Using Population Pharmacokinetic Modeling and Monte Carlo Simulations To Determine whether Standard Doses of Piperacillin in Piperacillin-Tazobactam Regimens Are Adequate for the Management of Febrile Neutropenia

ABSTRACT

Changes in the pharmacokinetics of piperacillin in febrile neutropenic patients have been reported to result in suboptimal exposures. This study aimed to develop a population pharmacokinetic model for piperacillin and perform dosing simulation to describe optimal dosing regimens for hematological malignancy patients with febrile neutropenia. Concentration-time data were obtained from previous prospective observational pharmacokinetic and interventional therapeutic drug monitoring studies. Nonparametric population pharmacokinetic analysis and Monte Carlo dosing simulations were performed with the Pmetrics package for R. A two-compartment model, with between-subject variability for clearance (CL), adequately described the data from 37 patients (21 males, age of 59 ± 12 years [means ± standard deviations] and weight of 77 ± 16 kg). Parameter estimates were CL of 18.0 ± 4.8 liters/h, volume of distribution of the central compartment of 14.3 ± 7.3 liters, rate constant for piperacillin distribution from the central to peripheral compartment of 1.40 ± 1.35 h⁻¹, and rate constant for piperacillin distribution from the peripheral to central compartment of 4.99 ± 7.81 h⁻¹. High creatinine clearance (CL_CR) was associated with reduced probability of target attainment (PTA). Extended and continuous infusion regimens achieved a high PTA of >90% for an unbound concentration of piperacillin remaining above the MIC (fT_>MIC) of 50%. Only continuous regimens achieved >90% PTA for 100% fT_>MIC when CL_CR was high. The cumulative fraction of response (FTA, for fractional target attainment) was suboptimal (<85%) for conventional regimens for both empirical and directed therapy considering 50% and 100% fT_>MIC. FTA was maximized with prolonged infusions. Overall, changes in piperacillin pharmacokinetics and the consequences on therapeutic dosing requirements appear similar to those observed in intensive care patients. Guidelines should address the altered dosing needs of febrile neutropenic patients exhibiting high CL_CR or with known/presumed infections from high-MIC bacteria.

INTRODUCTION

Altered antibiotic dosing requirements in febrile neutropenic patients have been documented previously (1–3). Changes in the pharmacokinetics (PK) of hydrophilic antibiotics appear common and can result in low plasma and tissue antibiotic exposure when conventional dosing regimens are used. The drivers for altered PK of antibiotics are thought to be the pathophysiologic phenomena associated with systemic inflammation, including increased cardiac output and organ blood flow and movement of fluid into the interstitial space (3). There are also additional causes of altered PK associated with iatrogenic factors, such as high intravenous fluid loading, a common intervention in patients with hematological malignancies, which can affect drug volume of distribution (4).

In a single-dose pilot study (5), we previously described the altered PK of piperacillin in febrile neutropenic patients with hematological malignancy. We observed markedly altered PK with elevations in volume of distribution as well as clearance leading to suboptimal exposure. This was reflected in a low percentage of the dosing interval for which the unbound concentration of piperacillin remained above the MIC (fT_>MIC). We observed that 10 (83%) and eight (67%) participants had less than 50% fT_>MIC against Pseudomonas aeruginosa and Enterobacteriaceae, respectively.

Subsequently, we hypothesized that, given the unpredictability of PK alterations, therapeutic drug monitoring (TDM)-guided dose optimization is required to ensure adequate exposure in all patients. Accordingly, we conducted a randomized controlled study to test the utility of piperacillin TDM in febrile neutropenic patients (6). We found that TDM was able to increase the success rate of target attainment from a baseline of 19% to 73%, in contrast to a decrease from 25% to 7% in the control group. Although TDM was able to significantly improve drug exposure, there was a large delay for most patients in achieving therapeutic concentrations, and some patients never achieved the targets. The results of this study highlight the difficulty with empirical prediction of dosing requirements based simply on a measured TDM concentration which may not achieve ideal concentrations until better and quicker real-time TDM is available. To this end, a population pharmacokinetic model that is able to individualize initial dosing based on patient covariate data, e.g., renal function and/or body weight, or that can be used for Bayesian forecasting in combination with TDM would enable more accurate dosing (7). Unfortunately, there is a paucity of such models for piperacillin in adult patients with febrile neutropenia and hematological malignancies.

