Population Pharmacokinetic Analyses for Plazomicin Using Pooled Data from Phase 1, 2, and 3 Clinical Studies

Plazomicin is an aminoglycoside with activity against multidrug-resistant Enterobacteriaceae. Plazomicin is dosed on a milligram-per-kilogram-of-body-weight basis and administered by a 30-min intravenous infusion every 24 h, with dose adjustments being made for renal impairment and a body weight (BW) of ≥125% of ideal BW.

The clinical pharmacokinetic (PK) characteristics of plazomicin are generally consistent with those of other aminoglycoside antibiotics (22). Plazomicin displays linear and dose-proportional PK (23,24), does not undergo metabolism, and is eliminated from the body primarily via urinary excretion of the parent drug (25). An in vitro, equilibrium dialysis experiment that evaluated plazomicin at 5, 50, and 100 g/ml in human plasma showed that plasma protein binding is concentration independent and low (Ϸ20%; data on file). In a human mass-balance study, 97.5% of the intravenously administered dose of plazomicin was recovered as the parent drug in the urine (25). Given the consistency in PK characteristics with other aminoglycoside antibiotics, plazomicin dosing in patient studies has generally followed typical aminoglycoside dosing recommendations (26,27), which consider creatinine clearance (CL CR ) to be a measure of renal function and use adjusted body weight (ABW) when body weight (BW) exceeds the ideal body weight (IBW). Thus, throughout the development program, plazomicin was administered on a milligram-per-kilogram-of-body-weight basis (with ABW in the two phase 3 studies), and dose adjustments were performed in patients based on CL CR . The recommended starting dose regimen in the drug product label (21) is plazomicin at 15 mg/kg administered every 24 h (q24h) as a 30-min intravenous infusion in patients with normal renal function or mild renal impairment (CL CR Ͼ 60 ml/min).
Given that therapeutic drug management (TDM) is recommended to optimize exposures and clinical outcomes in patients treated with aminoglycosides (28,29), additional dose adjustments based on TDM were implemented in one of the phase 3 studies (30). In this study, patients with serious infection (bloodstream infection [BSI], hospital-acquired bacterial pneumonia [HABP], ventilator-associated bacterial pneumonia [VABP], cUTI, or AP) due to carbapenem-resistant Enterobacteriaceae (CRE) received starting doses based on CL CR and ABW or IBW. Plazomicin doses after the initial dose were determined based on TDM, in which dose adjustments were implemented to maintain the area under the plasma concentration-time curve (AUC) within a target range. AUC-based TDM was considered appropriate for this critically ill patient population; critical illness may be associated with a high PK variability of antibiotics, particularly those that are cleared by the kidneys (31)(32)(33).
Although not tested clinically, the plazomicin product label recommends trough concentration-based TDM in patients with cUTI who have a CL CR of Ͼ30 to 90 ml/min (i.e., mild to severe renal impairment) to maintain plasma trough concentrations below 3 g/ml (21). Initial doses of plazomicin are based on CL CR and ABW or IBW in all patients with cUTI, and dose adjustments are necessary in renally impaired cUTI patients. Subsequent doses are informed by the trough concentrations of plazomicin. The rationale for this approach is that cUTI patients with renal impairment may be at increased risk of nephrotoxicity, and trough concentration-based TDM dose adjustments may mitigate this risk (21).
Herein, we describe an analysis that represents the culmination of several population PK modeling activities that were carried out to support the plazomicin clinical development program. The initial population PK model was developed using data from the phase 1 first-in-human study (23), and this model was then more fully elaborated upon with the availability of additional data from phase 1 and 2 studies in healthy subjects and cUTI patients (34)(35)(36). Development of the final population PK model, described herein, ensued upon completion of a phase 1 thorough QT study (24) and two phase 3 studies (37,38). The analysis includes data from patients with cUTI, including AP, and patients with BSI or HABP/VABP due to CRE. The objective of this analysis was to identify patient factors that account for sources of variability in plazomicin PK and to determine if dose adjustments are warranted based on covariates.

