Pharmacokinetics of piperacillin–tazobactam: intermittent dosing versus continuous infusion

Pharmacokinetics of piperacillin–tazobactam: intermittent dosing versus continuous infusion

International Journal of Antimicrobial Agents 25 (2005) 62–67 Pharmacokinetics of piperacillin–tazobactam: intermittent dosing versus continuous infu...

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International Journal of Antimicrobial Agents 25 (2005) 62–67

Pharmacokinetics of piperacillin–tazobactam: intermittent dosing versus continuous infusion Christine Bucka , Norbert Bertramb , Thomas Ackermanna,∗ , Tilman Sauerbrucha , Hartmut Derendorfc , Wilhem Dieter Paara a

Department of General Internal Medicine, University of Bonn, Sigmund-Freud-Strasse 25, Bonn, Germany b LTA-Labor f¨ ur Toxikologie und Analytik, Friedrichh¨oher Strasse 28, K¨onigswinter, Germany c Department of Pharmaceutics, University of Florida, Gainesville, FL 32610, USA Received 25 April 2004; accepted 20 August 2004

Abstract In the present study 24 hospitalized patients requiring empirical antibiotic treatment were randomly assigned to receive the ␤-lactam antibiotic/␤-lactamase inhibitor combination piperacillin–tazobactam either as an intermittent or as a continuous infusion. According to pharmacokinetic modelling, the daily dose was reduced by 33% in patients receiving continuous infusion compared with intermittent infusion. Dose reduction because of impaired renal function was required in the intermittent dosing group for 5 of 12 patients compared with 1 of 12 patients in the continuous infusion group. However, the mean daily dose in the continuous group was 15% less than the intermittent infusion group. Mean serum concentrations of piperacillin were to 39.0 ␮g/ml after the end of bolus distribution, exceeding by far the minimal inhibitory concentration of the most clinically relevant pathogens. The corresponding mean value for tazobactam was 6.3 ␮g/ml. Pharmacokinetic/pharmacodynamic modelling suggests that both treatment schemes should produce virtually identical anti-infective responses to sensitive, intermediate and resistant strains. In the present study the continuous infusion of piperacillin/tazobactam provided adequate antibacterial activity over the 24-h dosing period and offers the potential for a substantial reduction in the total daily dose. © 2004 Elsevier B.V. and the International Society of Chemotherapy. All rights reserved. Keywords: Piperacillin; Tazobactam; Antimicrobial therapy; ␤-Lactam antibiotics; Continuous infusion

1. Introduction Improved characterization of the pharmacodynamic properties of antimicrobials has led to revisions in recommendations on dosing in infections. Aminoglycosides have been found to display concentration-dependent killing. For this reason this class of antimicrobials shows highest activity when peak serum drug concentration-to-MIC ratio is maximized [1]. In contrast, the bactericidal activity of ␤-lactam antibiotics is not significantly increased by multiples of the MIC [2]. These antimicrobials show time-dependent killing, e.g. the time the serum concentration is above the MIC is crucial for therapeutic success. Maximization of the time above the MIC can be obtained by administering ␤-lactam ∗

Corresponding author. Tel.: +49 228 287 5216; fax: +49 228 287 4323. E-mail address: [email protected] (T. Ackermann).

antibiotics via continuous infusion [3]. It has been shown that continuous infusion may lead not only to a reduced time to prepare the daily intravenous regimen, but also to a reduction of the total amount of the antibiotic used per day [4]. The objective of this study was to compare the concentration–time profiles of piperacillin and tazobactam administered either by continuous infusion or intermittent bolus infusions in hospitalized patients with different infections.

2. Patients and methods 2.1. Subjects Male and female patients of at least 18 years who were hospitalized or admitted to the Department of General

0924-8579/$ – see front matter © 2004 Elsevier B.V. and the International Society of Chemotherapy. All rights reserved. doi:10.1016/j.ijantimicag.2004.08.012

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Table 1 Demographic data and clinical response of 12 patients randomly assigned to receive intermittent infusion of piperacillin–tazobactam for different indications Patient

Sex

Age

Weight

Cr-clearance (ml/min)

Dose/24 h (g piperacillin/tazobactam)

Indication for antibiotic therapy

Response

I.B. R.D.