Therefore, the aim of this work was to develop a population PK model for piperacillin and perform dosing simulations to describe optimized dosing regimens for piperacillin-tazobactam for the treatment of febrile neutropenia.

RESULTS

Demographic and clinical data.

Data from 37 patients were used for population PK analysis. Patient demographics and clinical characteristics are presented in Table 1. PK samples during the first dosing interval were available from 12 patients, and steady-state samples during intermittent dosing were available from 25 patients. A total of 184 concentration-time data points were included in the analysis.

TABLE 1.

Characteristics of study participants

Characteristica	n (%) or median (IQRb)
Age (yr)	61 (53–66)
Sex
Male	21 (57)
Female	16 (43)
Body mass index (kg/m2)	25.7 (23.0–28.1)
Weight (kg)	78 (63–87)
Creatinine clearance (ml/min/1.73 m2)	94 (71–132)
Albumin (g/liter)	27 (23–28)
Malignancy
Acute myeloid leukemia	14 (38)
Multiple myeloma	10 (27)
Hodgkin's lymphoma	4 (11)
Non-Hodgkin's lymphoma	4 (11)
Diffuse large B-cell lymphoma	2 (5)
B-lymphoblastic lymphoma	1 (3)
Follicular lymphoma	1 (3)
Primary CNS lymphoma	1 (3)
Positive blood culture	14 (38)
Organisms isolated
Bacillus cereus	2 (5)
Escherichia coli	1 (3)
Enterobacter cloacae	1 (3)
Enterobacter aerogenes	1 (3)
Klebsiella pneumonia	2 (5)
Pseudomonas aeruginosa	1 (3)
Staphylococcus sp.	3 (8)
Viridans streptococci	3 (8)
Additional antibiotics
Gentamicin	36 (97)
Vancomycin	4 (11)
Ciprofloxacin	1 (3)
Metronidazole	1 (3)
Trimethoprim-sulfamethoxazole	1 (3)

^aCNS, central nervous system.

^bIQR, interquartile range.

Pharmacokinetic model building.

The concentration-time data were adequately described by a two-compartment model with linear elimination from the central compartment and linear intercompartmental distribution. Only creatinine clearance (CL_CR) resulted in significant reduction in the log likelihood ratio and showed improved model fit as assessed by goodness-of-fit plots. The lowest value of objective function and better goodness-of-fit plots (Fig. 1; see also Fig. S1 and S2 in the supplemental material) were observed when CL_CR was normalized to 100 ml/min/1.73 m². The final covariate model thus was given by the equation piperacillin clearance = TVCL × (CL_CR/100), where TVCL is the typical value of clearance. Parameter estimates for the final covariate model are given in Table 2.

FIG 1.

Diagnostic plots for the final covariate model, observed versus individual-predicted (left) and population-predicted (right) concentrations.

TABLE 2.

Estimates of piperacillin pharmacokinetic parameters for the final covariate model

Parametera	Mean (SD)	%CVb
CL (liters/h)	18.02 (4.80)	26.63
V (h)	14.30 (7.31)	51.09
Kcp (h−1)	1.40 (1.35)	96.28
Kpc (h−1)	4.99 (7.81)	156.49

^aCL, clearance; V, volume of distribution of central compartment; Kcp, rate constant for piperacillin distribution from central to peripheral compartment; Kpc, rate constant for piperacillin distribution from peripheral to central compartment.

^bCV, coefficient of variation.

Dosing simulations.

