drug half-life of 1 h was simulated.

Fig 2.

First dose range experiment for amoxicillin, characterizing the effect of each regimen on the total and resistant populations of B. anthracis. The resistant B. anthracis grew on agar supplemented with 3 times the MIC of amoxicillin.

Treatment failures were due to isolates with inducible beta-lactamase production. These isolates had wild-type agar-derived MICs of amoxicillin of 0.06 μg/ml when the colonies collected from the amoxicillin-supplemented agar were passed on drug-free agar prior to susceptibility testing. When the same colonies that grew on the amoxicillin-supplemented agar plates were first passed on a fresh amoxicillin-supplemented agar plate before they were subjected to susceptibility testing, the MICs for these isolates ranged from 2 to 32 μg/ml.

The results of these two trials were inconsistent, suggesting that outcomes associated with amoxicillin therapy may not be predictable because of the random induction of beta-lactamases in the treatment arms. The subsequent HF experiments were designed to examine this hypothesis.

Dose fractionation studies simulating a serum half-life of 1 h.

The PK-PD values generated in two dose fractionation studies in which the half-life of 1 h was simulated are shown in Table 2. For each trial, the measured concentration-time profiles were within 15% of the targeted values (data not shown).

Table 2.

Targeted PK-PD parameters simulated in two combined dose-ranging and dose fractionation hollow-fiber studies using an amoxicillin half-life of 1 h^a

^aThe MIC of amoxicillin in MHB was 0.25 μg/ml. Shaded rows are for dose range regimens in which amoxicillin was given on a q8h schedule. NA, not applicable.

For the experimental arms in which the amoxicillin dose of 3,000 mg/day was examined, only amoxicillin at 500 mg q4h (the most fractionated regimen) was successful in both trials. The other arms had inconsistent results between the experiments, although the most fractionated regimens (which have the greatest T>MIC and trough/MIC values) were successful in each trial.

For the first trial, in which a dose of 3,750 mg/day was fractionated, the two most fractionated regimens (amoxicillin at 937.5 mg q6h and 625 mg q4h) were successful, while the two least fractionated regimens failed (Table 2, second-to-last column). Failure was due to isolates that had inducible beta-lactamase production and MICs of amoxicillin that were 4 to 64 μg/ml. In the second trial, the results were not interpretable since the most and least fractionated arms were successful while the midfractionated arm failed (Table 2, last column). Some of the arms that failed in the second trial were due to B. anthracis isolates with inducible beta-lactamase production with MICs of amoxicillin of 4 to 32 μg/ml, while other arms failed with outgrowth of isolates that had stable overexpression of beta-lactamases. The latter isolates had amoxicillin MICs of 128 to 256 μg/ml.

Of the arms that achieved T>MIC values of 100% of the dosing interval, 7 of 10 were successful among the two trials, for a success rate of 70%, while 6 of 10 (60%) that achieved T>MIC values of ≤98.8% failed (Table 2, last two columns). Thus, despite the inconsistencies within the dose fractionation experiments, the overall data suggest that T>MIC or trough/MIC was the PD index predictive of treatment success for amoxicillin.

Further analysis of the data in Table 2 revealed that 4 of 4 experimental arms that achieved a trough/MIC ratio of ≥6.99 were successful, while trough/MIC ratios of 0.76 to 2.89 had a 57% failure rate. A trough/MIC ratio of 0.07 had a 100% failure rate. Although the number of experimental arms was small, these data suggested that trough/MIC ratio may be a better predictor of treatment success than T>MIC.

Dose range studies simulating a postpartum amoxicillin serum half-life of 1.6 h.

These HF experiments were designed to distinguish whether a T>MIC of 100% of the dosing interval or the trough/MIC ratio was the PD index that best predicted treatment success for amoxicillin against B. anthracis.

In the first HF experiment, amoxicillin regimens of 62.5 to 1,250 mg q8h were simulated using a half-life of 1.6 h. Based on the results of the first trial, a smaller range of dosages was simulated in the second trial. Many of the experimental arms had T>MIC values of 100% but increasing trough/MIC ratios. The PK-PD values targeted for simulation, and the results of the two trials are shown in Table 3. In the first trial, only the highest dosage of amoxicillin, 1,250 mg q8h, was successful. Failure of the other regimens was due to selection of resistant subpopulations that had MICs of amoxicillin of >64 μg/ml. In the second trial, amoxicillin regimens of 500 mg q8h to 1,250 mg q8h were simulated. All of these arms had T>MIC values of 100%. In that experiment, a dose range effect was not observed, since the amoxicillin regimens of 500 and 1,000 mg q8h failed while regimens of 875 and 1,250 mg q8h were successful (Table 3, last 2 columns). Failures were due to selection of a mixture of amoxicillin-resistant mutants with inducible and stable overexpression of beta-lactamases.

Table 3.