F F

74 49

68 80

1 × 4/0.5 2 × 4/0.5 reduction to 1 × 4/0.5 on day 3

FUO Sepsis endocarditis

Yesb Noc

K.J. G.K. A.M. H.M. H.R. F.S. H.S.

M M M F F M F

76 53 66 61 32 68 73

67 71 75 57 48 88 74

3 × 4/0.5 1 × 4/0.5 3 × 4/0.5 3 × 4/0.5 3 × 4/0.5 3 × 4/0.5 3 × 4/0.5

Severe CAP FUO HAP Cholangitis FUO Cholangitis FUO

Nod Yese Noe Yesf Uncertaing Yese Yese

C.Sch. W.St. G.H.

M M M

64 51 50

94 50 63

<10a Initially 80, deterioration to <10 within 4 days 84 20a 85 90 87 60 Initially 58, deterioration to 30 within 4 days 25a 25 100

1 × 4/0.5 1 × 4/0.5 reduction to 3 × 2/0.25 3 × 4/0.5

FUO HAP HAP

Yese Yesh Yese

FUO: fever of unknown origin, CAP: community acquired pneumonia, HAP: hospital acquired pneumonia. a Haemodialysis. b Piperacillin/tazobactam was combined with vancomycin. c Piperacillin/tazobactam was combined with levofloxacin and amphotericin B. d Piperacillin/tazobactam was combined with erythromycin. e Antibiotic monotherapy with piperacillin/tazobactam. f Piperacillin/tazobactam was combined with levofloxacin. g Fever caused by lymphoma. h Piperacillin/tazobactam was combined with amikacin.

Internal Medicine of the University Hospital in Bonn for different reasons and suffered from either community- or hospital-acquired infections were included in the study. Exact inclusion criteria were as follows: (late onset) hospitalacquired pneumonia, severe community-acquired pneumonia, severe urinary tract infection, cholangitis in patients with risk factors, complicated peritonitis, patients at risk with fever

of unknown origin. Demographic data and indications for the initiation of piperacillin–tazobactam therapy are given in Tables 1 and 2. Exclusion criteria were lack of informed consent, pregnancy or lactation in women, known hypersensitivity or intolerance to piperacillin–tazobactam, and epilepsy. Written informed consent was obtained from all patients. The study was approved by the institutional review board.

Table 2 Demographic data and clinical response of 12 patients randomly assigned to receive continuous infusion of piperacillin–tazobactam Patient

sEX

Age (years)

Weight (kg)

Cr-clearance (ml/min)

Daily dose (g piperacillin /tazobactam)

Indication for antibiotic therapy

Response

B.B. H.B.

M F

50 68

79 65

8.0/1.0 8.0/1.0

Severe CAP FUO

Yesa Noa

J.H. O.K. R.K. H.L. B.S.

M M M M M

63 56 41 69 73

85 65 75 81 60

4.0/0.5 8.0/1.0 8.0/1.0 8.0/1.0 8.0/1.0

Sepsis FUO Sepsis, ARDS FUO Cholangitis

Noc Noa Yesd Yesa Yese

S.S. HD.S.

M M

69 47

85 65

8.0/1.0 Initially 8.0/1.0 reduction to 4.0/0.5 on day 3

FUO HAP

Yesa Noa

S.V. B.F. W.N.

M F M

64 61 70

75 62 88

80 Initially 70, deterioration to 20 within 3 days <10b 95–110 112 140 Before treatment 62, begin treatment 34, then improvement back to 43 84 Initially 50, deterioration to 25 within 3 days 88 110 93

8.0/1.0 8.0/1.0 8.0/1.0

HAP Cholangitis/biliom HAP

Yesa Yesf Yesa

a b c d e f

Antibiotic monotherapy with piperacillin/tazobactam. Haemodialysis. Piperacillin/tazobactam was combined with levofloxacin and teicoplanin. Piperacillin/tazobactam was combined with ciprofloxacin and teicoplanin, later meropenem. Piperacillin/tazobactam was pretreated with ampicillin/sulbactam. Piperacillin/tazobactam was combined with gentamicin.