The final covariate model was used for Monte Carlo dosing simulations. The PTA during the first 24 h for conventional intermittent dosing regimens of piperacillin for PK/pharmacodynamic (PD) targets of 50% fT_>MIC and 100% fT_>MIC at various levels of CL_CR are presented in Fig. 2. Similar PTA was observed at steady state (data not shown).The results show that for patients with normal CL_CR, the probability of attaining 50% fT_>MIC is low even for MIC values as low as 1 to 2 mg/liter. The PTA is very low when CL_CR is higher (140 and 160 ml/min/1.73 m²). PTA for 100% fT_>MIC is low even for very low MIC values (0.125 mg/liter) with normal to high CL_CR values (>100 ml/min/1.73 m²). The PTA from prolonged infusion dosing regimens is given in Tables 3 and 4. Generally, extended infusion (EI) and continuous infusion (CI) regimens achieve a high PTA (>90%) for 50% fT_>MIC, except for MIC values of ≥16 mg/liter in patients with a high CL_CR. However, only CI regimens achieve a high PTA for 100% fT_>MIC for a wide range of renal function and MIC values.

FIG 2.

Probability of target attainment for conventional intermittent dosing regimens of piperacillin for PK/PD targets of 50% fT_>MIC and 100% fT_>MIC. CL_CR, creatinine clearance in ml/min/1.73 m²; PTA, probability of target attainment; q8h, every 8 h intermittent infusion; q6h, every 6 h intermittent infusion.

TABLE 3.

PTA for alternative prolonged infusion dosing regimens during the first 24 h^a

Dosing regimen and CLCR (ml/min/1.73 m2)	PTA for 50% fT>MIC by MIC (mg/liter)								PTA for 100% fT>MIC by MIC (mg/liter)
	0.125	0.25	0.5	1	2	4	8	16	0.125	0.25	0.5	1	2	4	8	16
4.0-g EI over 4 h q8h
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−	−
60	+	+	+	+	+	+	+	+	+	+	+	+	−	−	−	−
80	+	+	+	+	+	+	+	+	+	+	−	−	−	−	−	−
100	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
120	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
140	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
160	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
4.0-g EI over 3 h q6h
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−
60	+	+	+	+	+	+	+	+	+	+	+	+	+	−	−	−
80	+	+	+	+	+	+	+	+	+	+	+	+	−	−	−	−
100	+	+	+	+	+	+	+	+	+	+	+	−	−	−	−	−
120	+	+	+	+	+	+	+	+	+	−	−	−	−	−	−	−
140	+	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−
160	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
4.0-g LD + 8.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
80	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
100	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
120	+	+	+	+	+	+	+	−	+	+	+	+	+	+	−	−
140	+	+	+	+	+	+	−	−	+	+	+	+	+	+	−	−
160	+	+	+	+	+	+	−	−	+	+	+	+	+	+	−	−
4.0-g LD + 12.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
80	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
100	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
120	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
140	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
160	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
4.0-g LD + 16.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
80	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
100	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
120	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
140	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
160	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−

^a+, PTA of ≥0.9; −, PTA of <0.9.

TABLE 4.

PTA for alternative infusional dosing regimens at pharmacokinetic steady state measured at 48 to 72 h^a

Dosing regimen and CLCR (ml/min/1.73 m2)	PTA for 50% fT>MIC by MIC (mg/liter)								PTA for 100% fT>MIC by MIC (mg/liter)
	0.125	0.25	0.5	1	2	4	8	16	0.125	0.25	0.5	1	2	4	8	16
4.0-g EI over 4 h q8h
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−	−
60	+	+	+	+	+	+	+	+	+	+	+	+	−	−	−	−
80	+	+	+	+	+	+	+	+	+	+	−	−	−	−	−	−
100	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
120	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
140	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
160	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−	−
4.0-g EI over 3 h q6h
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−	−
80	+	+	+	+	+	+	+	+	+	+	+	+	−	−	−	−
100	+	+	+	+	+	+	+	+	+	+	−	−	−	−	−	−
120	+	+	+	+	+	+	+	−	+	−	−	−	−	−	−	−
140	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
160	+	+	+	+	+	+	+	−	−	−	−	−	−	−	−	−
4.0-g LD + 8.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−
80	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
100	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
120	+	+	+	+	+	+	+	−	+	+	+	+	+	+	−	−
140	+	+	+	+	+	+	−	−	+	+	+	+	+	+	−	−
160	+	+	+	+	+	+	−	−	+	+	+	+	+	+	−	−
4.0-g LD + 12.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
80	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
100	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
120	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
140	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
160	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−
4.0-g LD + 16.0-g CI
40	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
60	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
80	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
100	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
120	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−
140	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	−
160	+	+	+	+	+	+	+	−	+	+	+	+	+	+	+	−

^a+, PTA of ≥0.9; −, PTA of <0.9.