PK-PD parameters in the two hollow-fiber dose-ranging studies for amoxicillin in which a 1.6-h half-life was simulated^a

Treatment arm	Total daily dose (mg)	Target half-life (h)	Free AUC/MIC ratio	Free Cmax/MIC ratio	Free trough/MIC ratio	Free T>MIC (%)	Dose fractionation study result
							First study	Second study
ΔSterne control	0	NA	0	0	0	0	NA	NA
Amoxicillin (mg) q8h
62.5	187	1.6	38.52	3.9	0.29	69	Failure	ND
125	375	1.6	77.03	7.8	0.57	85	Failure	ND
187.5	562	1.6	110.63	11.2	0.83	94	Failure	ND
250	750	1.6	154.07	15.6	1.16	100	Failure	ND
500	1,500	1.6	308.14	31.2	2.32	100	Failure	Failure
875	2,625	1.6	537.27	54.4	4.04	100	Failure	Success
1,000	3,000	1.6	616.28	62.4	4.63	100	Failure	Failure
1,250	3,750	1.6	739.49	74.9	5.57	100	Success.	Success

^aAmoxicillin was administered to all experimental arms on a q8h schedule. The MIC in broth was 0.25 μg/ml. NA, not applicable; ND, not done.

In these two dose-ranging studies, 6 of 9 arms with amoxicillin T>MIC values of 100% failed, while 3 of the arms were successful. This suggested that treatment failures of some of the experimental arms were random events that could not be predicted based on traditional PK-PD indices (AUC/MIC, C_max/MIC, and T>MIC). A trough/MIC ratio of ≥5.57 was predictive of successful outcomes in these dose range experiments.

Dose fractionation studies simulating an amoxicillin serum half-life of 1.6 h.

To determine if the T>MIC or the trough/MIC ratio was the PD index predictive of treatment success, two dose fractionation studies with 1.6-h half-lives for amoxicillin were conducted, in which all of the evaluated regimens had a T>MIC of 100% of the dosing interval. The trough/MIC ratios of the regimens examined ranged from 1.03 (1,213.5 mg q12h) to 17.32 (500 mg q4h) in the first trial. Two additional (higher) dosages of amoxicillin were examined in the second trial, providing a trough/MIC range of 1.03 to 25.76 (Table 4).

Table 4.

Targeted PK-PD parameters simulated in combined dose-range and dose fractionation hollow fiber studies simulating an amoxicillin half-life of 1.6 h^a

Treatment arm	Total daily dose (mg)	Target half-life (h)	Free AUC/MIC ratio	Free Cmax/MIC ratio	Free trough/MIC ratio	Free T>MIC (%)	Dose fractionation study result
							First study	Second study
ΔSterne control	0	NA	0	0	0	0	NA	NA
Amoxicillin (mg)
500 q8h	1,500	1.6	308.14	31.20	2.32	100	Failure	Failure
500 q6h	2,000	1.6	393.86	32.23	5.70	100	Failure	Failure
1,312 q12h	2,625	1.6	537.27	78.25	1.03	100	Failure	Success
875 q8h	2,625	1.6	537.27	54.40	4.04	100	Failure	Failure
656 q6h	2,625	1.6	537.27	43.96	7.77	100	Failure	Success
1,500 q12h	3,000	1.6	616.29	89.76	1.18	100	Failure	Success
1,000 q8h	3,000	1.6	616.28	62.40	4.64	100	Failure	Success
750 q6h	3,000	1.6	616.28	50.43	8.91	100	Success	Success
500 q4h	3,000	1.6	616.28	41.20	17.32	100	Success	Success
1,000 q6h	4,000	1.6	787.68	64.45	11.39	100	ND	Failure
750 q4h	4,500	1.6	916.46	61.27	25.76	100	ND	Success

^aNA, not applicable; ND, not done.

In the first dose fractionation study, amoxicillin at 750 mg q6h and 500 mg q4h (with total daily doses of 3,000 mg of drug) were successful, while regimens in which the same total daily dose was given as 1 or 2 divided doses each day failed (Table 4, second-to-last column). This suggested that a trough/MIC ratio of ≥8.91 was the PD index value predictive of successful treatment outcome. A trough/MIC ratio of ≤7.77 was associated with treatment failure. Since the regimens that failed and succeeded all had T>MIC values that were 100% of the dosing interval, T>MIC was not the PD index predictive of treatment outcomes.

Many arms that failed in the first dose fractionation study (simulated half-life, 1.6 h) were successful in the second dose fractionation experiment. Failure occurred randomly among the treatment arms (Table 4, last column).

For regimens in the second dose-fractionation trial, in which 2,625 mg/day of amoxicillin was examined, giving this total daily dose as 2 or 4 equally divided doses per day was successful, while delivering this total daily dose as 3 equally divided doses per day failed. Also, all of the fractionated regimens for 3,000 mg/day were successful, while giving amoxicillin at 4,000 mg/day as 1,000 mg q6h failed. The lowest trough/MIC ratio at or above which amoxicillin was successful in both dose fractionation studies was 17.32. This trough/MIC value was generated by the simulated regimen for amoxicillin of 500 mg q4h.

Dose range studies for amoxicillin given as continuous infusions.

In the preceding dose range and dose fractionation studies, the trough/MIC values associated with treatment success rose as the dosages of amoxicillin examined increased. This suggested that higher amoxicillin exposures induced the bacterium to produce larger amounts of beta-lactamase, providing greater resistance to amoxicillin therapy.