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2.2. Study design The study was a prospective, open, randomized clinical observational trial of continuous or intermittent infusion of a fixed combination of piperacillin–tazobactam. Patients were randomized by envelope to receive piperacillin–tazobactam either by intermittent bolus injection (group A) or continuous infusion (group B). Total daily dose in group B was reduced compared with group A according to pharmacokinetic modelling prior to the study [5]. After modelling the serum drug levels under continuous infusion we expected state levels of piperacillin to be in the range 20–30 ␮g/ml when administering a 30% lower total daily dose compared with intermittent infusion. In patients with normal renal function the following doses were prescribed: • Group A: Fixed combination of 4 g piperacillin and 0.5 g tazobactam (Tazobac® ; Wyeth Lederle, M¨unster, Germany) every 8 h, i.e. three times daily by intravenous intermittent bolus injection. • Group B: Fixed combination of 2 g piperacillin and 0.5 g tazobactam (Tazobac® ; Wyeth Lederle, M¨unster, Germany) loading dose by bolus injection over 1 h followed by 8 g piperacillin and 1 g tazobactam by constant rate infusion over 23 h (day 1) and 24 h from day 2. Creatinine clearance was calculated according to Cockroft and Gault [6]. In patients with impaired renal function dose was adjusted as shown in Table 3. 2.3. Blood sampling In patients receiving intermittent dosing baseline 10 ml blood samples were obtained before administration and 1, 4 and 8 h after the intravenous dose of piperacillin–tazobactam on three consecutive days at steady state. When piperacillin–tazobactam was infused via continuous infusion, 10 ml blood samples were taken prior to infusion and 1, 5, 10, 24, 36, 42, 48 and 60 h after the start of the infusion.

Shimadzu System Controller SCL-6B and a Shimadzu SPD6a variable UV wavelength detector (wavelength 400 nm). Chromatographic separation was carried out on a Hypersil C18 column (7 ␮m, 4.6 mm × 250 mm) with gradient elution. The mobile phase A consisted of acetonitrile and water in a 3:97 ratio (v/v) containing 0.01 M sodium dihydrogenphosphate buffer (NaH2 PO4 ), pH was adjusted to 2.7. The mobile phase B consisted of acetonitrile and water in a 50:50 ratio (v/v) also containing 0.01 M sodium dihydrogenphosphate buffer, pH was adjusted to 2.7. The chromatograms were generated using a linear gradient programme starting with 90% mobile phase A and 10% mobile phase B ending at 50% eluent A and 50% eluent B after 18 min. The flow rate was 1.5 ml/min. Benzylpenicillin was used as the internal standard. Pooled human serum was used to prepare standards, quality control samples and dilute serum samples as required. The assay was linear over the range 2.0–200.0 ␮g/ml and 0.2–20.0 ␮g/ml for piperacillin and tazobactam, respectively. Patient serum samples were adapted to room temperature and vortexed. Serum of 400 ␮l, 400 ␮l of internal standard (400 ␮g benzylpenicillin), 800 ␮l of buffer and 800 ␮l of acetonitrile were mixed. Samples were then vortexed for 10 s and centrifuged by 3500 U/min for 10 min. The supernatant was removed and transferred to an autosampler vial and 20 ␮l of the sample were injected to the column. Retention times for tazobactam, piperacillin and the internal standard were 5, 9 and 16 min, respectively. Daily calibration was performed. Interday coefficients of variation were determined at 15 days. Coefficients of variations were 1.9% for piperacillin at a mean concentration of 106.3 ␮g/ml and 4.7% for tazobactam at a mean concentration of 10.7 ␮g/ml. 2.5. Pharmacokinetic and statistical analysis Serum concentration time profiles were analysed using a pharmacokinetic two-compartment body model. Data analysis was performed by nonlinear regression using the software program SCIENTIST (MicroMath, Salt Lake City, UT). For the intermittent injections, serum concentrations were fitted using the following equation:

2.4. Analytical methods C= Serum piperacillin and tazobactam concentrations were determined by high-pressure liquid chromatography methods. Instruments and materials included two LC-6A pumps (Shimadzu, Kyoto, Japan), Shimadzu Autoinjector SIL-6B,

a e−αt (1 − e−nατ ) b e−βt (1 − e−nβτ ) + 1 − e−ατ 1 − e−βτ

(1)

where C is the concentration, t the time after the last injection, τ the dosing interval, n the number of doses and a, b, α and β are hybrid constants in the two-compartment body model.

