Optimizing Meropenem in Highly Resistant Klebsiella pneumoniae Environments: Population Pharmacokinetics and Dosing Simulations in Critically Ill Patients

ABSTRACT

Critically ill patients are characterized by substantial pathophysiological changes that alter the pharmacokinetics (PK) of hydrophilic antibiotics, including carbapenems. Meropenem is a key antibiotic for multidrug-resistant Gram-negative bacilli, and such pathophysiological alterations can worsen treatment outcomes. This study aimed to determine the population PK of meropenem and to propose optimized dosing regimens for the treatment of multidrug-resistant Klebsiella pneumoniae in critically ill patients. Two plasma samples were collected from eligible patients over a dosing interval. Nonparametric population PK modeling was performed using Pmetrics. Monte Carlo simulations were applied to different dosing regimens to determine the probability of target attainment and the cumulative fraction of response, taking into account the local MIC distribution for K. pneumoniae. The targets of 40% and 100% for the fraction of time that free drug concentrations remained above the MIC (ƒT>MIC) were tested, as suggested for critically ill patients. A one-compartment PK model using data from 27 patients showed high interindividual variability. Significant PK covariates were the 8-h creatinine clearance for meropenem and the presence of an indwelling catheter for pleural, abdominal, or cerebrospinal fluid drainage for the meropenem volume of distribution. The target 100% ƒT>MIC for K. pneumoniae, with a MIC of ≤2 mg/liter, could be attained by the use of a continuous infusion of 2.0 g/day. Meropenem therapy in critically ill patients could be optimized for K. pneumoniae isolates with an MIC of ≤2 mg/liter by using a continuous infusion in settings with more than 50% isolates have a MIC of ≥32mg/L.

INTRODUCTION

Critically ill patients in the intensive care unit (ICU) are at high risk of developing severe nosocomial infections owing to the frequent use of invasive interventions for diagnosis and therapy, as well as their severe physical condition (1, 2). Carbapenems are an antimicrobial group that has a broad spectrum, low toxicity, and high stability against β-lactamases. Meropenem, in particular, is commonly indicated as an empirical or targeted treatment for severe infections related to resistant Gram-negative pathogens. The pharmacokinetics and pharmacodynamics (PK/PD) of carbapenems are characterized by time-dependent bactericidal activity, in which the microbiological effects are best predicted by the fraction of time that free drug concentrations remain above the MIC for the causative pathogen (ƒT>MIC). In an ICU environment with highly resistant isolates, dose optimization based on the best PK/PD target for critically ill patients is challenging (3). This is because critically ill patients can often experience altered drug PK due to their morbidity and subsequent interventions, resulting in poorer outcomes, such as treatment failure, drug toxicity, and development of antimicrobial resistance (1, 2). In addition, the presence of antimicrobial-resistant bacteria creates a major challenge for achieving therapeutic success (4). The emergence of bacteria with decreased carbapenem susceptibility, such as that seen among isolates of Klebsiella pneumoniae, is a major clinical concern in many parts of the world. In Vietnam, an outbreak of carbapenem-resistant K. pneumoniae in tertiary hospitals was declared recently (5, 6). There is uncertainty on how best to optimize carbapenem treatment when faced with difficult-to-treat pathogens such as these (7).

Therefore, this study aimed (i) to determine the population PK profile of meropenem in a critically ill population where carbapenem-resistant K. pneumoniae is prevalent, and (ii) to propose optimized meropenem dosing regimens for this scenario by assessing PK/PD target attainment against a local MIC distribution for K. pneumoniae.

RESULTS

Patient demographics.

A total of 27 patients (18 males) were included in the study. Details of characteristics of all patients are listed in Table 1. The mean age was 59.4 years (±20.1 standard deviation [SD]). At the time of collection of blood plasma, the median value for Cockcroft-Gault creatinine clearance (CL_CR-CG) was 86.5 mL/min/1.73 m² (interquartile range [IQR], 65.0 to 112.1), and the median 8-hour creatinine clearance (CL_CR8h) was 110 mL/min/1.73 m² (IQR, 80.7 to 140.7).

TABLE 1.

