Materials and Methods
Study Design and Patient Population
This study was conducted in the PICU at St. Christopher's Hospital for Children, a 189-bed freestanding children's tertiary care teaching hospital with 33 critical care beds, in Philadelphia, PA. The PICU provides care for children with burns, trauma, congenital heart disease and children on extracorporeal membrane oxygenation. This study protocol was approved by the Drexel University College of Medicine Institutional Review Board, and the need for informed consent was waived because piperacillin/tazobactam therapeutic drug monitoring was being conducted as a quality improvement project. Patients admitted to the ICU who received piperacillin/tazobactam for empiric or definitive therapy with an expected duration of >48 hours were eligible for inclusion. Two to 4 blood samples per child were collected when patients admitted to the PICU received standard piperacillin/tazobactam dosing regimens to treat their infections. Blood samples were obtained, when possible, after the first dose of piperacillin/tazobactam, or after the next dose that permitted collection of each sample in succession. A minimum of 2 blood samples were obtained per patient. The first blood sample was typically obtained within 20 minutes from the end of the infusion but could be obtained up to 2 hours from the end of the infusion, and the subsequent blood samples were obtained a minimum of 1 hour after the first sample collection. For example, a typical sampling strategy was 0.25, 2 and 4 hours after the end of the infusion for the first dose. Patients who had cystic fibrosis, acute or chronic renal failure or who were receiving extracorporeal membrane oxygenation were excluded from this pharmacokinetic analysis.
Piperacillin Concentration Determination
Total drug concentrations for the piperacillin component of piperacillin/tazobactam in plasma were determined by bioassay at ARUP Laboratories (Salt Lake City, UT). Clostridium perfringens American Type Culture Collection 13124 was the organism used for the bioassay. Each blood sample was collected and immediately transferred to the chemistry laboratory at St. Christopher's Hospital for Children. Each sample was then spun down, and the serum was removed and stored on ice for shipment to ARUP laboratories. The standard curve ranged from 10 to 40 μg/mL. The interday assay variability was less than 15% across all check samples between 10 and 40 μg/mL. If samples were determined to be outside the standard curve on the upper limit of determination, then a 1:2 or 1:5 dilution of the sample was made until the sample fell within the standard curve. If samples were determined to be outside the standard curve on the lower limit of determination, these were reported at "undetectable" by the reference laboratory. Aminoglycosides were removed from the sample before bioassay using a cellulose phosphate binding procedure.
Population Pharmacokinetics
Piperacillin concentrations were modeled using Big Non-Parametric Adaptive Grid (BigNPAG) with adaptive γ by the methods of Leary and colleagues. One and 2 compartment models were discriminated using Akaike Information Criterion and the log-likelihood test. A 2 compartment model with first order elimination fit the data best. The structural model was built to incorporate body weight as a ratio term for volume of the central compartment (Vc) and CL, as these relationships were statistically significant during linear regression analyses of preliminary models (P = 0.03 and 0.018, respectively). Relationships between CL and creatinine CL, as calculated by the Schwartz method, were also tested, but due to the high creatinine CL range among the subjects, no relationship was observed (P = 0.908). Weighting was conducted by identifying the estimate of variance for an observation using the interday coefficient of variance for the plasma assay. Observed concentrations were then weighted by the inverse of the standard deviation (SD) squared. The final equation for weighting was standard deviation = γ × (0.022 + [0.0629 × C]), where C is the piperacillin concentration and γ was 1.068, representing a measure of all residual variability outside of the assay. A value of 1.068 indicates that there was acceptable process noise in the collection of data and selection of the final model. The mean weighted error of predicted versus observed concentrations was the estimate of bias. The bias-adjusted mean weighted squared error was employed as the estimate of precision.
For comparison with other studies, secondary pharmacokinetic parameters were calculated from the primary model derived parameters. Half-life (T1/2) was calculated as 0.693/β, where β is the root of the quadratic polynomial. Volume of the peripheral compartment (Vp) was calculated as (Vc × k12)/k21, and total volume of distribution (Vd) was the sum of Vc and Vp.
Monte Carlo Simulation
A 5000 patient Monte Carlo simulation was performed as previously described employing Crystal Ball (Oracle Corporation, Redwood Shores, CA) to determine the probability of target attainment (PTA) for the following piperacillin/tazobactam dosing regimens in a population of 1- to 6-year-old male children: 50 mg/kg (of the piperacillin component) every 4 hours, 80 mg/kg every 8 hours and 100 mg/kg every 6 hours. All dosing regimens were simulated as 0.5- and 3- or 4-hour infusions (ie, half the dosing interval). A 400 mg/kg continuous infusion was also simulated. Centers for Disease Control and Prevention weight for age charts were used for weight distributions during the simulation. The fraction unbound used during the simulations was 0.7 (ie, 30% protein bound). The fT>MIC for the piperacillin component of piperacillin/tazobactam was then calculated over a range of MICs from 0.03 to 128 μg/mL for each patient, and the PTA was calculated using a pharmacodynamic target of ≥50% fT>MIC. An a priori PTA ≥90% was defined as optimal.