RESULTS
PK analysis population. Summary statistics of the baseline characteristics for the analysis population are presented in Table 1. The demographics were diverse and  representative of the broader population of adult patients with cUTI/AP and serious  infections caused by CRE. PK data description and outlier analysis. The final population PK analysis data set included 564 subjects and 4,990 plazomicin plasma concentrations (see Table S1 in the supplemental material), which represented 98.4 and 97.0% of the possible subjects and plasma concentrations available for analysis, respectively. Reasons for sample exclusions included a plazomicin plasma concentration below the lower limit of quantification (BLQ) (46 samples) or designation as an outlier (106 samples). The phase 2 study case report form recorded geographic ancestry and grouped the following into one category: Americas (Native North American/Native South American/Canadian First Peoples). South American sites were high enrollers and likely account for many of the patients in this category. c Normal, CL CR Ն 90 ml/min/1.73 m 2 ; mild impairment, CL CR ϭ 60 to 89 ml/min/1.73 m 2 ; moderate impairment, CL CR ϭ 30 to 59 ml/min/1.73 m 2 ; severe impairment, CL CR Ͻ 30 ml/min/1.73 m 2 . In one of the phase 3 studies (study 007), 2/16 patients with mild renal impairment, 3/12 with moderate impairment, and 4/6 with severe impairment received continuous renal replacement therapy at some time during treatment with plazomicin. d Vasopressor use was defined as administration of adrenaline, dobutamine, etilefrine, isoproterenol, noradrenaline, or norepinephrine at any time during the study. Vasopressors were used as part of the medical management of shock in the critically ill patient population in study 007. Vasopressor use was handled as a categorical covariate (yes/no) to indicate use at any time during the study. e History of trauma was broadly defined and was commonly unrelated to the clinical condition at the time of plazomicin administration.

Population PK analysis. (i) Development of the structural population PK model.
A three-compartment model with zero-order input and first-order elimination best described the pooled plasma plazomicin concentration-time data from the seven studies. Interindividual variability (IIV) was described for total clearance (CL), volume of the central compartment (V c ), distributional clearance to peripheral compartment 1 (CL d1 ), volume of peripheral compartment 1 (V p1 ), distributional clearance to peripheral compartment 2 (CL d2 ), and volume of peripheral compartment 2 (V p2 ) using log-normal parameter distributions. Residual variability was described using a combined additiveplus-constant coefficient of variation (CCV) error model. CL CR was evaluated as a time-varying covariate for CL in the base structural model, and it was determined that a sigmoidal Hill-type function best described the relationship between CL and CL CR . Handling of clearance due to continuous renal replacement therapy (CRRT) is described in Materials and Methods. Given that this model provided an unbiased fit to the data, alternative structural models were not explored further.
All model parameters were estimated with acceptable precision according to the asymptotic errors from the population PK model (standard error of the estimate [SEE], Ͻ67%). Goodness-of-fit plots for the base structural population PK model (data not shown) demonstrated that the three-compartment model including the relationship between CL and CL CR provided an excellent fit to the plasma plazomicin concentrationtime data across renal function groups. There were no noticeable biases in the model fit when examining these plots, and there was good agreement between both the population mean (coefficient of determination [r 2 ] ϭ 0.738) and the individual post hoc (r 2 ϭ 0.935) predicted concentrations with the observed concentrations.
(ii) Covariate analysis. A complete summary of the parameter-covariate relationship determined to be the most statistically significant in each step of forward selection is provided in Table S2. The full multivariable model included 17 parameter-covariate relationships, in addition to the relationship between CL and CL CR , which was included a priori as part of the structural PK model.