Baseline demographics and laboratory and clinical data for patients^a

Characteristic	Result (N = 27)
Age (yrs)	59.4 (±20.1)
Male	18 (66.7)
Total body wt (kg)	50.0 (43.2–62.5)
Ht (cm)	159.3 (±8.0)
BMI (kg/m2)	19.6 (18.8–22.7)
APACHE II score	14 (±5.6)
SOFA score	4 (3.0–6.0)
Type of infection
Respiratory tract	26 (96.3)
Central nervous system	5 (18.5)
Bloodstream	4 (14.8)
Abdominal	3 (11.1)
Urinary tract	2 (7.4)
Drainage catheter for
Abdominal fluid	2 (7.4)
Cerebrospinal fluid	2 (7.4)
Pleural fluid	3 (11.1)
Septic shock	8 (29.6)
Serum albumin (g/liter)	25.7 (±6.5)
Serum creatinine (μmol/liter)	68 (54.0–83.5)
CLCR-CG (mL/min/1.73 m2)	86.5 (65.0–112.1)
CLCR8h (mL/min/1.73 m2)	110 (80.7–140.7)

^aData presented are means (± SD), medians (with IQR), or number percentages. BMI, body mass index; SOFA, sequential organ failure assessment; APACHE II, acute physiology and chronic health evaluation II; CL_CR-CG, creatinine clearance estimated by Cockroft-Gault equation for clearance at the time of blood plasma collection; CL_CR8h, 8-h creatinine clearance at the time of blood plasma collection.

Population pharmacokinetic model.

A total of 27 urine samples and 54 plasma samples were obtained. Population pharmacokinetic modeling supported a one-compartment model with additive error. Specifically, CL_CR8h significantly affected clearance of meropenem (CL), while an indwelling catheter was the significant covariate for the meropenem volume of distribution (V) (Table 2). The relationships of these two covariates with population PK parameters were demonstrated based on power and exponential association, as follows: CL = 8.35 × [(CL_CR8h)/115]^0.49; V = 16.46 × e^0.24 (patient with indwelling catheter), where CL and V are the clearance and volume of distribution of meropenem, respectively. Fig. 1A show the relationship between the meropenem observed versus predicted concentration at a population level (R² = 0.483, bias = 1.4, imprecision = 53.8) and after Bayesian optimization (R² = 0.991, bias = 0.113, imprecision = 0.355). The visual predictive check (VPC) plot of the final model (Fig. 1B) showed that the observations were evenly distributed around the 50th percentile and 79.2% of them were within the 5th and 95th simulated percentiles.

TABLE 2.

Pharmacokinetic parameters of meropenem estimated from one-compartment model^a

Model value	Population parameter					Bootstrap analysis
	Mean	SD	CV%	Median	% Shrinkage	Median	95% confidence interval
CL = θ1 × [(CLCR8h/115)]θ2
θ1	9.38	4.91	52.33	8.35	5.45	8.35	5.63–11.26
θ2	0.23	1.32	585.82	0.49	4.79	0.49	0.00–0.69
V = θ3 × eθ4
θ3	30.72	27.53	89.60	16.46	12.07	16.46	11.35–49.60
θ4	1.23	3.52	285.54	0.24	2.65	0.24	0.00–1.53

^aModel value definitions: θ₁ is the population value of meropenem clearance (in liters per hour); θ₂ is the power value; θ₃ is the population value for the meropenem volume of distribution (in liters); θ₄ is the exponential value for patients with an indwelling catheter for pleural, abdominal, or cerebrospinal fluid drainage; θ₄ = 0 when patients do not have any of those catheters. CL_CR8h, creatinine clearance (in milliliters per minute); CV, coefficient of variation.

FIG 1.

Goodness-of-fit plots (A) and visual predictive check (B) of the final covariate model of meropenem. (A, left) Observed versus population-predicted concentrations: R² = 0.483, bias = 1.4, and imprecision = 53.8. (A, right) Individual predicted concentrations: R² = 0.991, bias = 0.113, and imprecision = 0.355. (B) The observed meropenem concentrations are represented by circles and black lines that are the 5th, 50th, and 95th simulated percentiles. The gray area shows the 95% confidence interval of the simulated meropenem concentrations.