The fraction of response (FTA, for fractional target attainment) for various dosing regimens of piperacillin against the EUCAST MIC distributions of Escherichia coli, Klebsiella pneumoniae, and Pseudomonas aeruginosa for the different simulated renal functions (CL_CR) is given in Tables 5 and 6. For E. coli, the FTA for intermittent dosing regimens was suboptimal (<85%) for both empirical and directed therapy considering 50% and 100% fT_>MIC, particularly at high CL_CR. Both EI and CI regimens achieved high coverage at all CL_CR levels for empirical and directed therapy targeting 50% fT_>MIC. However, only CI achieved optimal FTA for 100% fT_>MIC at all CL_CR levels. For K. pneumoniae, high-dose CI (4.0-g loading dose over 1 h [LD] plus 16.0-g CI) or more frequent EI (4.0 g every 6 h [q6h] with 3-h EI) was required for empirical coverage at 50% and 100% fT_>MIC. For directed therapy, all of the EI or CI regimens achieved optimal FTA for 50% fT_>MIC, but only CI regimens achieved optimal FTA for 100% fT_>MIC. For P. aeruginosa, none of the tested dosing regimens achieved optimal FTA for empirical therapy, but for directed therapy, EI regimens and CI regimens (except the 8-g CI) provided good coverage at 50% fT_>MIC. At 100% fT_>MIC, only two of the CI regimens (12.0 g and 16.0 g with 4.0-g LD) achieved optimal FTA.

TABLE 5.

FTA for various dosing regimens of piperacillin against the EUCAST MIC distributions of E. coli, K. pneumoniae, and P. aeruginosa during the first 24 h

^aShaded area indicates optimal FTA of greater than or equal to 85%.

TABLE 6.

Steady-state FTA for various dosing regimens of piperacillin against the EUCAST MIC distributions of E. coli, K. pneumoniae, and P. aeruginosa

^aShaded area indicates optimal FTA of greater than or equal to 85%.

Table 7 presents a comparison of the model-predicted steady-state concentrations (for continuous infusions) and steady-state trough concentrations at 72 h (for extended infusion and intermittent infusion) for a low and high simulated CL_CR.

TABLE 7.

Comparison of model-predicted steady-state concentrations for low and high creatinine clearance

CLCR (ml/min/1.73 m2) and simulated dosing regimen	Model-predicted Cssa
	Median (mg/liters)	IQR (mg/liters)	Maximum Css/trough (mg/liters)
40
4.0 g q8h	14.2	6.1–22.8	68.9
4.0 g q6h	28	16.5–42.7	87.2
4.0 g q8h, 4-h EI	25.8	5.0–39.8	74.8
4.0 g q6h, 3-h EI	43.1	13.1–62.3	107.5
4.0-g LD + 8.0-g CI	56.3	34.1–56.3	88.2
4.0-g LD + 12.0-g CI	67.8	51.2–84.3	132.0
4.0-g LD + 16.0-g CI	88.3	67.7–112.1	172.2
140
4.0 g q8h	0.1	BLOQ of −0.4	10.6
4.0 g q6h	0.4	0.1–1	15.8
4.0 g q8h, 4-h EI	0.591556	0.2–1.3	11.3
4.0 g q6h, 3-h EI	1.803293	0.7–3.3	16.9
4.0-g LD + 8.0-g CI	12.91229	10.8–16.1	25.6
4.0-g LD + 12.0-g CI	19.36153	16.1–24.2	38.1
4.0-g LD + 16.0-g CI	25.25549	21.3–32.0	49.5

^aData for continuous infusion regimens are for steady-state concentration (Css) between 48 and 72 h and trough concentrations at 72 h for intermittent and extended infusion regimens. BLOQ, below the limit of quantification of the assay method for the model data (<0.1 mg/liter).