To verify that the trough/MIC ratio and not the T>MIC was the pharmacodynamic index associated with the probability of successful treatment outcomes, two dose range studies were conducted with amoxicillin given as continuous infusions. A continuous infusion maintains the same concentration of the drug in a study arm for the duration of the experiment. If higher peak levels of amoxicillin were linked with the progressive increase in breakpoint values for success in consecutive trials, the trough/MIC values predictive of treatment success in the continuous-infusion studies should be less than the breakpoint values identified in the dose range/dose fractionation studies in which pulse dosing of amoxicillin was employed.

A dose-response effect was seen in the continuous-infusion studies (results are given in Fig. 3 for the first trial and in Table 5 for both trials). Regimens that produced constant concentrations of amoxicillin approximating 0.5 to 2 times the MIC (0.125 to 0.5 μg/ml) failed. The time of failure was sequential from lowest to highest exposures within this range (Fig. 3). Two of regimens that failed (continuous infusions of amoxicillin at 0.25 and 0.5 μg/ml) had T>MICs of 100% of the dosing interval. Amoxicillin continuous infusions of ≥4 times the MIC (and free trough/MIC ratio of ≥4) caused progressive reductions in the B. anthracis population and did not select for resistance. Regrowth in the arms that failed had bacteria with agar-derived MICs of amoxicillin that ranged from 1 to >32 μg/ml. Random failure of treatment arms was not observed in the continuous-infusion experiments.

Fig 3.

First dose range study with amoxicillin, in which the antibiotic was administered as a continuous infusion (CI). (A) Total B. anthracis populations for all experimental arms. (B to I) Total population and subpopulation with MICs of amoxicillin that were at least 3 times higher than the MIC for the parent strain.

Table 5.

PK-PD parameters simulated in the hollow-fiber experiments in which amoxicillin was administered as a continuous infusion (CI) to achieve the concentrations specified in the treatment arms^a

Treatment arm	Free 24-h AUC/MIC ratio	Free Cmax/MIC ratio	Free trough/MIC ratio	Free T>MIC (%)	CI study result
					First study	Second study
ΔSterne control	0	0	0	0	NA	NA
Amoxicillin (μg/ml)
0.125	3	0.5	0.5	0	Failure	Failure
0.25	6	1	1	100	Failure	Failure
0.5	12	2	2	100	Failure	Failure
1.0	24	4	4	100	Success	Success
1.5	36	6	6	100	Success	Success
2.0	48	8	8	100	Success	Success
2.5	60	10	10	100	Success	Success

^aThe MIC of amoxicillin for the ΔSterne strain was 0.25 μg/ml. NA, not applicable.

Contribution of beta-lactamase production by B. anthracis to amoxicillin treatment efficacy (i.e., random failure of treatment arms): use of dicloxacillin as a probe. (i) Dicloxacillin susceptibility studies.

The MIC of 0.25 μg/ml for dicloxacillin did not change with the method used to prepare the B. anthracis suspension or with the addition of a beta-lactamase inhibitor clavulanate. The MICs of amoxicillin decreased >32-fold when clavulanate was added to amoxicillin for B. anthracis suspensions prepared using the “standard CLSI method” and with ciprofloxacin pretreatment (see Table S2 in the supplemental material).

Broth macrodilution MICs of amoxicillin and dicloxacillin were assessed over 96 h for a B. anthracis suspension that was prepared with ciprofloxacin pretreatment. The MICs of amoxicillin progressively increased from 0.5 to 4 μg/ml over 96 h, while the MICs of dicloxacillin remained unchanged at 0.25 μg/ml over this time frame (see Fig. S2A in the supplemental material).

The concentration of amoxicillin measured in the test tubes containing drug and bacterium decreased faster over the first 24 h than the concentration in a control arm which contained only amoxicillin (see Fig. S2B in the supplemental material). In contrast, the concentration of dicloxacillin in test tubes containing bacteria together with this drug decreased at a rate similar to that for dicloxacillin that was in test tubes without bacteria (see Fig. S2C in the supplemental material), showing that amoxicillin was inactivated by the beta-lactamase produced by B. anthracis while dicloxacillin was not.

(ii) Dose range and dose fractionation studies with dicloxacillin.

Dose range and dose fractionation studies with dicloxacillin assessed the contribution of beta-lactamase production by B. anthracis to the random and inconsistent failures of amoxicillin treatment arms that were observed in the HF experiments.

In the dose range study, the simulated clinical regimens for dicloxacillin at 500 mg q6h and 500 mg q4h both failed (Table 6, last column) due to amplification of mutants with MICs of dicloxacillin of 2 to >32 μg/ml versus an MIC of 0.25 μg/ml for the wild-type strain. These simulated regimens achieved T>MIC values of 53 and 80%, respectively, and trough/MIC ratios of <1. The experimental arm in which the dicloxacillin was administered to simulate the concentration-time profile for amoxicillin at 500 mg q8h also failed. This regimen achieved a T>MIC value of approximately 80%. Regimens that generated free T>MIC values of ≥94% and trough/MIC ratios of 0.69 and 0.76 were associated with treatment success.