K. pneumoniae MIC distribution.

The MIC distribution for meropenem is depicted in Fig. 2. Notably, 56/110 (50.9%) K. pneumoniae isolates had an MIC of ≥32 mg/liter.

FIG 2.

MIC distribution of meropenem against 110 K. pneumoniae isolates collected in the intensive care unit department during the study period.

Dose optimization.

The meropenem total daily dose for achieving 90% probability of target attainment (PTA) was plotted with the respective MIC values (Fig. 3). Using a target ƒT>MIC of 40%, all regimens achieved 90% PTA for an MIC of <16 mg/liter, irrespective of renal function. However, when the more aggressive target of 100% ƒT>MIC was applied, a continuous infusion (CI) was required to be able to reach 90% PTA for higher MICs. Taking toxicity limits into consideration, the CI dosing regimen of 4.0 g/day would cover pathogens for which the MIC was ≤8 mg/liter, while dosing regimens for 3-h extended infusion (EI) at intervals of 6 h (EI6) or 8 h (EI8) would only cover isolates with MICs of ≤0.25 mg/liter and ≤1 mg/liter in augmented renal clearance (ARC) and non-ARC patients, respectively. The presence of ARC may have had a minor effect on the PTA when a CI dosing regimen was used.

FIG 3.

Simulated meropenem total daily dose for achieving at least 90% probability of target attainment for different MIC values at targets of 40% ƒT>MIC (A) and 100% ƒT>MIC (B). Green lines, continuous infusion; orange lines, extended infusion with 6-h interval (EI6); black lines, extended infusion with 8-h interval (EI8); solid lines, augmented renal clearance; dashed lines, nonaugmented renal clearance; dashed gray lines, exposure beyond toxicity thresholds.

The cumulative fraction of response (CFR) obtained from three groups of K. pneumoniae isolates in our hospital are depicted in Fig. 4. In tandem with PTA, CI demonstrated the highest CFR with acceptable daily dose for all scenarios irrespective of the presence of ARC. Using the a priori target of 40% ƒT>MIC, the CFR of 95% could be achieved for pathogens with an MIC of ≤2 mg/liter, regardless of the infusion method. However, for a target 100% ƒT>MIC and taking ARC into account, no EI8 or EI6 dosing regimen could attain ≥95% CFR. With a CI toxicity threshold of 10.2 g/day or 10.4 g/day in ARC or non-ARC patients, respectively, a CI dosing regimen of 1.8 g/day (ARC patients) or 0.9 g/day (non-ARC patients) was the sole administration method that could achieve ≥95% CFR for pathogens with intermediate resistance (MIC = 2 mg/liter). For resistant strains with MICs of ≥4 mg/liter, no dosing regimen could be applicable, because the dose to reach the PK/PD target required a potentially toxic exposure.

FIG 4.

Cumulative fraction of response (CFR) and percentage of patients exceeding toxicity thresholds, based on increasing the daily dose of meropenem administered as a continuous infusion, 6-hour extended infusion, and 8-hour extended infusion dosing regimens for targets of 40% ƒT>MIC and 100% ƒT>MIC against 3 subpopulations of K. pneumoniae in patients with and without augmented renal clearance. Black lines, CFR for K. pneumoniae with MIC of ≤1 mg/liter; yellow lines, CFR for K. pneumoniae with MIC of 2 mg/liter; blue lines, CFR for K. pneumoniae with MIC of ≥4 mg/liter; red lines, percentage of patients having meropenem plasma exposure exceeding the upper limit concentration. The upper horizontal dashed line represents 95% of simulated profiles achieving the target, and the lower horizontal dotted line represents the 10% cutoff for patients reaching the toxicity threshold.

DISCUSSION

Our study shows that PK data of meropenem in this small cohort of sparsely sampled ICU patients are best described by a one-compartment model with a high interindividual variability in which CL_CR8h is a significant covariate for meropenem CL. Taking into account the PK alterations in critically ill patients and the reduced susceptibility of the potential pathogens in an ICU environment, using a CI regimen is better for achieving the intensive target of 100% ƒT>MIC, compared to using an EI regimen.