IIV models for the full multivariable model showed that the distributions of each of the individual error terms were normally distributed and symmetric around zero. Revisions were made to the model as part of the full multivariable model assessment. The first step tested a full variance-covariance matrix. Various reduced models estimating different combinations of covariance terms were then evaluated at this stage of the analysis. Parsimony was achieved with the model in which the covariance terms between IIV on clearance ( CL ) and IIV on volume of the central compartment ( V c ), CL and IIV on the distributional clearance to peripheral compartment 1 ( CL d1 ), and V c and CL d1 were estimated, resulting in a 364-unit decrease in the minimum value of the objective function (MVOF) (P Ͻ 0.000001). Subsequently, the model with the abovementioned covariance terms was modified by adding separate error terms for each study phase (phase 1, 2, or 3); this model resulted in a 588-unit drop in the objective function (P Ͻ 0.000001). The final step of model refinement was to test interoccasion variability (IOV) on various model parameters; the occasions were categorized as days 1 to 2, 3 to 6, 6 to 9, and Ͼ9. The only IOV term that was found to be statistically significant was the one relating to CL. This refined model was used as the comparator model for backward elimination.
The full multivariable population PK model was then subjected to a backward elimination procedure in which each covariate effect in the model except CL CR was removed in a univariate fashion and tested for statistical significance (␣ ϭ 0.001). Five rounds of backward elimination were required, and four parameter-covariate relationships (between infection type and V p2 and between age and each of V c , CL d1 , and CL) were removed (Table S2).
(iii) Final covariate model refinement. After completing the backward elimination, the model was refined to make it more parsimonious. First, proportional shifts in CL for HABP/VABP and cUTI appeared to have only a minor impact (low fractional change) and were dropped from the model, which resulted in no statistically significant changes (an increase of Ϸ2 units in the MVOF). Second, proportional shifts in PK parameters based on infection type that had similar estimates (i.e., cUTI and AP, HABP/VABP and BSI) were evaluated as a single group and tested for statistical differences. Finally, the sieving coefficient was reestimated, as it had been fixed to the value from the base structural model (0.926) during covariate analysis; the resultant fitted value was 0.734.
The model that resulted from the steps described above was then subjected to a nonparametric bootstrap procedure. The relationships between V p1 and vasopressor use, CL d1 and HABP/VABP infection type, CL d1 and BSI type, and V p1 and each of HABP/VABP infection and BSI types were dropped from the model due to unacceptably poor precision based on the percent SEE.
(iv) Final population PK model. The final population PK model for plazomicin included a fixed zero-order input for the intravenous infusion and first-order elimination. CRRT CL (CL CRRT ) was estimated only during those periods when CRRT was operative, utilizing the patient-specific and ultrafiltrate flow rate (UFR) and dialysate flow rate (DFR) and the estimated sieving coefficient. IIV was estimated for CL, V c , CL d1 , V p1 , CL d2 , and V p2 using exponential error models. Random IOV on CL was retained in the model, as it resulted in a statistically significant improvement in the MVOF, despite the small magnitude of the effect (coefficient of variation [CV], 3.59%), which suggests that CL is relatively stable across occasions. An additive-plus-CCV error model best described residual variability with separate CCV error terms for the phase 1 studies, the phase 2 study, and the phase 3 studies.
The population PK parameter estimates and their associated precision (percent SEE) for the fit of the three-compartment model are provided in Table 2. Goodness-of-fit plots (Fig. S1) for the final model showed stronger agreement between the observed plasma concentrations and the population predicted concentrations from the final population PK model (r 2 ϭ 0.793) than from the base structural three-compartment population PK model (r 2 ϭ 0.738). However, the agreement between the observed plasma plazomicin concentrations and the individual post hoc predicted concentrations decreased marginally (r 2 ϭ 0.919 versus 0.935 in the base model).
The relationship between renal clearance (CL R ) and CL CR was described using a sigmoidal Hill-type function, and the relationship between total CL of plazomicin and CL CR included an intercept to represent nonrenal clearance. The other parameters describing the relationship between CL and CL CR were CL R maximum, CL CR50 , and a Hill coefficient. CL R maximum is the maximum renal clearance (i.e., at a very high value of CL CR ), CL CR50 is the CL CR value at which CL R is half-maximal, and the Hill coefficient defines the shape of the sigmoidal relationship. Based upon these relationships, the population mean total CL and CL R would be 4.57 liters/h (76.2 ml/min) and 4.08 liters/h (68.0 ml/min), respectively, in a typical cUTI or HABP/VABP patient with a BW of 75 kg, a body surface area (BSA) of 1.73 m 2 , and a CL CR of 90 ml/min.
