Application of Population Pharmacokinetic Modeling, Exposure-Response Analysis, and Classification and Regression Tree Analysis to Support Dosage Regimen and Therapeutic Drug Monitoring of Plazomicin in Complicated Urinary Tract Infection Patients with Renal Impairment

ABSTRACT

In 2018, the FDA approved plazomicin for the treatment of complicated urinary tract infections (cUTI) including pyelonephritis in adult patients with limited or no alternative treatment options. The objective of this article is to provide the scientific rationales behind the recommended dosage regimen and therapeutic drug monitoring (TDM) of plazomicin in cUTI patients with renal impairment. A previous population pharmacokinetic (PK) model was used to evaluate the dosage regimen in cUTI patients with different degrees of renal impairment. The exposure-response analysis was conducted to identify the relationship between plazomicin exposure and nephrotoxicity incidence in cUTI patients with renal impairment. Classification and regression tree (CART) analysis was utilized to assess the TDM strategy. The receiver operating characteristics curve was plotted to compare two TDM thresholds in cUTI patients with renal impairment. The analyses suggested that dose reduction is necessary for cUTI patients with moderate or severe renal impairment. TDM should be implemented for cUTI patients with mild, moderate, or severe renal impairment to reduce the risk of nephrotoxicity. The trough concentration of 3 μg/mL is a reasonable TDM threshold to reduce the nephrotoxicity incidence while maintaining efficacy in cUTI patients with renal impairment. The application of population PK modeling, exposure-response analysis, and CART analysis allowed for the evaluation of a dosage regimen and TDM strategy for plazomicin in cUTI patients with renal impairment. Our study demonstrates the utility of pharmacometrics and statistical approaches to inform a dosage regimen and TDM strategy for drugs with narrow therapeutic windows.

INTRODUCTION

In 2018, the FDA approved plazomicin for the treatment of complicated urinary tract infections (cUTI) including pyelonephritis in adult patients with limited or no alternative treatment options. The recommended dosage is 15 mg/kg of body weight daily through intravenous infusion over 30 min, with the treatment duration ranging from 4 to 7 days based on the severity of infection. No dose adjustment is necessary for patients with mild renal impairment (creatinine clearance [CL_CR], 60 to 90 mL/min, estimated by the Cockcroft-Gault formula). The recommended dosage is 10 mg/kg daily and 10 mg/kg every other day for cUTI patients with moderate renal impairment (CL_CR, 30 to 59 mL/min) and severe renal impairment (CL_CR, 15 to 29 mL/min), respectively. There is insufficient information to recommend a dosage regimen in patients with end-stage renal disease (CL_CR, 0 to 14 mL/min). Therapeutic drug monitoring (TDM) is recommended in cUTI patients with mild, moderate, or severe renal impairment to maintain trough concentrations below 3 μg/mL prior to the second dose (1).

The recent global emergence of multidrug-resistant and extensively drug-resistant Gram-negative pathogens has led to renewed interest in the aminoglycoside class (2). TDM is employed as a standard clinical practice in conjunction with aminoglycoside dosing regimens. Aminoglycosides are concentration-dependent antibiotics. The peak concentration (C_max) or area under the drug concentration-time curve (AUC) of aminoglycosides is associated with antimicrobial activity. In general, C_max and AUC are highly correlated with the same dosing interval, and discrimination between them seems not to be necessary. However, when there is variation in the half-life, the correlation between C_max and AUC may disappear (3). The trough concentration (C_min) of aminoglycosides is associated with nephrotoxicity and ototoxicity. For patients receiving aminoglycoside therapy, blood samples at the time of C_max and C_min are usually collected to facilitate dose adjustment as part of a TDM process (4). Notably, the target C_max and C_min differ for each aminoglycoside. The target C_max ranges are 4 to 10 μg/mL for gentamicin and tobramycin and 15 to 30 μg/mL for amikacin and streptomycin. The C_min should be lower than 2 μg/mL for gentamicin and tobramycin and 5 to 10 μg/mL for amikacin and streptomycin (5). The target C_max range is selected based on the accepted rationale that the ratio of C_max to the MIC for corresponding bacterial strains should be 8 or greater (6). The C_min values, serving as critical TDM thresholds for aminoglycosides, are mostly derived from clinical experience, with limited analysis to confirm their precision and accuracy. Mostly, once-daily administration of aminoglycosides is used to minimize toxicity and for more convenient administration and drug level monitoring (7, 8).

Plazomicin is a new aminoglycoside with activity against multidrug-resistant Enterobacterales, including organisms capable of producing aminoglycoside-modifying enzymes (9). The efficacy and safety of plazomicin in adult patients with cUTI were evaluated in a randomized, double-blind phase 3 study, in which intravenous plazomicin at 15 mg/kg daily was compared to intravenous meropenem at 1,000 mg every 8 h for 4 to 7 days, followed by an option to switch to oral levofloxacin at 500 mg daily for a total of 7 to 10 days of treatment (ClinicalTrials.gov identifier NCT02486627) (10). The co-primary endpoints were composites of clinical cure and microbiological eradication on day 5 and the test-of-cure (TOC) visit. Plazomicin demonstrated noninferiority to meropenem at both day 5 (88.0% versus 91.4%) and the TOC visit (81.7% versus 70.1). The efficacy and safety of plazomicin in cUTI patients was also supported by a randomized, double-blind phase 2 cUTI study, in which intravenous plazomicin dosages of 10 mg/kg and 15 mg/kg daily were compared to intravenous levofloxacin 750 mg daily (ClinicalTrials.gov identifier NCT01096849) (11, 12). TDM was not performed in the aforementioned two clinical studies.