The ICU environment in our study was characterized with a high prevalence of K. pneumoniae isolates with reduced meropenem susceptibility. When applying CLSI clinical breakpoints to our K. pneumoniae isolates (8), the resistance rate would be defined at 71.8%. This is comparable to some reported rates in other ICUs, including in Georgia (43.5%), Greece (62.3%), and Israel (80%) (9, 10). Previous data from three Vietnamese ICUs showed carbapenem-resistant K. pneumoniae rates of 55.1% (11). Given the high rate of resistance, unfavorable outcomes for critically ill patients with K. pneumoniae bloodstream infection are common, with a fatality rate of up to 35.5% (12). In environments with a high prevalence of carbapenem-resistant K. pneumoniae, a high-dose regimen using prolonged infusion is a valid consideration (13, 14).

Population pharmacokinetic modeling suggested that a one-compartment, additive error model best fit the data. The sparse sampling schedule suitable for the clinical setting in our institute could explain why the one-compartment model was better than the two-compartment model in describing the data. The model showed acceptable bias and imprecision values with high interpatient variability. The model in our study showed typical CL and V of 8.35 liters/h and 16.46 liters, respectively. These values were in line with those of critically ill patients reported in other studies (15, 16, 17). The observed mean CL in our study was lower than that of healthy volunteers (CL = 12.4 to 17.2 liters/h) (18). It is well understood that critically ill patients in an ICU have substantial PK alterations, including renal dysfunction or ARC (2). The coefficient of variation of CL_CR8h was 53.6%, implying a high variation in renal function of ICU patients in our study. Similar findings have also been recorded in patients with early sepsis and septic shock or severe infections (16, 19, 20). CL_CR8h was the significant covariate for CL, which is in agreement with previous findings. With the assumption that meropenem was eliminated mostly by the renal system, the nonrenal clearance term was not added in the model (21). The indwelling catheter for pleural, abdominal, or cerebrospinal fluid drainage was a significant covariate relating to a higher V. This result could be explained by the extravasation of fluid from plasma into these peripheral compartments, triggering an expansion of the V (22, 23). The high variability in pharmacokinetics observed in this study suggests that a high-dose strategy employing CI for meropenem, perhaps in combination with therapeutic drug monitoring (TDM), should be considered in critically ill patients (24–30).

Previous studies have applied EUCAST MIC breakpoints in their dosing simulations; thus, the proposed meropenem doses were adequate (24, 27, 28). Nevertheless, in the context of a high MIC as observed in extensively drug-resistant Pseudomonas aeruginosa septic shock, a dose as high as 12 g/day EI6 under TDM guidance showed a positive outcome (25). Cojutti et al. also proposed a meropenem dose of 11 g/day through continuous infusion to treat K. pneumoniae with an MIC of ≤64 mg/liter to achieve the target of 100% fT>MIC, even in ARC patients (26). It should be noted that exposure-related toxicity associated with such high doses was not mentioned or predicted. In our study, we proposed an approach to optimize meropenem dosing for a highly resistant K. pneumoniae environment in which not only the likelihood to attain PK/PD targets for efficacy was evaluated but also the risk of exceeding toxicity thresholds.

We applied two different toxicity thresholds for EI and CI regimens due to the different pharmacokinetic profiles (31). For the EI, the concentration fluctuated, and a previous study suggested using the trough concentration (C_min) as a surrogate parameter to predict toxicity of meropenem (32). In the case of CI, concentration reached a steady-state plateau level, and therefore the steady-state concentration (C_ss) was used to predict the toxicity (33). With comparable exposure, the C_ss for CI was equivalent to the average steady-state concentration in EI, which was obviously higher than the C_min. It should be noted, however, that these C_ss thresholds were set arbitrarily by Pea and colleagues and that there were no exposure-related adverse events observed by those investigators, even with a C_ss of up to 143 mg/liter (33).