Table 6.

PK-PD parameters for simulation in a dose range study in which dicloxacillin was administered to hollow-fiber systems to simulate the free (non-protein-bound) PK profiles for several amoxicillin regimens^a

Treatment arm	Daily dose (mg)	Half-life (h)	Free AUC/MIC ratio	Free Cmax/MIC ratio	Free trough/MIC ratio	Free T>MIC (%)	Study result
Control	0	NA	0	0	0	0	NA
Dicloxacillin, 500 mg
q6h (clinical regimen)	2,000	1	23.24	2.24	0.14	53	Failure
q4h (supraclinical regimen)	3,000	1	31.11	2.23	0.56	80	Failure
Amoxicillin (g) q8h (PK profile using dicloxacillin)
500	1,500	1	165.97	20.80	0.33	81	Failure
875	2,625	1	352.35	44.16	0.69	94	Success
1,000	3,000	1	389.38	48.80	0.76	96	Success

^aThe free PK and PD values for the clinical regimen of dicloxacillin at 500 mg q6h and the supraclinical regimen of 500 mg q4h are also evaluated (21). The protein binding rates for dicloxacillin and amoxicillin were 95% and 20%, respectively. NA, not applicable.

For the dose fractionation study in which the PK profiles for amoxicillin were simulated using dicloxacillin in place of amoxicillin, administering the total daily dose as two equally divided doses every 12 h failed, while the more fractionated regimens were successful. In these trials T>MIC values of ≤69% failed, while T>MIC values of ≥94% of the dosing interval were successful (see Table S3 in the supplemental material). Random failure of treatment arms was not seen with dicloxacillin. Thus, for dicloxacillin, a drug which was not inactivated by the type I beta-lactamase produced by B. anthracis, the T>MIC was predictive of the killing of the susceptible B. anthracis population and of preventing amplification of the resistant population.

Analysis of the data by the classification and regression tree (CART) method.

Because of the inconsistent results for amoxicillin and the random failure of some of these arms, it was not possible to identify a single breakpoint above which treatment success for amoxicillin was predictable by inspection of the HF study results. Thus, recursive partitioning analysis was used to identify breakpoint values and the pharmacodynamic indices linked with treatment success using the data generated from the dose range and dose fractionation studies with amoxicillin. The results for 60 HF experimental arms were evaluated. Recursive partitioning analysis was conducted by evaluating the peak/MIC ratio and then the trough/MIC ratio as the possible pharmacodynamic index that was linked with killing of the wild-type strain of B. anthracis and with prevention of emergence of resistance to amoxicillin. The exposure to amoxicillin needed for treatment success increased as higher dosages of amoxicillin were evaluated. This suggested that amoxicillin induced larger amounts of beta-lactamase production by B. anthracis as the dosages of the drug were increased. Thus, recursive partitioning analysis was also conducted to identify the optimal peak/MIC ratio assuming that the breakpoint trough/MIC ratio identified by CART analysis was achieved.

The univariate recursive partitioning analysis with peak/MIC ratio (PKMICRATIO) as the independent variable and success/failure as the independent variable showed that there was a minimum peak/MIC ratio that was required for success. When the value of this index was less than 20.8, the success rate was zero, and when it exceeded or equaled this value, the success rate was 50.9% (see Fig. S3A in the supplemental material).

The univariate CART analysis with trough/MIC ratio (TRMICRATIO) as the independent variable and success/failure as the independent variable showed that there was a minimum trough/MIC ratio that was required for success. When the value of this index was less than 6.99, the success rate was 37.5%, and when it exceeded or equaled this value, the success rate was 83.3% (see Fig. S3B in the supplemental material).

The peak/MIC ratio and trough/MIC ratio are colinear (i.e., as peak goes up, trough rises for any single dosing interval). The breakpoint of peak/MIC ratio of <20.8 indicated that there was a low trough. The constant-infusion data suggested that the trough/MIC ratio was the true linked variable.

CART analysis for the breakpoint for success for trough/MIC followed by peak/MIC was conducted. A trough/MIC breakpoint value of ≥6.99 alone had an 83% likelihood of regimen success, but a regimen that produced a trough/MIC ratio of ≥6.99 together with a peak/MIC ratio of <43.96 had a 100% success rate (Fig. 4). This finding is consistent with the hypothesis that regimens with lower peak/MIC ratios are less likely to induce beta-lactamase production by B. anthracis.

Fig 4.

Recursive partitioning analysis: breakpoint for success for trough/MIC analysis followed by peak/MIC ratio analysis. The trough and C_max values based on an amoxicillin MIC of 0.25 μg/ml are also shown. SD, standard deviation.

Logistic regression analysis showed that a trough/MIC ratio of ≥6.99 together with a peak/MIC ratio of <45.96 was predictive of treatment success compared with regimens that did not meet both of these criteria (P = 0.011). Furthermore, a two-tailed Fisher exact test showed that regimens which had peak/MIC ratios of <43.96 and trough/MIC ratios of ≥6.99 (optimal regimens) had a greater probability of treatment success than regimens in which the peak/MIC ratio and/or trough/MIC ratio did not fall in the optimal range (nonoptimal regimens) (P = 0.04).