Similar to other aminoglycosides, plazomicin displays linear pharmacokinetics (PK), low plasma protein binding (∼20%), and minimal metabolism. Because urinary excretion is the primary elimination pathway, the impact of renal function on the PK of plazomicin was evaluated in a dedicated renal impairment study (ClinicalTrials.gov identifier NCT01462136) (13). The results suggested that the exposure of plazomicin was comparable in subjects with mild renal impairment and those with normal renal function, while the plazomicin exposure in subjects with moderate and severe renal impairment was 2-fold and 4.4-fold higher, respectively, than in subjects with normal renal function. This study provided compelling evidence for recommending a dose reduction in cUTI patients with moderate or severe renal impairment. Moreover, plazomicin, as a member of the aminoglycosides, may potentially cause nephrotoxicity, which necessitated a thorough assessment of the TDM strategy in cUTI patients receiving plazomicin therapy.

Population PK modeling and exposure-response analysis are commonly used approaches to support dose adjustment in special populations (e.g., renal impairment or hepatic impairment) and dose selection in pivotal clinical studies. Classification and regression tree (CART) analysis is one of the statistical algorithms that are frequently used to develop decision trees. Decision tree methods classify a population into branch-like segments that construct an inverted tree with a root node, internal nodes, and leaf nodes (14). In this paper, we present a case study exemplifying the implementation of CART analysis along with comprehensive evaluation of PK, efficacy, and safety data to support regulatory decision-making, particularly the use of TDM with plazomicin prescribing in cUTI patients.

RESULTS

Dose evaluation using population PK modeling.

The parameter estimates of the population PK model were reported previously (15). The predicted AUC over 48 h (AUC_0–48) in simulated cUTI patients with different degrees of renal impairment are presented in Fig. 1. The results revealed that cUTI patients with normal renal function and mild, moderate, or severe renal impairment who received doses of 15 mg/kg daily, 10 mg/kg daily, and 10 mg/kg every other day, respectively, are expected to have comparable total exposure (AUC_0–48). After dose adjustment, the total exposures for cUTI patients with renal impairment are well covered by the exposure range derived from the phase 3 study.

FIG 1.

Predicted AUC_0–48 with different degrees of renal function. The dashed lines represent the 25% and 75% quantiles of AUC_0–48 (324 mg · h/L and 523 mg · h/L) in patients with normal renal function for visual comparison. The dashed-dotted line indicates the 95% quantile of AUC_0–48 (783 mg · h/L) in patients with cUTI from the phase 3 study.

Exposure-response analysis for nephrotoxicity.

A total of 22 of 367 subjects experienced nephrotoxicity in the phase 2 or phase 3 study. Thirteen of the 22 subjects developed nephrotoxicity within 10 days after the first dose and did not have an episode of nephrotoxicity after 10 days. Nine of the 22 subjects developed nephrotoxicity at least once after 10 days after the first dose. Five of the 9 subjects developed nephrotoxicity more than once, which occurred both before and after 10 days after the first dose (16).

Only one cUTI patient with severe renal impairment was enrolled in the phase 2 or phase 3 study. The nephrotoxicity incidence in cUTI patients with normal renal function and mild or moderate renal impairment is summarized in Table 1. cUTI patients with mild or moderate renal impairment appeared to be more vulnerable to nephrotoxicity than cUTI patients with normal renal function. cUTI patients with normal renal function in the plazomicin arm had a lower nephrotoxicity incidence than those in the control arm (meropenem or levofloxacin). Thus, the exposure-response analysis was conducted only in cUTI patients with renal impairment.

TABLE 1.

Comparison of nephrotoxicity incidence by renal function

Treatment	% nephrotoxicity (n/Na)
	Mild or moderate	Normal
Plazomicin	8.6 (21/244)	0.8 (1/123)
Active controlb	4.1 (10/243)	3.1 (3/97)

^an, number of patients with nephrotoxicity; N, number of patients.

^bMeropenem or levofloxacin.

The predicted plazomicin C_min following doses evaluated in the phase 3 study was plotted over the treatment period (5 to 7 days) for each patient (Fig. 2). The results indicated that C_min did not change substantially over the treatment period. Therefore, C_min prior to the second dose (C_{1st, min}) was deemed to be a reasonable PK metric to conduct the exposure-response analysis for nephrotoxicity.

FIG 2.

Predicted C_min over treatment period for cUTI patients from the phase 2 and phase 3 studies. Each line represents C_min over treatment period for each patient; different shades of gray (from light to dark) represent the 1st, 2nd, 3rd, and 4th quartiles of C_1st,min, respectively.