The simulations plotted in Fig. 3 could potentially be used as nomograms to guide dosing in facilities where a K. pneumoniae MIC is not available or during the turnaround time of microbiological susceptibility testing. For settings where more than 50% of K. pneumoniae isolates have a MIC of ≥32 mg/liter, we propose a dosing scheme base on simulated CFR as depicted in Fig. 4. As can be inferred from these two figures, dosage and administration modes can be selected based on pathogen MIC, renal function, or PK/PD targets. Specifically, PTA and CFR of EI regimens were significantly different between the two PK/PD targets, while such discrepancies were not observed with CI dosing regimens. The target of 100% ƒT>MIC is encouraged to maximize the antibacterial activity of β-lactam in ICU patients. In some studies, a more intensive target of 100% ƒT that is >4× the MIC may be considered to suppress resistance, given the high resistance rate in ICU environments (27, 34, 35, 36, 37). These in vitro studies demonstrated that a target C_min/MIC ranging from 2 to 6 may be required to suppress the emergence of resistance. The clinical benefits of such a dosing approach have not been established. Thus, a CI regimen could potentially be more feasible to help achieve such targets, although achievement of the more intensive target was not investigated in our analysis.

From our study, in settings with ≥50% of K. pneumoniae isolates having MICs of ≥32mg/liter, the dose of 2 g/day CI could be used to cover K. pneumoniae isolates with MICs of ≤2 mg/liter when treating empirically to achieve a ≥95% CFR. When K. pneumoniae susceptibility is known, a dose of 8 g/day CI could cover pathogens with a MIC of ≤16 mg/liter using a target of 100% ƒT>MIC, meaning that a target of 100% ƒT that is >4× MIC could be achieved for isolates with an MIC of 4 mg/liter. To cover isolates with an MIC of 32 mg/liter, a 12-g/day CI is needed, but this dosing regimen exceeds the upper C_ss exposure threshold of 100 to 120 mg/liter.

We are aware of limitations in our study. First, the toxicity and efficacy thresholds used in this study are still being debated in the literature. It should be noted that the toxicity threshold for the EI regimen was derived from a retrospective study with small sample size (72 patients evaluated for nephrotoxicity), in which only 5 patients developed nephrotoxicity (32). To date, data on dose-response relationships between β-lactam antibiotic drug concentrations and toxicity are limited. Second, our population is limited to only patients not receiving renal replacement therapy (RRT), plasma exchange, or extracorporeal membrane oxygenation (ECMO), so this may limit the generalizability of the results to all ICU patients. Moreover, our sample size was relatively small, and we applied sparse sampling in our study, leading to lack of data to adequately describe the meropenem PK profile as a two-compartment model in other studies and the uncertainty in model prediction with low concentrations, as can be seen in the VPC plot. However, our approach should be acceptable, as an intensive sampling program may not always be feasible given that it is labor-intensive.

Conclusion.

Using PK data from our ICU together with locally collected K. pneumoniae isolates, we proposed feasible meropenem dosing regimens based on current epidemiological and toxicity information for the treatment of resistant K. pneumoniae. In settings with more than 50% of isolates having MICs of ≥32mg/liter, we identified CI dosing regimens which would be more favorable for achieving the target of 100% ƒT>MIC for K. pneumoniae isolates with MICs of ≤2 mg/liter. Further studies, however, are warranted to assess toxicity-related and clinical outcomes using the proposed dosing regimens.

MATERIALS AND METHODS

Study population.

This prospective, observational cohort study was undertaken in the ICU of Bach Mai Hospital from October 2018 to March 2019. Eligible patients were aged ≥18 years with meropenem administration, ICU stay of >24 h, and a urine catheter in situ. Patients receiving RRT, plasma exchange, or ECMO prior to study enrollment were excluded.

Ethics statement.

Ethical approval was obtained from the Institutional Review Board of Bach Mai hospital with the reference number of 126/QD-BM for the protocol BM-2018-1028-45. Written informed consent was obtained from either the patients or their legally acceptable representative if they could not give consent themselves (e.g., comatose or ventilated patients).

Antimicrobial administration, plasma sample collection, and assay.

(i) Meropenem administration. Initiation of treatment and meropenem dose were at the discretion of the treating team. Sodium chloride (0.9%) or glucose (5%) were used for reconstitution and dilution before the meropenem dose was administered intravenously as a 3-h infusion.