The possibility that the different half-lives of amoxicillin in the different patient populations had an effect on treatment outcomes was also assessed. The half-life was treated as a categorical variable in the likelihood ratio test since the simulated half-lives in the HF model evaluations were fixed at either 1.0 or 1.6 h. The likelihood ratio test placed the P value for half-life at 0.119, indicating that the impact on the likelihood of regimen success was not significant.

Finally, the likelihood ratio test found that the trough/MIC ratio was a significant predictor of treatment outcomes (P < 0.013).

To build a mathematical model for predicting treatment outcomes for amoxicillin, all the covariates evaluated were considered for model building. They were entered in order of P value significance. The variable PKTRMICBRK was the categorical covariate where regimens either had an optimal peak/MIC ratio and trough/MIC ratio or did not. This covariate was most significant and thus served as the base model in the model-building process. We attempted to add the other covariates stepwise and evaluated the significance of model expansion with a likelihood ratio test. Adding either TRMICRATIO (trough/MIC ratio) as a continuous covariate or half-life (categorical covariate) to PKTRMICBRK (categorical covariate) did not cause a significant change in the log likelihood by the likelihood ratio test (the additions had 2× log likelihood differences of 2.21 and 2.65, respectively).

The final model included only the breakpoint variable, indicating the importance of attaining a relatively low peak/MIC ratio while having a high trough/MIC ratio (small peak/trough fluctuation), similar to what would be achieved with frequent administration of small dosages of amoxicillin or by giving this drug as a continuous infusion, as was done in our HF experiments.

Because of the duration of postexposure prophylaxis is 60 days in people, adherence will become very suboptimal if the dosing interval is shorter than 8 h. Consequently, we explored in Monte Carlo simulation the highest amoxicillin dose (1 g every 8 h) known to be tolerable to human adults. For children, doses of 45 and 90 mg/kg/day given as 3 equally divided doses each day were simulated.

Monte Carlo simulations and target attainment calculations.

Population parameter values for women in their second and third trimesters as well as postpartum (patients were studied in all three physiological states) were taken from the data reported by Andrew et al. (11). The CART analysis showed that a C_max/MIC ratio of <43.59 in conjunction with a trough/MIC ratio of ≥6.99 was associated with a success rate of 100% in the HF experiments, where success was defined as the killing of the wild-type ΔSterne strain of B. anthracis without resistance emergence. For these ratios, the MIC was 0.25 μg/ml as determined by the broth microdilution technique conducted using bacterial suspensions that were pretreated with ciprofloxacin. Thus, a C_max value of <10.898 μg/ml and a trough value of ≥1.748 μg/ml were associated with a 100% success rate.

The MICs of amoxicillin were highly dependent upon how the B. anthracis suspension was prepared and on whether susceptibility testing was determined in broth or on agar. In this project, only one strain of B. anthracis was evaluated. Thus, for the Monte Carlo simulations, target attainment for selected amoxicillin regimens was determined relative to C_max and trough values (and not the C_max/MIC or trough/MIC ratio) for treatment success and failure that were derived from the recursive partitioning analysis. Doing so removed the uncertainty of the meaning of the MIC values in the interpretation of the data, as the regimens were the drivers for the values and the variability in the MIC by method would be a simple scalar through all regimens.

Based on the breakpoints derived from the CART analysis, the combination of the C_max and trough levels achieved with any amoxicillin regimen would fall into one of four categories. Reanalysis of the success rates in the HF experiments that were associated with the four possible categories of C_max and trough values that could be achieved relative to a breakpoint C_max value of <10.989 μg/ml and a breakpoint trough value of ≥1.748 μg/ml provided the following results: category I, where for a C_max of <10.989 and a trough ≥1.748 μg/ml, 4/4 (1.00) regimens succeeded; category II, where for a C_max of ≥10.989 and a trough of ≥1.748 μg/ml, 4/6 regimens (0.667) succeeded; category III, where for a C_max of <10.989 and a trough of <1.748 μg/ml, 6/21 regimens (0.286) succeeded; and category IV, where for a C_max of ≥10.989 and a trough of <1.748 μg/ml, 14/29 regimens (0.483) succeeded.

A 9,999-subject Monte Carlo simulation was conducted for amoxicillin at 1 g q8h and amoxicillin at 500, 750, and 1,000 mg given every 6 h in women in their second and third trimesters of pregnancy and 3 months postpartum. The predicted success rates for all of these regimens were suboptimal, ranging from 30.6% to no higher than 73.4% (Table 7).

Table 7.