As summarized in Table 2, several statistically significant relationships were identified between covariates and IIV for PK parameters: BW and infection type on CL; BSA and infection type on V c ; infection type on CL d1 ; BSA, age, and infection type on V p1 ; height and infection type on CL d2 ; and BW and vasopressor use on V p2 .
Model evaluation. The prediction-corrected visual predictive check (PC-VPC) plots generally showed reasonable agreement between the observed concentrations and the individual simulated concentrations across time intervals and showed no bias with respect to renal function, infection type, or first versus multiple doses across healthy subjects and patients (Fig. 1), which suggests no substantial issues with respect to the fixed or random-effects parameters in the model and which supports the future use of this model for simulations. Furthermore, the bootstrap analysis showed that all of the population PK model parameters were estimated with reasonable precision (Table 2).
Plazomicin exposures and secondary PK parameter estimates. Summary statistics for the key exposures and secondary PK parameters are provided in Table 3. The plazomicin half-lives (t 1/2 ) associated with the three-compartment structural model indicate an initial distribution phase (␣-phase half-life, 0.328 to 1.58 h), followed by a secondary distribution phase (␤-phase half-life, 2.77 to 5.38 h) and a terminal elimination phase (␥-phase half-life, 25.8 to 36.5 h). Table 3 reports PK results for 54 healthy subjects and 71 patients with cUTI/AP who received plazomicin at 15 mg/kg by a 30-min infusion. The mean peak plasma concentration (C max ) values were 84.6 mg/liter (CV, 21.0%) and 54.5 mg/liter (CV, 41.4%), respectively, indicating that the 15-mg/kg dose produced a higher C max in healthy subjects than in patients with cUTI/AP. This is likely attributed to a smaller V c in healthy subjects than in patients with cUTI/AP. Overall, the mean volume of distribution at steady state (V ss ) of plazomicin in healthy subjects and patients with cUTI/AP ranged from 25.0 to 31.5 liters, which is typical for an aminoglycoside and approximately twice  . c For phase 2/3 studies, C min is the lowest concentration observed in the first 48 h of therapy (typically, the trough concentration after the first dose). For study 006, C min is the lowest concentration in the first 24 h after the single 15-mg/kg dose (always at 24 h). d In study 006, plazomicin was administered at 15 mg/kg to 54 healthy subjects. In study 002, plazomicin was administered at 15 mg/kg to 71 cUTI/AP patients. In study 009, the dose was based on the baseline renal function, as described in Table 4, footnote a, and was administered to 281 cUTI/AP patients. In study 007, the dose was based on the baseline renal function, as described in Table 4, footnote a, and was administered to 48 CRE patients. Two subjects in study 007 received q12h dosing starting at Ϸ24 h after the first dose of plazomicin, subsequent to therapeutic drug management. the extracellular fluid volume (39). A larger V ss of 56.6 liters was observed in BSI and HABP/VABP patients with CRE infections, most likely due to the severity of illness in this patient group (40). The estimates of the mean plazomicin area under the plasma concentration-time curve from time zero to 24 h (AUC 0 -24 ) for a plazomicin dose of 15 mg/kg or a reduced dose based on the baseline renal function were generally consistent across the patient studies with moderate variability (38.5 to 43.4%). Mean plazomicin minimum plasma concentration (C min ) values ranged from 0.494 to 0.880 mg/liter for patients with cUTI/AP and were higher (2.10 mg/liter) in patients with CRE infections.