(ii) Plasma sample collection. Due to the difficult conditions of the ICU and clinical setting, we employed a sparse sampling strategy with two time points (15, 38). At assumed steady-state (after at least 3 doses), 2-mL blood samples were collected using a 5-mL lithium heparin vacutainer at 0.5 h and 2 h (if the dosing interval was 6 h) or 0.5 and 3 h (if the dosing interval was 8 h) post-completion of meropenem infusion. After centrifugation at 4,000 rpm over 10 min, a volume of 1 mL plasma was immediately mixed with 1 mL aqueous solution of 0.5 M 3-morpholino-propane-sulfonic (MOPS) buffer, pH 6.8 (Sigma-Aldrich, Co., St. Louis, MO, USA) and then stored at −40°C until assay. In addition, an 8-h urine sample was simultaneously collected via urine catheter to determine the 8-h creatinine clearance (CL_CR8h).

(iii) Meropenem assay. Plasma concentrations of meropenem were quantified using a validated high-performance liquid chromatography method with UV detection (HPLC-UV) at the Department of Analytical Chemistry and Toxicology of Hanoi University of Pharmacy (39). Briefly, 0.1 mL imipenem (20 mg/liter) as internal standard was added into 0.2 mL plasma and 0.2 mL of 0.5 M MOPS buffer, pH 6.8. For protein precipitation, a volume of 0.5 mL acetonitrile was then added, vortexed, and centrifuged at 6,500 rpm for 10 min. A volume of 0.5 mL supernatant was evaporated under nitrogen stream, and the residual was dissolved in 0.2 mL 0.5 M MOPS buffer, pH 6.8. An injection solution of 0.05 mL was put onto the stationary phase of a Supelco Ascentis C₈ guard column (20 × 4 mm and 5 μm; Supelco, Bellefonte, PA, USA) and a C₈ Supelco Ascentis C8 HPLC column (150 × 4.6 mm and 5 μm; Supelco, Bellefonte, PA, USA). The analytes were eluted using a mobile phase consisting of a phosphate buffer at 0.05 M, pH 7.4, and methanol in gradient elution at a flow rate of 1 mL/min. The proportion of phosphate buffer in solvent gradient was as follows: 0 to 4 min, 96%; 4 to 7 min, decrease from 96% to 30%; 7 to 9 min, kept at 30%; after 9 min, increased to 96%. The analysis time was 12 min. The detection wavelength was set at 298 nm. The lower limit of quantification was 0.5 mg/liter. The calibration curve was linear from 0.5 to 50 mg/linear (R² = 0.9999). The method was proven to be accurate and precise with the intraday recovery at low-, medium-, and high-quality control concentrations (1, 20, and 40 mg/liters) of 87.0%, 104.1%, and 91.1%, respectively, and the precision was 3.9%, 8.1%, and 5.0%, respectively. The interday recoveries at those three concentrations were 102.0%, 102.6%, and 100.7%, respectively, and the precision was 5.7%, 6.2%, and 9.9%, respectively. The method was validated according to the FDA’s Guidance for Bioanalytical Method Validation (40).

Microbiological susceptibility data.

From January 2018 to June 2019, a total of 110 K. pneumoniae isolates from clinical samples from ICU patients were identified in the Microbiology Department using matrix-assisted laser desorption ionization–time of flight mass spectrometry (Bruker). The MIC of each isolate was determined by the Etest (bioMérieux, Lyon, France).

Population pharmacokinetic modeling.

Population PK modeling was performed using the nonparametric adaptive grid (NPAG) algorithm with the help of Pmetrics software package for R v.3.5.3 (41). Both one-compartment and two-compartment structural models with first-order elimination were tested.

In Pmetrics, each observation is weighted by 1/error². These errors capture the extra process noise related to observation, misspecified dosing, and observation times. Two types of error models in NPAG are presented as follows: error = SD × γ and error = (SD² + λ²)^0.5, respectively. SD is the standard deviation of each observation, γ represents multiplicative term, and λ represents additive term (42).

Demographic and clinical data that may influence meropenem PK, including age, total body weight, sex, serum albumin, 24-h fluid balance, diuretics, sepsis, septic shock, and CL_CR8h on the day of PK sampling, were tested as covariates for the model. In addition, an indwelling catheter for pleural, abdominal, or cerebrospinal fluid drainage could be associated with the deviation in the volume of distribution (V) and therefore this was tested as a potential covariate. The influences of covariates on the structural parameters were modeled using a linear, power, or exponential function (43). The final model was identified using a two-stage approach. In the first step, covariates were separately added to the structural model. A decrease in the log-likelihood of ≥6.64 (P ≤ 0.01) from the structural model was considered statistically significant. In the second step, a full model including all the significant covariates from step 1 was added to the model and a backward selection was applied subsequently. Covariates that resulted in an increase in the log-likelihood of ≥10.83 (P ≤ 0.001) were retained in the final model.