Table 3 Dose adjustment of piperacillin–tazobactam in patient with impaired renal function Creatinine clearance ml/min)

>60 25–60 <25 PIP: piperacillin; Taz: Tazobactam.

Group A, intermittent bolus dosing

Group B, constant rate infusion

Total daily dose

Number of dose/day

Total daily dose

12 g (PIP) 1.5 g (Taz) 8 g (PIP) 1.0 g (Taz) 4 g (PIP) 0.5 g (Taz)

3 2 1

8 g (PIP) 1.0 g (Taz) 6 g (PIP) 0.75 g (Taz) 4 g (PIP) 0.5 g (Taz)

C. Buck et al. / International Journal of Antimicrobial Agents 25 (2005) 62–67

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For the continuous infusion model, serum concentrations were fitted using the following equation: R0 Vc  −αt  e (1 − eαT )(k21 − α) e−βt (1 − eβT )(k21 − β) × + α(α − β) β(β − α) (2)

C=

where C is the concentration, t the total time, T the infusion time, R0 the infusion rate, Vc the volume of distribution of the central compartment, k21 the first-order distribution constant describing the transfer from the peripheral department into the central compartment, and α and β are hybrid constants in the two-compartment body model. A two-compartment model was chosen since application of the one-compartment model did not result in satisfactory curve fits. Eq. (2) was applied to the loading dose infusion (duration of infusion 1 h, dose 2 g piperacillin and 0.5 g tazobactam) as well as to the continuous maintenance infusion (8 g piperacillin and 1 g tazobactam per day). Total concentrations were calculated as the sum of loading and maintenance infusion.

Fig. 1. Mean serum concentrations (±S.D.) of piperacillin (䊉) and tazobactam () in 12 patients after multiple intravenous bolus injections (piperacillin 4 g, tazobactam 0.5 g, q8h, group A).

2.6. Clinical assessments and response criteria Since clinical or bacteriological success was not the primary objective of the study, evaluation of response to antibiotic treatment with piperacillin–tazobactam was mainly based on clinical evaluation. Response was defined as resolution or improvement of clinical and laboratory signs of infection, such as resolution of fever, decrease of C-reactive protein, decrease or normalization of leukocytosis, normalization of urinary sediment or radiographic resolution of lung infiltrates.

Fig. 2. Mean serum concentrations (±S.D.) of piperacillin (䊉) and tazobactam () in 12 hospitalized patients receiving a continuous infusion (piperacillin/tazobactam 8/1 g per day, with a loading dose of piperacillin/tazobactam 2/0.5 g, group B).

3. Results 4. Discussion The average piperacillin and tazobactam serum level profiles of the patients receiving intermittent bolus dosing (group A) are shown in Fig. 1. The average clearance and volume of distribution (Vdss ) were 5.7 l/h and 31.4 l for piperacillin and as 7.4 l/h and 37.5 l for tazobactam, respectively. In patients receiving continuous infusion (group B) mean serum steady state concentrations of piperacillin and tazobactam after the end of the bolus distribution were determined to be 39 and 6.3 ␮g/ml. These concentrations are equivalent to an AUC0–24 h of 936 and 151 ␮g/ml h. Fig. 2 shows the average piperacillin and tazobactam serum concentrations as well as the curve fit using Eq. (2). For group B, the average clearance and volume of distribution (Vdss ) were 8.9 l/h and 26.2 l for piperacillin and as 7.4 l/h and 24.4 l for tazobactam, respectively. Clinical outcomes in the intermittent and continuous dosed groups were comparable. In both groups 8 of 12 patients responded to antibiotic therapy (Tables 1 and 2).

In 1976, Shah and associates proposed different patterns of bactericidal activity for antibiotics [7]. The bactericidal activity of penicillins is characterized by an initial rise in the killing rate with increasing concentrations, but only until concentrations reach four to five times the MIC. No enhancement of bactericidal activity is shown with higher concentrations. It has been shown in vitro that bactericidal activities of ␤-lactams are only minimally enhanced by increasing drug concentrations. The extent of bactericidal activity in tissues depends more on the duration of exposure to drug levels above the MIC than on the magnitude of antibiotic concentrations [8]. These findings have been confirmed in vivo. To date it is widely accepted that clinical outcome with ␤-lactams correlates with the time the concentration in serum remains above the MIC for a pathogen (T > MIC) [3,9–11]. As a consequence continuous infusion of ␤-lactams, optimizing the