Monte Carlo simulation predictions of treatment success rates for several amoxicillin regimens in pregnant and postpartum women and in children

Amoxicillin regimen	Success rate (%) in:
	Women			Children
	Second trimester of pregnancy	Third trimester of pregnancy	3 mo postpartum
1,000 mg q 8 h	35.8	33.0	55.6
500 mg q 6 h	32.8	30.6	54.4
750 mg q 6 h	48.2	50.7	65.3
1,000 mg q 6 h	63.2	73.4	69.7
45 mg/kg/day (15 mg/kg q 8h)				38.4
90 mg/kg/daya
30 mg/kg q 8 h				43.8
22.5 mg/kg q 6 h				43.4

^aThis dosage is twice the ACIP recommendation of 45 mg/kg/day; 90 mg/kg/day has been given to children with otitis media (5, 34).

The recommended regimen of amoxicillin at 45 mg/kg/day (not to exceed 500 mg per dose) for children had a predicted success rate of only 38.4% when administered as 3 divided doses every 8 h. Amoxicillin doses as high as 90 mg/kg/day have been given to children with acute otitis media (31, 33, 34). This total daily dose was predicted be successful in only 43.4 to 43.8% of children when it is administered as four equally divided doses every 6 h and three equally divided doses every 8 h (Table 7).

The outcomes for amoxicillin therapy will depend upon the MIC distribution among B. anthracis strains. We could not use the MIC distributions reported by others to predict the likelihood of treatment success for an MIC distribution among B. anthracis strains because the methods used by others for susceptibility testing were different from those employed in this project (i.e., ciprofloxacin pretreatment of the bacterial suspensions).

DISCUSSION

The purpose of this study was to apply mathematical models to the results of HF experiments to determine the pharmacodynamic index predictive of the activity of amoxicillin and to predict the efficacy of amoxicillin at 500 mg orally q8h as postexposure prophylaxis of anthrax in pregnant women, postpartum women who could be breastfeeding, and children. This regimen was selected by the ACIP for postexposure prophylaxis of anthrax based on PK studies conducted in nonpregnant adults and children and the assumption that amoxicillin needed to be measurable in the sera of infected individuals at concentrations above the MIC of the pathogen for 75 to 100% of the dosing interval. It was assumed that this T>MIC target would prevent B. anthracis from acquiring resistance to amoxicillin during therapy (5).

The ACIP dosing guidelines for amoxicillin did not consider the differences in volumes of distribution and half-lives of the drug that may exist between pregnant and nonpregnant women. In a PK study in which a single 500-mg dose of amoxicillin was given orally to women who were in their second and third trimesters of pregnancy and to the same women when they were 3 months postpartum, Andrew et al. (11) found that the mean serum half-lives of amoxicillin in those groups of women were 1.2, 1.3, and 1.6 h, respectively. Monte Carlo simulations conducted by Andrew et al. suggested that for pregnant and postpartum women, an oral amoxicillin regimen of 500 mg given every 4 h (not every 8 h) would be necessary to achieve a T>MIC serum concentration of amoxicillin for 75 to 100% of the dosing interval (11). It is highly probable that a prescription for a 60-day regimen of amoxicillin using a 4-hourly administration schedule would be associated with a high rate of nonadherence and possibly increased toxicity, and therefore, this is not practical.

In the HF experiments, amoxicillin provided inconsistent results. This was in contrast to the reproducible performance of ciprofloxacin, moxifloxacin, and linezolid (18, 26, 27, 35) and meropenem (unpublished data) in previous HF studies with B. anthracis. In a few HF experiments, a dose-response effect for amoxicillin was observed. However, in most studies, a random failure of amoxicillin treatment arms occurred in addition to what appeared to be dose-response effects, thus complicating the interpretation of the study results. Furthermore, the overall outcomes of the dose fractionation studies suggested that trough/MIC ratio, and not T>MIC, was the pharmacodynamic index that was predictive of an antimicrobial effect and prevention of resistance. However, the breakpoint value in the individual dose range and dose fractionation studies above which 100% of treatment arms were successful increased with subsequent experiments in which higher dosages were evaluated. The higher dosages were examined in an attempt to define a clear-cut breakpoint for which random failures would not occur. Inspection of the results of the initial HF studies in which the half-life of 1.0 h for amoxicillin was simulated suggested that a trough/MIC ratio of ≥6.99 resulted in success for 100% of arms in one HF experiment. However, as dosages with higher peak and AUC exposures were examined in subsequent studies, the breakpoint trough/MIC values for consistent treatment success increased to values of as high as 17.32. When amoxicillin was administered to HF systems as continuous infusions, a constant concentration/MIC ratio of as low as 4 was associated with a 100% success rate. Random failures were not seen in the continuous-infusion experiments.

The increase in the amount of amoxicillin needed for treatment success that was seen in HF experiments in which higher dosages of drug were simulated suggested that the beta-lactamase that is produced by B. anthracis was inducible, as was previously shown by Lightfoot et al. (36). The data also suggested that the amount of beta-lactamase produced by B. anthracis increased in the presence of higher amoxicillin peak concentrations. The reduction in the C_max/MIC ratio to 4 in the continuous-infusion studies was consistent with this hypothesis, since continuous infusions minimized the peak concentration values for any drug dosage.