DISCUSSION

Compared to data from healthy volunteers, changes in the pharmacokinetic parameters of piperacillin and other hydrophilic antibiotics have been described in some special patient populations, such as febrile neutropenic patients receiving cancer chemotherapy (1, 3), surgical and medical intensive care unit patients (8), patients with cystic fibrosis (9), and obese patients (10). The change in primary pharmacokinetic parameters (volume of distribution and clearance) have been attributed to disease-specific physiological perturbances and iatrogenic interventions (1, 11). The estimated mean population central volume of distribution in the current study (14.3 ± 7.3 liters) is comparable with a previously reported population estimate (14.5 ± 6.6 liters) for critically ill patients (12). These values are only slightly higher than reported values for healthy individuals, e.g., 12.7 liters (13) and 10.4 liters (14). However, other population pharmacokinetic analyses have reported significant expansion of the volume of distribution in critically ill and hospitalized patients, e.g., 19.4 liters (15) and 21.7 liters (16), which appears highest in obese critically ill patients (49.0 ± 19.0 liters) (17).

On the other hand, the estimated mean population clearance of piperacillin in this analysis (18.2 ± 4.8 liters/h) is higher than that reported for healthy volunteers (10.1 liters/h [13] and 11.3 liters/h [13]. The increased clearance in this study is consistent with the study cohort which included a substantial proportion of patients with high CL_CR (32% of patients had CL_CR greater than 120 ml/min/1.73 m²). Indeed, clearance of piperacillin is highly dependent on the renal function of the study cohort, and this in many ways explains the different reported mean piperacillin clearances in different patient populations. In the critically ill, for instance, clearance could be elevated (e.g., 17.1 liters [18]) or similar/slightly higher (e.g., 13.8 liters/h [15, 16] and 14.0 ± 7.1 liters [17]) or may even be reduced (e.g., 3.6 liters/h [19] and 5.6 ± 3.2 liters/h [12]) compared to healthy volunteers (13). It could be particularly high in those patients with burns and trauma (20). For example, a pharmacokinetic model for burn patients predicts elevated clearance of 16 liters/h for patients when CL_CR is 130 ml/min and 20 ml/min when CL_CR is 160 ml/min (21). This is comparable to the elevated mean clearance observed in the current study (18.2 ± 4.8 liters/h) and, consistent with other studies, contributes to suboptimal therapeutic exposure from traditional dosing regimens.

Indeed, results of this pharmacometric analysis suggest that commonly employed intermittent piperacillin doses (4.0 g every 6 to 8 h) are highly likely to result in subtherapeutic exposures, particularly when higher-MIC Gram-negative bacteria are targeted in patients with high CL_CR (Fig. 2). Although the prevalence of Gram-negative infection in febrile neutropenia is low in the developed world, e.g., 10.7% in a French hematology center (22), in other parts of the world the majority of bacteremia in these patients are attributed to Gram-negative pathogens, e.g., 60.3% in Malaysia (23) and 78.8% in Lebanon (24). Given the relatively high MIC of Gram-negative pathogens, subtherapeutic exposure is highly likely in patients with high CL_CR, as observed in this study (Tables 5 to 7). Increased renal elimination of antibiotics, termed augmented renal clearance (ARC), has been described previously for piperacillin and other antibiotics predominantly eliminated by renal excretion (6, 25). In a previous trial of febrile neutropenic patients, we observed that 31% of the study cohort exhibited ARC. This is comparable to other reports for intensive care unit (ICU) patients: 33% by Ruiz et al. (26), 38.7% by Kawano et al. (27), and 28% by Campassi et al. (28). A higher incidence in ICU patients was also reported by other authors, e.g., 55.8% (29) and 65.1% (30). In patients with ARC (commonly defined as CL_CR of ≥130 ml/min/1.73 m²), intermittent dosing regimens of piperacillin are highly likely to result in poor exposure (31). While this is in agreement with the findings of the current study, our results also suggest that underexposure occurs even in patients without ARC. The FTA of piperacillin-directed therapy at the traditional dosing regimen of 4.0 g every 8 h (q8h) against the common pathogens E. coli, K. pneumoniae, and P. aeruginosa was inadequate (<85%) for CL_CR values as low as 100, 80, and 60 ml/min/1.73 m², respectively, even for the conservative target 50% fT_>MIC (Tables 5 and 6). Similarly, dosing with 4.0 g every 6 h also fails to provide adequate FTA for normal to high CL_CR values. Importantly, both intermittent regimens show poor FTA for a wide range of low to high CL_CR values if 100% fT_>MIC is the desired treatment target (Tables 5 and 6). These findings are consistent with previous observations of altered antibiotic PK in febrile neutropenic patients that result in frequent failure of conventional intermittent dosing regimens to meet PK/PD dosing targets (3). Thus, the use of traditional intermittent dosing regimens of piperacillin-tazobactam in the treatment of febrile neutropenia should be critically reevaluated in clinical studies, particularly if it is to be used as a monotherapy either for directed therapy against pathogens with higher MIC breakpoints (≥8 mg/liter) or for initial empirical coverage.