To aid in identifying subgroups of patients who are likely to experience important differences in plazomicin exposures, the post hoc plazomicin PK estimates (AUC 0 -24 , C max , C min , and CL) were investigated relative to patient covariates of interest (CL CR , BW, body mass index [BMI], age, sex, race, infection type, and vasopressor use). The assessments of clinical relevance focused on AUC and C min in patients in the phase 2 and phase 3 studies. AUC is of interest for plazomicin because the AUC/MIC ratio is the PK/pharmacodynamic (PD) index that best correlated with efficacy in an animal infection model (41). C min is of interest based on the precedent of clinical use with other aminoglycoside antibiotics, which commonly involve monitoring of C min to improve the safety profile. While the exposure results reported below are confined to AUC, the same conclusions were reached for exposure based on C min . Figure 2 presents the relationships between post hoc parameter estimates for AUC 0 -24 and CL and the covariates. Total CL increased in a sigmoidal fashion with increasing CL CR . Given that the initial dose was selected based on the baseline CL CR in the phase 3 studies, AUC 0 -24 was similar across renal function groups. The scatter plots show no important trends between AUC 0 -24 and each of BW, BMI, or age. Box plots show broadly overlapping values of CL in males and females, as well as broadly overlapping values of AUC 0 -24 in patients who received vasopressors versus those who did not. Box plots of AUC 0 -24 versus race suggest that black patients may have slightly lower plasma exposures than patients of other races; however, race was not a significant covariate in the final population PK model, and apparent differences among racial categories are likely due to small sample sizes and potential imbalances in other factors (e.g., renal function, infection type). Box plots of AUC 0 -24 versus infection type suggest slightly higher plasma exposures in patients with BSI, which reflects an 18.9% decrease in CL relative to that in patients with cUTI or HABP/VABP (Table 2).

DISCUSSION
The objective of this analysis was to identify patient factors that account for sources of variability in plazomicin PK and to determine if dose adjustments are warranted based on covariates. The population PK model for plazomicin that best described the data was a three-compartment model with a zero-order rate constant for the intravenous infusion and with first-order elimination kinetics. The relationship between CL R and CL CR , the most clinically significant covariate, was described by a sigmoidal Hill-type function. As glomerular filtration is the predominant mechanism of aminoglycoside elimination, the relationship between plazomicin CL and the term used to capture renal clearance might be expected to be linear. However, the observed data showed a sigmoidal relationship, where increases in plazomicin CL were less pronounced at the highest CL CR values (Fig. 2). It is important to consider that CL CR is used in this empirical population PK model as a surrogate of glomerular filtration rate (GFR), and CL CR may be less predictive of GFR at the upper range of CL CR estimates due to other factors which influence endogenous creatinine production. Despite this limitation, the sigmoidal relationship supports the objective of this analysis (i.e., identifying important patient covariates for plazomicin CL). It should also be noted that data were sparse for CL CR of Ͼ150 ml/min; therefore, caution should be exercised when using the model to predict exposures in subjects with CL CR above this level.
Plazomicin dosing was based on adjustments for the baseline CL CR in the phase 3 clinical studies (studies 007 and 009; Table 3), and these dosage adjustments are reflected in the product label (21). As the clearance of plazomicin is primarily through glomerular filtration, it may be reasoned that plazomicin dosing should be based on GFR. The gold standard for estimating GFR is by using inulin, which is highly precise but impractical for routine use in guiding drug dosing (42). The Cockcroft-Gault (CG) formula estimates CL CR as a surrogate for GFR, and most guidelines for aminoglycoside dosing recommend use of the CG formula. This formula requires the patient weight, which may be adjusted for IBW, lean BW, or BSA to account for differences in body size and obesity among patients (43). Alternative equations for estimated GFR (eGFR) are available, such as the Modification of Diet in Renal Disease (MDRD) and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formulas (44,45). These eGFR formulas were developed from well-conducted population studies and are primarily used to detect end-stage chronic kidney disease. While they represent an alternative to the CG formula to guide aminoglycoside dosing, they have not been as widely adopted as the CG formula. Moreover, studies suggest that the CG, MDRD, and CKD-EPI formulas are not interchangeable and may result in different renal function estimates, leading to differences in antimicrobial dosing. Given these caveats, the population PK analysis of plazomicin focused on CG, which was used in the phase 3 clinical studies (Table 4) and was thus integral to the overall assessment of benefit-risk in the intended patient populations.