Random failure of amoxicillin regimens occurred by two mechanisms of increased beta-lactamase production by B. anthracis isolates. In some experiments, failure was associated with outgrowth of mutants that had stable increases of the agar MICs of amoxicillin of >64 μg/ml. The wild-type isolate had an agar MIC of amoxicillin of 0.06 μg/ml. The higher agar MIC values for amoxicillin persisted in these strains even after the isolates were passed twice on drug-free agar prior to being evaluated in susceptibility studies. Resistance to amoxicillin in these mutants was likely due to derepression of the promoter for the type I beta-lactamase that is found in B. anthracis.

The second mechanism of treatment failure was amplification of B. anthracis isolates that were able to transiently increase their beta-lactamase production when exposed to amoxicillin. The agar dilution MICs for amoxicillin in these isolates can increase to >32 μg/ml in the presence of this antibiotic. The agar dilution MICs reverted to those for the wild-type isolate (agar MIC, 0.06 μg/ml) quickly after antibiotic pressure was removed.

Dicloxacillin was another tool that enabled us to understand the role of the B. anthracis beta-lactamase in defining the pharmacodynamic index that was predictive of treatment success for amoxicillin. Dicloxacillin is a beta-lactam antibiotic that has unique properties as it pertains to Bacillus species. Similar to the case for amoxicillin, this drug kills B. anthracis by binding to and inhibiting the function of its penicillin binding proteins. However, unlike amoxicillin, dicloxacillin also directly inactivates the beta-lactamase that is produced by this bacterium (21, 22). The dose-ranging/dose fractionation studies in which dicloxacillin was administered to HF systems to simulate the PK profiles for amoxicillin clearly demonstrated that T>MIC (and not trough/MIC ratio) was the pharmacodynamic index that best predicted the killing of the wild-type B. anthracis strain and prevention of emergence of resistance when the effect of the beta-lactamase on drug activity was neutralized. Furthermore, random failures of treatment regimens were not observed with dicloxacillin. The studies with dicloxacillin suggested that the beta-lactamase was responsible for the unpredictable, random failures seen with amoxicillin. A T>MIC value for dicloxacillin of ≤81% was associated with outgrowth of the microbe, while a T>MIC value for dicloxacillin of ≥94% predicted treatment success.

Unfortunately, in humans the non-protein-bound serum concentration-time profiles for dicloxacillin and amoxicillin differ significantly. Also, dicloxacillin is not absorbed by the gastrointestinal tract as well as amoxicillin (29). The clinically prescribed regimen of dicloxacillin at 500 mg q6h produced a free T>MIC value that was only 53% of the dosing interval, which was much less that the 94% value that was associated with treatment success for this antibiotic as identified in the current project. Thus, the clinical dosage for dicloxacillin is expected to fail if it is used as postexposure prophylaxis of anthrax in humans.

The random failure and inconsistent performance of amoxicillin regimens between experimental trials showed that a single breakpoint value that clearly separated regimens with 100% treatment failure from those with 100% success did not exist for amoxicillin. Thus, recursive partitioning analysis was applied to the outcomes of the 60 HF arms with amoxicillin that were conducted over the course of this project. CART analysis provided a statistical method for identifying breakpoint exposures that best correlated with treatment success and failure. The analysis found that a trough/MIC ratio of ≥6.99 was associated with a success rate of 83.3%, where success was defined as the killing of B. anthracis without selection for resistance to amoxicillin. A trough/MIC ratio of ≥6.99 together with a C_max/MIC ratio of <43.59 was associated with a 100% success rate. Regimens which generated C_max/MIC and trough/MIC values outside these parameters were less effective (with success rates as low as 28.6%).

To minimize the interday variability of MIC values obtained between experiments, our laboratory routinely prepares bacterial suspensions for use in antibiotic susceptibility testing by measuring the optical density (OD₆₃₀) of the suspensions with a spectrophotometer to calculate the concentration (log CFU/ml) of the microbe from a standard curve specific for the microbe. The bacterial suspensions were then diluted to approximately 1 × 10⁶ CFU/ml before they were added at 1:1 (vol/vol) to antibiotic-containing medium to produce a final bacterial concentration of 5.5 × 10⁵ CFU/ml in the broth microdilution wells.

After completion of the current project, we learned that the final concentration of B. anthracis in the wells of a microdilution broth susceptibility study is approximately 3 × 10⁴ CFU/ml (38) when the starting bacterial suspension is adjusted to a 0.5 McFarland standard. This concentration is more than 1 log/CFU/ml lower than the concentrations used in the current project. The 0.5 McFarland corresponds to a 1 × 10⁸ to 2 × 10⁸ CFU/ml concentration of Escherichia coli and is used to estimate the bacterial density for other bacterial species (23). Since E. coli exists as single small bacilli while B. anthracis forms long chains of large bacilli, the biomass that corresponds to 1 CFU of E. coli is substantially lower than the biomass for 1 CFU of B. anthracis. In our hands, a 0.5 McFarland standard corresponds to quantitative culture values of approximately 1.2 × 10⁸ CFU/ml of E. coli and 0.98 × 10⁷ CFU/ml of B. anthracis.