On the other hand, in accordance with previous observations (2), the dosing simulations presented in this paper suggest that for optimal piperacillin exposure covering common pathogens isolated from patients with febrile neutropenia (E. coli, K. pneumoniae, and P. aeruginosa), particularly those with higher MICs, prolonged infusion dosing regimens (EI or CI) are necessary. High PTA values for 50% fT_>MIC were observed for EI regimens (Tables 3 and 4) with high FTA against susceptible strains of E. coli, K. pneumoniae, and P. aeruginosa. Similar results were observed with CI regimens, except that low-dose (8-g) CI may result in underexposure against P. aeruginosa when patients have high CL_CR (≥140 ml/min/1.73 m²) (Tables 5 and 6). These findings are in accordance with previous studies which reported that EI or CI regimens achieve better PK/PD exposure for the time-dependent beta-lactam antibiotics, including piperacillin (32–34).

However, the current PK analysis shows that despite the high PTA for EI or CI regimens within the susceptible MIC range, the FTA for empirical therapy, especially against the MIC distribution of P. aeruginosa, was very poor across the wide range of simulated CL_CR (Tables 5 and 6). Therefore, monotherapy with piperacillin-tazobactam even with prolonged infusion is unlikely to provide consistent empirical coverage against P. aeruginosa. Similarly for K. pneumoniae, CI may not provide empirical coverage in those patients with high CL_CR, even at the maximum recommended total daily doses. Although some guidelines suggest routine combination of piperacillin-tazobactam with an aminoglycoside (e.g., gentamicin), other guidelines still recommend monotherapy with conventional intermittent dosing regimens of piperacillin-tazobactam as a first-line empirical therapy for febrile neutropenia (35, 36). When culture results are available and the susceptibility of the pathogen is known, directed therapy with EI or CI regimens of piperacillin-tazobactam monotherapy could provide adequate exposure against high-MIC pathogens in the susceptible range if the conservative target of 50% fT_>MIC is considered the optimal target. However, there is as yet no clear data on which PK/PD target is optimal for beta-lactams in general, although for the immunocompromised febrile neutropenic patients, studies suggested a more aggressive 100% fT_>MIC is prudent. For the higher exposure of 100% fT_>MIC, results of this study suggest CI is necessary to cover for high-MIC pathogens. FTA was optimal (≥85%) only for the CI and was suboptimal both for intermittent and EI regimens when 100% fT_>MIC was targeted (Tables 5 and 6). Given that most beta-lactams share similar PK properties, these findings also highlight that for all beta-lactams, CI may be necessary in neutropenic patients with ARC when exposure at 100% fT_>MIC is considered to maximize outcomes.