Model diagnostics.

Model evaluation was performed by visual assessment of the goodness of fit of individual and population plots, as well as the coefficient of determination of the linear regression of the observed versus predicted values. The predictive performance was also assessed for mean prediction error (bias) and the mean biased-adjusted squared (imprecision) of the population and individual posterior predictions. A VPC plot was used to internally determine the validity of the model. Furthermore, a nonparametric bootstrap analysis (n = 1,000) was used to obtain the 95% confidence interval for the parameters. Due to high variation and limited samples, we set any 95% confidence interval value from <0 to 0.00.

Monte Carlo simulation for determination of feasible meropenem dosing regimens in treating K. pneumoniae-infected patients. (i) Probability of PK/PD target attainment. The final population PK model was used to optimize the dose for the treatment of severe K. pneumoniae infection. Monte Carlo simulations (1,000 simulated subjects) were performed for each daily dose of each infusion method to assess the PTA at 72 h after dosing to ensure steady state was obtained. Daily doses ranged from 0.0 g to 20.0 g/day with a 100-mg incremental step and were simulated to determine the respective PTA. Different prolonged infusion methods, including continuous infusion (CI), 3-h extended infusion (EI) with dosing intervals of 6 h (EI6) and 8 h (EI8), were tested. In the simulation, we simulated the maintenance doses for the CI regimen. In this study, we sought to assess the ability to attain PD targets of 40% ƒT>MIC and 100% ƒT>MIC with MICs between 0.125 mg/liter and 32 mg/liter. The former target has been generally accepted as a minimum target for carbapenem to express bactericidal action (44), while the latter has been suggested for β-lactam treatment in critically ill patients for maximal bacterial killing effect (33, 45). The PTAs for ARC patients, defined as CL_CR8h of ≥130 mL/min/1.73 m², and non-ARC patients were also examined (46).

(ii) Cumulative fraction of response. The obtained PTA was then used to calculate the CFR, which is determined against the MIC distribution for isolated K. pneumoniae, as follows:

$$\mathrm{CFR}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \sum }_{i=1}^n\mathrm{PT}{\mathrm{A}}_i\hspace{0.17em}\times \hspace{0.17em}{F}_i$$

where i indicates the MIC category ranked from lowest to highest MIC value of a K. pneumoniae population, PTA_i is the PTA of each MIC category, and F is the fraction of the K. pneumoniae population at each MIC category (47).

The cumulative fractions of response of ARC and non-ARC patients were examined on three pathogen groups based on Clinical and Laboratory Standards Institute (CLSI) methods: susceptible, MIC ≤ 1 mg/liter; intermediate, MIC = 2 mg/liter; resistant, MIC ≥ 4 mg/liter. If isolates were reported with a MIC of >32 mg/liter, we set those MICs as 64 mg/liter as the extrapolated successive increment on the MIC scale for the CFR calculation.

(iii) Dose optimization. Sufficient efficacy of doses was assumed if at least 90% of PTA or 95% of CFR was obtained. For safety purposes, doses were limited to ensure <10% simulated profiles had concentrations above the toxicity threshold. For EI regimens, the toxic thresholds were set at C_min of 44.5 mg/liter. The key rationale in favor of this choice was based on previous studies stating a risk of 50% nephrotoxicity if C_min is >44.5 mg/liter (32). For CI regimens, we chose an upper threshold at 100 mg/liter for C_ss. This threshold was based on a real-time meropenem TDM paper, which set a maximum steady-state concentration between 100 and 120 mg/liter (33).

Statistical analysis.

Where applicable, continuous data are presented as means (± SD) or medians (with IQR). Categorical data are presented as numbers and percentages.

Data availability.

The data sets used and/or analyzed during the current study are available from the corresponding author on reasonable request.