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T > MIC ratio probably has advantages over the intermittent application [3]. The first publication using continuous infusion as a method to administer ␤-lactam drugs to cancer patients dates back more than 20 years [12]. Since then there was growing evidence on the theoretical advantage of continuous ␤lactam application, whereas sufficient clinical data are still lacking. Existing clinical data on continuous infusion of ␤lactam are almost completely related to cephalosporins. In a variety of patient groups, continuous infusion of ceftazidime results in Css exceeding 20 mg/l [13]. Nicolau et al. found that continuous infusion of ceftazidime led to a substantial optimization of the pharmacodynamic and pharmacoeconomic profile of this antimicrobial [14]. Population pharmacokinetics of continuous administered ceftizoxime had been studied in 72 clinically ill patients [15]. Severe infections with Gram-negative bacteria (Burkholderia pseudomallei) have been treated recently with continuous ceftazidime infusion [16] demonstrating lower dose requirements and hence cost reduction. Egerer et al. treated 81 patients with neutropenic fever by continuous ceftazidime infusion using a portable infusion pump [17]. This approach led to the possibility of outpatient treatment in 72% of patients. In this trial, efficacy of ceftazidime monotherapy was 64%, and was comparable to efficacy rates of intermittent treatment based regimens in neutropenic patients. The present study compared the pharmacokinetics of two different dosing regimes of piperacillin and tazobactam in fixed combination. The intermittent treatment utilized a total daily dose of 12 g piperacillin and 1.5 g of tazobactam, whereas the continuous infusion used 8 g of piperacillin and 1 g of tazobactam. For the continuous infusion of piperacillin, higher clearance values were observed than for the intermittent treatment that is in agreement with a previous report of nonlinear behaviour for piperacillin [18]. No such nonlinearity was seen for tazobactam. After obtaining the respective pharmacokinetic profiles, the question arises if they can be compared with respect to their expected clinical efficacy. A comparison can be performed based on pharmacokinetic/pharmacodynamic parameters from a dynamic in-vitro model for piperacillin and tazobactam described previously [19]. For the three strains, the expected kill curves for both treatments were calculated and resulted in virtually identical kill curve profiles, indicating that very similar clinical outcome may be expected from using the two dosing regimens compared. This is consistent with the general property of ␤-lactam antibiotics to show a good correlation between the time above the MIC and bacteriological killing whereas there is a lack of correlation between their AUCs and microbiological outcome [3,5,13]. The present paper presents pharmacokinetic data on a continuous infused broad-spectrum penicillin/ ␤-lactamase inhibitor combination. Mean serum levels of piperacillin obtained during continuous infusion far exceeded the MIC of most clinically relevant pathogens (e.g. Citrobacter freundii (4 mg/l); Enterobacter (8 mg/l); Klebsiella pneumoniae

(16 mg/l); Enterococcus faecalis (4 mg/l)). Piperacillin and the ␤-lactamase inhibitor tazobactam proved to be stable in continuous infusion. When analysing the infusion solution by HPLC, no breakdown was observed within 24 h after preparation. Tazobactam levels in patients receiving continuous infusion remained stable within the application period (Fig. 2). In the present investigation the clinical outcome was comparable in groups A and B (Table 1). However, evaluation of the clinical outcome was not the primary objective of this trial. To evaluate the ultimate place of continuous piperacillin/tazobactam within clinical practice larger randomized trials are needed. The present study gives pharmacokinetic evidence that continuous piperacillin/tazobactam infusion may be used in hospitalized patients with various infections, allowing a considerable dose reduction. Expressed on daily drug costs about D 10 per day were saved per patient and day in the present study. Savings in nursing staff time for preparation and administration of a single infusion rather than three doses have to be added to this figure. This may outweigh disadvantages of the continuous application approach such as reduced mobility of the patient and need for a 24 h intravenous access. As a consequence we consider continuous infusion of piperacillin/tazobactam at present, nearly exclusively, in patients who are immobilized by the underlying condition.

5. Acknowledgment This study was sponsored by grants from Wyeth Lederle, M¨unster, Germany. We thank Professor Heiner Berthold for the collaboration in the pharmacokinetic modelling prior to the study.