On the other hand, in patients with low creatinine clearance, CI regimens may result in high sustained steady-state concentrations (Table 7; see also Fig. S3 in the supplemental material). Although piperacillin and the beta-lactams in general have a wide safety margin, very high concentrations remain a concern due to potential neurotoxicity (37). Nevertheless, there is a lack of clearly defined cutoffs for steady-state concentrations that mark the risk of toxicity. Centers that perform beta-lactam TDM use an arbitrary cutoff of 6 to 10 times the MIC to denote concentrations above which greater effectiveness is unlikely, rather than where toxicity is more likely (i.e., toxicity is likely to be related to a concentration threshold rather than a concentration/MIC ratio) (38). Considering the EUCAST breakpoints for Enterobacteriaceae (8 mg/liter) and P. aeruginosa (16 mg/liter), this would mean concentrations as high as 80 mg/liter and 160 mg/liter, respectively. Steady-state concentrations predicted for the CI regimens when CL_CR is 40 ml/min/1.73 m² were generally within this range (Table 7). However, low-dose intermittent infusions (e.g., 4.5 g piperacillin-tazobactam every 8 hours) may be safe and provide adequate exposure in patients with low CR_CL (Tables 3 to 7).

This study has several limitations. First, only total concentrations of piperacillin were available for modeling, and plasma protein binding was assumed to be similar in all patients (30%). Of note, however, patients in the study cohort did not exhibit high variability in albumin concentrations except for a slight hypoalbuminemia (5, 6). Further, a protein binding study by Wong et al. (39) showed that 30% binding is a reasonable assumption for piperacillin. Second, CL_CR was calculated using the Cockcroft–Gault formula or the Jelliffe equation and was not directly measured. Mathematical equations generally provide poor estimates at extremes of CL_CR and may not be optimal for accurate dosing, although they are commonly used clinically (40). Third, the current analysis provides only the effect of different dosing regimens on PK/PD exposure and not clinical outcome.

Conclusions.

The traditional intermittent dosing regimens of piperacillin-tazobactam are unlikely to provide adequate exposure for empirical management of febrile neutropenia. Subtherapeutic exposure is highly likely if Gram-negative pathogens with susceptibility close to clinical breakpoints are causative of the underlying infection. Patients with ARC are particularly vulnerable to underexposure even with the use of EI or CI regimens. Directed therapy with EI or CI regimens are highly likely to achieve adequate exposure in the majority of patients. At least for patients at high risk of subtherapeutic exposure (presence of high-MIC pathogens and/or ARC), guidelines should consider the altered dosing requirements of piperacillin-tazobactam. We suggest the use of EI or CI regimens unless TDM is performed to confirm appropriateness of exposures from intermittent regimens, particularly when used alone as a monotherapy.

MATERIALS AND METHODS

Patients and study setting.

Patient data were retrieved from a previously described prospective observational PK study (5) and a prospective interventional TDM study (6). The study population and settings were similar in both studies and included febrile neutropenic patients aged ≥18 years and undergoing treatment for hematological malignancies at The Queen Elizabeth Hospital (TQEH) in Adelaide, Australia. Febrile neutropenia was defined as the presence of a single oral temperature of ≥38.4°C (101°F) or a temperature of ≥38.0°C (100.4°F) for 1 h, with a neutrophil count of <500 cells/mm³ or a count of <1,000 cells/mm³ with a predicted decrease to <500 cells/mm³ (41). Ethics approval was granted from local institutional human research ethics committees (HREC/13/TQEHLMH/301; HREC/12/TQEHLMH/157).

Population pharmacokinetic modeling.

Piperacillin concentration-time data after intermittent dosing of piperacillin-tazobactam in the aforementioned studies (5, 6) were included in the population PK analysis. For patients who participated in both studies, only data from the prospective PK study with more frequent sampling was used. All included patients received 4.5 g piperacillin-tazobactam every 8 h. For 12 patients receiving intensive serial blood sampling, the concentration-time data were collected after the first dose: first sample at the end of line flushing (45 min) and then at 1 h, 2 h, 3 h, 4 h, 5 h, 6 h, and 7 h after the start of infusion, with a final sample just before the second dose (7.8 h). For the remaining 25 patients, blood samples were collected at steady state. Available data were included from mid-dose intervals and/or trough samples collected after the third dose (20 h and 23.8 h), sixth dose (44 h and 47.8 h), and ninth dose (71.8 h).