The population PK analysis used traditional covariate model-building techniques to identify patient descriptors that are associated with the IIV in plazomicin PK. After pooling of the data across phase 1, 2, and 3 studies, the resultant data set contained a large, diverse population, which facilitated the identification of several statistically significant relationships (Table 2). Infection type appeared to reduce IIV in a variety of PK parameters, especially CL d1 , which may reflect changes in hemodynamic status and other critically ill patient characteristics with the inclusion of patient data from the phase 3 study in patients with serious infections due to CRE. The relatively small drop in IIV for CL is a consequence of the fact that CL CR , which was part of the base structural model, is by far the largest predictor of the IIV in plazomicin CL.
Post hoc assessments, which showed a compelling relationship between CL and CL CR , provided support for dose adjustments based on CL CR . In contrast, none of the other statistically significant covariates had a clinically meaningful impact on plazomicin exposure. Thus, dose adjustments in adults do not appear to be warranted on the basis of age, infection type, vasopressor use, or body size (further to milligram-perkilogram dosing using either total BW or ABW).
Post hoc assessments further enabled comparison of AUC 0 -24 values in the two phase 3 studies (studies 007 and 009; Table 3). The geometric mean AUC 0 -24 was 235 mg·h/liter (CV, 42.0%) in patients with infections due to CRE in study 007 and 234 mg·h/liter (CV, 38.5%) in patients with cUTI/AP in study 009, indicating that the dosing paradigm produced only moderate variability in the exposure parameter that is considered most relevant to efficacy. This suggests that it is appropriate for plazomicin to be administered on a milligram-per-kilogram basis with adjustments for CL CR and BW of Ն125% of IBW.
In conclusion, a three-compartment structural PK model with a zero-order rate constant for the intravenous infusion and linear first-order elimination kinetics provided good fits of the plasma concentration-time data. A robust description of the plasma PK of plazomicin in the population of healthy subjects and patients was achieved, such that the derived measures of plazomicin exposure are expected to be both accurate and precise. The population PK analysis successfully identified patient factors that are sources of variability in PK parameters, while further showing that most of these covariate relationships do not have an important impact on plasma exposure to plazomicin. Post hoc estimates of AUC 0 -24 in the phase 3 studies suggest that it is appropriate for plazomicin to be administered on a milligram-per-kilogram basis with dose adjustments for CL CR and BW of Ն125% of IBW, while adjustments based on other covariates are not warranted. Although it was beyond the scope of the population PK analysis, it merits mention that initial dosing on a milligram-per-kilogram basis with adjustments for CL CR and BW of Ն125% of IBW is recommended in all patients, and subsequent adjustments based on TDM are recommended in certain patient subsets, including the critically ill and those with cUTI/AP and coexisting renal impairment.  [37]). Table 4 summarizes the clinical studies and their dosing and PK sampling schemes. The phase 1 studies were conducted in healthy subjects in whom plazomicin was administered strictly on a milligramper-kilogram basis (no adjustments for CL CR or IBW). Studies 001 and 003 explored the safety, tolerability, and PK of plazomicin over single-and multiple-dose regimens. Study 004 explored the effect of renal Three multiple-dose studies were performed in patients with cUTI, including AP (studies 002 and 009) or serious infection (BSI, HABP, VABP, cUTI, or AP), due to CRE (study 007). In all three patient studies, plazomicin blood samples were collected using sparse PK sampling schemes (Table 4). Studies 002 and 009 were randomized phase 2 and phase 3 cUTI trials, respectively, where plazomicin was compared with levofloxacin or meropenem, respectively. Study 007 was a randomized phase 3 trial of plazomicin versus colistin in critically ill patients with infections due to CRE. In study 002, plazomicin was administered at 10 or 15 mg/kg based strictly on BW, and in studies 007 and 009, plazomicin was administered at up to 15 mg/kg with adjustment for renal function and ABW where BW was Ն125% of IBW (see Table 4 footnotes). In study 007, plazomicin doses after the initial dose were determined based on therapeutic drug management, in which dose adjustments were implemented to maintain AUC within a target range.