References [1] Nicolau DP, Quintiliani R, Nightingale CH. Once-daily aminoglycosides. Conn Med 1992;56:561–3. [2] Vondracek TG. Beta-lactam antibiotics: is continuous infusion the preferred method of administration? Ann Pharmacother 1995;29:415–24. [3] Craig WA, Ebert SC. Continuous infusion of ␤-lactam antibiotics. Antimicrob Agents Chemother 1992;36:2577–83. [4] Nightingale CH, Quintilliani R, Nicolau DP. Intelligent dosing of antimicrobials. In: Remington SC, Swartz MN, editors. Current Clinical Topics in Infectious Disease, vol. 14. Blackwell Scientific Publishers; 1994. [5] Kuti JL, Nightingale CH, Quintiliani R, Nicolau DP. Pharmacodynamic profiling of continuously infused piperacillin/tazobactam against Pseudomonas aeruginosa using Monte Carlo analysis. Diagnostic Microbiol Inf Dis 2002;44:51–7. [6] Cockroft DW, Gault HM. Prediction of creatinine clearance from serum creatinine. Nephron 1976;16:31–41. [7] Shah PM, Junghanns W, Stille W. Dosis-Wirkungs-Beziehung der Bakterizidie bei E. coli, K. pneumoniae, and Staphylococcus aureus. Dtsch Med Wochenschr 1976;101:325–8.

C. Buck et al. / International Journal of Antimicrobial Agents 25 (2005) 62–67 [8] Gerber AU, Feller C, Brugger HP. Time course of the pharmacological response to beta-lactam antibiotic in vitro and in vivo. Eur J Clin Microbiol 1984;3:592–7. [9] Onyeji CO, Nicolau DP, Nightingale CH, Quintiliani R. Optimal times above MICs of ceftibuten and cefaclor in experimental intra-abdominal infections. Antimicrob Agents Chemother 1994;38:1112–7. [10] Roosendaal R, Bakker-Woodenberg IA, van den Berg JC, Michel MF. Therapeutic efficacy of continuous versus intermittent administration of ceftazidime in an experimental Klebsiella pneumoniae pneumonia in rats. J Infect Dis 1985;152:373–8. [11] Vogelman B, Gudmundsson S, Leggett J, Turnidge J, Ebert S, Craig WA. Correlation of antimicrobial pharmacokinetic parameters with efficacy in an animal model. J Infect Dis 1988;158:831–47. [12] Bodey GP, Ketchel SJ, Rodriguez VA. A randomized study of carbenicillin plus cefamandole or tobramycin in the treatment of febrile episodes in cancer patients. Am J Med 1979;67:608–16. [13] MacGowan AP, Bowker KE. Continuous infusion of ␤-lactam antibiotics. Clin Pharmacokinet 1998;35:391–402. [14] Nicolau DP, Nightingale CH, Banevicius MA, Fu Q, Quintiliani R. Serum bactericidal activity of ceftazidime: continuous infu-

[15]

[16]

[17]

[18]

[19]

67

sion versus intermittent injections. Antimicrob Agents Chemother 1996;40:61–4. Facca B, Frame B, Triesenberg S. Population pharmacokinetics of ceftizoxime administered by continuous infusion in clinically ill adult patients. Antimicrob Agents Chemother 1998;42:1783–7. Angus BJ, Smith D, Suputtamongkol Y, et al. Pharmacokineticpharmacodynamic evaluation of ceftazidime continuous infusion vs. intermittent bolus injection in septicaemic melioidosis. Br J Clin Pharmacol 2000;49:445–52. Egerer G, Goldschmidt H, Salwender H, et al. Efficacy of continuous infusion of ceftazidime for patients with neutropenic fever after highdose chemotherapy and peripheral blood stem transplantation. Int J Antimicrob Agents 2000;15:119–23. Vinks AA, den Hollander JG, Overbeek SE, Jeliffe RW, Mouton JW. Population pharmacokinetic analysis of nonlinear behavior of piperacillin during intermittent or continuous infusion in patients with cystic fibrosis. Antimicr Agents Chemother 2003;47:541–7. Dalla Costa T, Nolting A, Rand K, Derendorf H. Pharmacokineticpharmacodynamic modeling of the in vivo antiinfective effect of piperacillin–tazobactam combinations. Int J Clin Pharm Ther 1997;35:426–33.