An R package for nonparametric adaptive grid algorithms, Pmetrics version 1.5.0, was used for pharmacometric analysis. A stepwise approach was followed in the model-building process: (i) determination of the structural base model, (ii) selection of the best-fit statistical error model, (iii) development of covariate model, and (iv) model evaluation.

Determination of the structural base model.

Different structural models, based on one, two, or three compartments, were fitted to the concentration-time data. The elimination of piperacillin from the central compartment and intercompartmental distribution were modeled as linear processes.

Selection of statistical error models.

Both the additive and multiplicative error models available in the Pmetrics package were tested. The multiplicative error model takes the form of Error = SD × γ, where SD is standard deviations of observations and γ is the process noise associated with observations. The additive error model is given by Error = (SD² + λ²)^0.5. The SD was further modeled by a second-degree polynomial function, beginning with coefficients deduced from assay data and further iterative optimization based on model diagnostics.

Development of covariate model.

Available clinical covariates were assessed for biological plausibility and subsequently evaluated in the covariate analysis. Selected covariates that were tested on the structural model parameters (volume[s] of distribution and clearance) include age, sex, weight, and creatinine clearance (calculated by the Cockcroft-Gault formula if renal function was stable or the Jelliffe equation if not; expressed in ml/min/1.73 m²). A standard covariate evaluation algorithm was followed through forward addition and backward elimination in a stepwise fashion.

Model evaluation.

Diagnostic plots and statistical examination through objective function values were used for comparison and selection of models. Diagnostic plots included scatter plots of observed concentrations versus predicted concentrations, scatter plots of residuals versus predicted concentrations, scatter plots of residuals versus time, a histogram of residuals with a test of normality (D'Agostino test), and visual predictive checks. The log-likelihood ratio test for the nested model, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were each examined. In addition, model bias and imprecision were examined to discriminate between models. Model bias in Pmetrics is defined as the mean weighted error of predicted minus observed concentrations, ∑(predicted-observed/standard deviation)/N, and imprecision is defined as the bias-adjusted, mean weighted squared error of predicted minus observed concentration, i.e., ∣∑[(predicted-observed)²/(standard deviation)²]/N∣ − ∣∑(predicted-observed)/standard deviations/N∣, where N is the number of observations/predictions.

Dosing simulations.

Monte Carlo simulations (n = 1,000) were performed to determine the probability of target attainment (PTA) for different dosing regimens and renal function (CL_CR) for PK/PD targets of 50% and 100% fT_>MIC and 30% plasma protein binding (39). The dosing regimens were simulated up to steady state from 0 to 72 h for CL_CR of 40, 60, 80, 100, 120, 140, and 160 ml/min/1.73 m² and included 4.0-g intermittent infusion (II) over 30 min q8h, 4.0-g II over 30 min q6h, 4.0-g extended infusion (EI) over 4 h q8h, 4.0-g EI over 3 h q6h, 4.0-g loading dose over 1 h (LD) plus 8.0-g continuous infusion (CI), 4.0-g LD plus 12-g CI, and 4.0-g LD plus 16.0-g CI. PTA was determined at two stages of therapy, during the first 24 h and at steady state from 48 h to 72 h.

The fractional target attainment (FTA), during the first 24 h and at steady state from 48 h to 72 h, was calculated for Escherichia coli, Klebsiella pneumoniae, and P. aeruginosa based on the MIC distribution of the European Committee for Antimicrobial Susceptibility and Testing (EUCAST) database (available at www.eucast.org). FTA describes the proportion of the bacterial population for which the selected PK/pharmacodynamics (PD) target is attained given the Monte Carlo simulation and the MIC distribution. FTA was calculated both for empirical therapy, i.e., considering all of the categories of the entire MIC distribution, and for directed therapy, i.e., considering those categories of MIC distribution within the susceptibility range defined by clinical breakpoints (8 mg/liter for Enterobacteriaceae and 16 mg/liter for P. aeruginosa). Doses were considered optimal if the FTA was greater than 85%.