MATERIALS AND METHODS
Subject characteristics. Subject demographic and disease characteristics recorded before administration of study drug were used to characterize the analysis population and informed assessments of IIV in key PK parameters.
Renal function was approximated using CL CR , as calculated by the CG equation (46) as follows: CL CR (in milliliters per minute) for males ϭ (140 -age [in years] · BW [in kilograms])/(72 · SCr [in milligrams per deciliter]) and CL CR for females (in milliliters per minute) ϭ male CL CR · 0.85, where the serum creatinine concentration (SCr) was capped to a lower bound of 0.50 mg/dl. The calculated CL CR values for each individual were normalized to a BSA of 1.73 m 2 , determined using the equation from Du Bois and Du Bois (47); BSA (in millimeters squared) ϭ BW (in kilograms) 0.425 · height (in centimeters) 0.725 · 0.007184, to help control for body size differences when estimating renal function for the purposes of constructing a population PK covariate model.
If SCr data were available on different days during repeated dosing of plazomicin within a given patient, CL CR was calculated and updated for each day where SCr was measured and used as a time-changing covariate in the analysis data set. Before updating the CL CR calculation, linear interpolation was used to calculate SCr between actual measured SCr values.
For patients on CRRT, the timing of CRRT, UFR, and DFR was assigned based upon the source data. Drug concentration assay. In each study, blood samples for PK analysis were collected in Vacutainer tubes containing K 2 EDTA. Plasma was separated from whole-blood components by centrifugation and immediately frozen at -20°C or colder until analysis (Alturas Analytics, Inc. Moscow, ID, USA). Plasma plazomicin concentrations were determined using a validated liquid chromatography-tandem mass spectrometry method with a lower limit of quantification of 0.01 mg/liter. The same assay methodology was used for every study included in the population PK analysis.
Handling of outliers and samples assayed as having BLQ plazomicin plasma concentrations. PK samples without both date and time information or with BLQ plazomicin concentrations were excluded from the population PK analysis.
An outlier was defined as an aberrant observation that substantially deviated from the rest of the observations within an individual. PK outlier concentrations were excluded from this analysis according to U.S. Food and Drug Administration guidance (48). The outlier detection was based primarily upon visual inspection of individual and pooled plasma concentration-time data for plazomicin. Searching for additional outliers during the analysis was based upon graphical exploration of individual and population conditional weighted residuals during structural PK model development.
Population PK analysis. The population PK analysis was conducted using NONMEM software (v7.2; ICON Development Solutions, Ellicott City, MD, USA), implementing the first-order conditional estimation method with interaction. During various stages of model development, population PK models were minimally assessed using the following criteria: (i) evaluation of individual and population mean PK parameter estimates for plazomicin and their precision, as measured by the percent standard error of the population mean estimate; (ii) graphical examination of standard diagnostic and population analysis goodness-of-fit plots with possible stratification by various factors, such as patient population or plazomicin dose group; (iii) graphical examination of the agreement between the observed and individual post hoc predicted plazomicin concentration-time data; (iv) reductions in both residual variability and IIV; and (v) comparison of MVOF for nested models or Akaike's information criterion for nonnested models (49).
(i) Development of the structural population PK model. For developing the structural population PK model, a previously developed three-compartment structural PK model using data from the phase 1 and 2 studies (studies 001, 003, 004, and 002), in which CL, V c , V p1 and V p2 , and CL d1 and CL d2 were estimated as model parameters, was refined in this analysis after including additional data from studies 006, 007, and 009 pooled with the previous phase 1 and 2 study data. As a general rule, other model structures (e.g., a two-compartment model) were attempted only if it was deemed necessary based upon the fit of the structural model to the pooled data set. Development of the base structural population PK model for the present analysis included CL CR as a time-varying covariate a priori for all subjects in the full data set who had more than one central laboratory SCr measurement. The functional form for the relationship between CL CR and CL was selected based upon the fit of different functional forms (i.e., linear, power, sigmoidal). Clearance due to CRRT was set to the sum of the actual patient-specific DFR and UFR, and multiplied by an estimate of the sieving coefficient (which represents the membrane permeation of the drug) on the study days when CRRT was used. For this submodel, DFR and UFR were fixed based on the source data and the sieving coefficient was a fitted parameter. The total CL for patients while on CRRT was equal to the sum of residual CL and the CRRT CL.