For susceptibility studies in which a 0.5 McFarland standard was used to prepare the B. anthracis suspension, we found the microdilution broth MICs of both penicillin G and amoxicillin were 0.03 μg/ml after 16 h of incubation and 0.06 μg/ml after 24 h of incubation. For susceptibility studies that are conducted using bacterial suspensions that are initially adjusted to a 0.5 McFarland turbidity, the CLSI categorizes B. anthracis isolates that have MICs of ≤0.125 μg/ml for penicillin G (23) (and by extrapolation amoxicillin) (5) as susceptible to these antibiotics. For bacterial suspensions that were prepared using an OD₆₃₀ to calculate the B. anthracis concentration, the MICs of penicillin G and amoxicillin were 16 and 8 μg/ml, respectively, at 16 h of incubation and >64 μg/ml after 24 h of incubation. Thus, the MIC values of penicillin G and amoxicillin are highly influenced by the B. anthracis inoculum. The higher bacterial concentration contributed to the unpredictable effects of amoxicillin on the killing of the wild-type B. anthracis in the current project.

The MICs of amoxicillin differed with the method used to prepare the B. anthracis suspension for susceptibility testing and the bacterial concentration examined. However, it cannot be overstressed that the antimicrobial effect of amoxicillin on B. anthracis in the HF experiments was determined by the interaction of the amoxicillin regimens with the amount of B. anthracis inoculated into the HF systems. The outcomes were not altered by the method used to determine the amoxicillin MIC values. Thus, to eliminate the uncertainty of the meaning of the MIC value for the interpretation of the HF study results, the Monte Carlo simulations and target attainments for selected amoxicillin regimens were determined relative to the C_max and trough breakpoint values (and not the C_max/MIC and trough/MIC ratios) which were predicted by the recursive partitioning analysis to maximize the probability of treatment success.

Among the groups of women evaluated by Andrew et al. (11), the longest mean serum half-life for amoxicillin of 1.6 h was seen in women who were 3 months postpartum. Thus, amoxicillin would be expected to perform the best in this population. Monte Carlo simulations predicted that the success rate for an oral regimen of amoxicillin at 1 g q8h would be 55.6% in these women. For amoxicillin given orally as 500, 750, and 1,000 mg q6h, the predicted success rates were 54.4 to 69.7%, where success was defined as a progressive killing of the B. anthracis isolate without resistance emergence. For women who were in their second and third trimesters of pregnancy (mean serum half-lives for amoxicillin of 1.2 and 1.3 h, respectively), the predicted success rates for the amoxicillin regimen of 1,000 mg q8h decreased to 33.0 to 35.8%. For amoxicillin given orally as 500, 750, and 1,000 mg q6h, the predicted success rates in the pregnant women ranged from 30.6% to 73.4%.

A dosage of 45 mg/kg/day (up to 500 mg per dose) is recommended for children who weigh less than 40 kg. The success rate for these children was predicted to be 38.4% when the drug is administered as three equally divided doses every 8 h. A higher dose of 90 mg/kg/day of amoxicillin has been given to children to treat otitis media infections (31). Monte Carlo simulations predicted that giving this total daily dosage as 3 and 4 equally divided doses per day would provide success rates of only 43.8% and 43.4%, respectively, in children. As with adults, the predicted success rates for these amoxicillin regimens as postexposure prophylaxis of anthrax in children were suboptimal. The predicted success rates for amoxicillin given every 4 h were not examined in adults and children because these regimens would likely be associated with high nonadherence rates and therefore are impractical.

It is important to underscore that in our in vitro studies the AUC exposures for the dosages of amoxicillin simulated within the HF systems increased in proportion to the dose (i.e., doubling the dose doubled the 24-h AUC exposure). We did not consider the known reduction in the absorption of orally administered amoxicillin that occurred in people as the dosage was increased, because the doses simulated within the HF systems extended above the highest dosage (3,000 mg) that has been reported in clinical investigations (30, 37). Also, the clinical studies examined the oral absorption of single doses of amoxicillin, while the current project used multidose regimens. Furthermore, we did not consider the decreased absorption of amoxicillin by the gastrointestinal tract in the Monte Carlo simulations. In a single-dose study in adults, orally administered dosages of amoxicillin of 750 and 1,500 mg generated AUCs that were 86% and 70% of the AUC generated with a 375-mg oral dose, assuming nonsaturable absorption (30). Only 39% of a 3-g dose of amoxicillin compared to a 500-mg dose was absorbed by the gastrointestinal tracts of adults, assuming linear kinetics (33). If this factor were included in the Monte Carlo simulations, the predicted performances of the various amoxicillin regimens would be worse than discussed above.

This study did not determine the duration of treatment that was necessary for treatment success. However, based on the current recommendation of 60 days of antibiotic therapy for postexposure prophylaxis of anthrax that was proposed by the ACIP (5), regimens in which amoxicillin is given more than three times daily are impractical from the patient compliance standpoint. Furthermore, the toxicity of these dosages when taken for 60 days has not been established. Based on the findings of this project, amoxicillin is unlikely to be effective as postexposure prophylaxis for B. anthracis in pregnant and breastfeeding women and in children.