IIV was modeled for each PK parameter, where appropriate, using an exponential error model that assumed that these parameters are log-normally distributed and that the variance is constant. Residual variability was initially modeled by a combined additive-plus-CCV error model. Other models for residual variability were explored as necessary.
(ii) Covariate analysis. After constructing the structural population PK model, a covariate analysis was initiated. Patient factors were evaluated as continuous or categorical descriptors, as summarized in Table 1.
A formal univariate analysis of each covariate that demonstrated an observable trend with a structural PK model parameter and that had a biologically plausible relationship was performed in NONMEM during each step of forward selection. This was carried out to assess statistical significance based upon the resulting decrease in MVOF from the base structural model using a likelihood ratio test. The most statistically significant parameter-covariate relationship (␣ ϭ 0.01) was added to the model during each step of forward selection; stepwise forward selection was concluded when none of the remaining covariates tested resulted in a statistically significant decrease in MVOF relative to that for the updated base structural model from the previous step of forward selection.
After completing forward selection, the refinement of the full multivariable model was conducted. The IIV models were first reevaluated through pairwise comparisons of the interindividual error terms () for each parameter, and potential adjustments to the IIV models or the variance-covariance matrix structure were made. Focus was then shifted toward correcting any potential biases or seeking ways to simplify the residual variability model, and if necessary, the additive-plus-CCV residual error model was simplified to a CCV error model at this stage of the analysis.
Univariate stepwise backward elimination was performed after all adjustments were made to the IIV and residual variability models by removing each parameter-covariate relationship and assessing whether the resulting increase in MVOF remained statistically significant (␣ ϭ 0.001). The final population PK model for plazomicin was generated after it was determined that all parameter-covariate relationships in the model remained statistically significant.
(iii) Final model evaluation. The final population PK model analysis was qualified by performing a PC-VPC, which examined the agreement between the 5th, 50th, and 95th percentiles of the observed and the individual simulated plazomicin concentrations across time intervals. The PC-VPC normalizes both the observed and the simulated plasma concentration-time data by the median population mean predictions during each time interval to adjust for the differences due to independent variables in the final population PK model and to avoid having to stratify by single-versus multiple-dose data, dose group, or other significant covariate effects included in the model (50). This was also necessary due to the fact that patients could have doses altered secondary to TDM in study 007.
To assess the robustness of the final population PK model for plazomicin, a nonparametric bootstrap evaluation was performed (51,52). Histograms of the bootstrap population mean PK parameter and variance estimates were also generated to assess the general shape of the distribution for each term in the model. The purpose of this was to further assess the precision of the final population PK parameter estimates in response to perturbations in the data and to assist with assessing potential areas of weaknesses and identifying limitations of the model.
Calculation of secondary PK parameters and exposure estimates. The individual post hoc PK parameter estimates (CL, V c , CL d1 , CL d2 , V p1 , and V p2 ) were obtained from the final model and directly reported. These parameters were used to calculate secondary PK parameters, such as V ss (which is equal to V c ϩ V p1 ϩ V p2 ), as well as the ␣-, ␤-, and ␥-phase half-lives (t 1/2,␣ , t 1/2,␤ , and t 1/2,␥ , respectively). For most of the comparisons in this analysis, the individual post hoc PK parameters were also used to simulate predicted plasma plazomicin concentration-time data to generate plasma exposure estimates, such as C max , C min , and AUC 0 -24 .

SUPPLEMENTAL MATERIAL
Supplemental material for this article may be found at https://doi.org/10.1128/AAC .02329-18.