In cUTI patients with mild or moderate renal impairment, a significant exposure-response relationship was identified between plazomicin C_{1st, min} and nephrotoxicity incidence (Fig. 3). Plazomicin treatment duration of more than 5 days was not associated with nephrotoxicity.

FIG 3.

Exposure-response analysis for nephrotoxicity incidence in cUTI patients with mild or moderate renal impairment from the phase 2 and phase 3 studies. The black points represent the individual C_min for patients with nephrotoxicity (labeled as 1) or without nephrotoxicity (labeled as 0). The solid black line represents the logistic regression fit. The shaded region represents the 95% confidential interval for the fit.

CART analysis.

The CART analysis in the cUTI patients illustrated that a C_{1st, min} of 3 μg/mL (rounded from 2.955 μg/mL) may be a critical threshold associated with higher nephrotoxicity incidence (Fig. 4). To further confirm the appropriateness of the threshold, the C_{1st, min} ranges and the corresponding nephrotoxicity incidence are summarized in Table 2 for cUTI patients with mild or moderate renal impairment. The results aligned with the CART analysis showing that nephrotoxicity incidence escalates from 10% to 30% for C_{1st, min} range increases from 2 to 3 μg/mL to 3 to 4 μg/mL. According to previously published literature (17), nephrotoxicity occurs in 5% to 15% of patients treated with aminoglycosides. For patients with C_{1st, min} at or above 3 μg/mL, the nephrotoxicity incidence is higher than 15%, indicating that a C_{1st, min} of 3 μg/mL may be a reasonable TDM threshold for plazomicin.

FIG 4.

CART analysis for cUTI patients with mild or moderate renal impairment from the phase 2 and phase 3 studies. The total number of subjects in the CART analysis is 244, with a nephrotoxicity incidence of 8.6% (0.086). The threshold of 2.955 μg/mL was selected by the CART analysis. Based on the threshold, the subjects would be divided into two groups; one group (C_{1st, min} < 2.955 μg/mL) had 216 subjects, with a nephrotoxicity incidence of 5.1% (0.051), and the other (C_{1st, min} ≥ 2.955 μg/mL) had 28 subjects, with a nephrotoxicity incidence of 35.7% (0.357).

TABLE 2.

Summary of nephrotoxicity incidence by C_{1st, min} range in cUTI patients with mild or moderate renal impairment

C1st, min range (μg/mL)	% nephrotoxicity (n/Na)
≥4	40.0 (6/15)
≥3 and <4	30.8 (4/13)
≥2 and <3	9.8 (4/41)
≥1 and <2	5.0 (4/80)
<1 μg/mL	3.2 (3/95)
Total	8.6 (21/244)

^an, number of patients with nephrotoxicity; N, number of patients.

Given that a C_min of 2 μg/mL is a widely used TDM threshold for several aminoglycosides, including gentamicin and tobramycin (5), the sensitivity and specificity were compared for TDM thresholds of 2 μg/mL and 3 μg/mL. The receiver operating characteristic (ROC) curve is presented in Fig. 5. The specificity was defined as the percentage of patients without nephrotoxicity who can be correctly classified as needing no dose adjustment. Sensitivity was defined as the percentage of patients with nephrotoxicity who can be correctly classified as needing dose adjustment. The results (Table 3) revealed that the TDM threshold of 3 μg/mL provided a higher specificity while the TDM threshold of 2 μg/mL provided a better sensitivity in cUTI patients with mild or moderate renal impairment. The Youden index showed that both 2 μg/mL and 3 μg/mL are plausible TDM thresholds. Another comparison of two thresholds in cUTI patients with renal impairment is presented in Table 4. More patients would need dose adjustment if the threshold of 2 μg/mL is selected than if 3 μg/mL is selected (28.8% versus 11.5%). However, as a result, the predicted nephrotoxicity incidence in patients who do not need dose adjustment is reduced from 5.1% to 1% for the threshold of 2 μg/mL compared to 3 μg/mL.

FIG 5.

ROC curve for cUTI patients with mild or moderate renal impairment from the phase 2 and phase 3 studies. The ROC curve represents the percentage of true positives and percentage of false positives for each threshold (such as 0.5, 1, 2, 3, and 4). AUC represents the area under the ROC curve and is a performance measurement for the classification problem at various thresholds.

TABLE 3.

Sensitivity, specificity and Youden index comparison by TDM thresholds

C1st, min cutoff (μg/mL)	Sensitivity (%)	Specificity (%)	Youden index
2	67	75	0.42
3	48	92	0.40

TABLE 4.

Comparison of two TDM thresholds in cUTI patients with mild or moderate renal impairment^a

Threshold (μg/mL)	% of patients needing dose adjustment (N1/N)	% nephrotoxicity in patients:
		Needing dose adjustment (n/N1)	Not needing dose adjustment (n/[N − N1])
2	28.3 (69/244)	20.3 (14/69)	1.0 (7/175)
3	11.5 (28/244)	35.7 (10/28)	5.1 (11/216)

^aN1, number of patients with C_{1st, min} at or above the threshold; N, number of patients; n, number of patients with nephrotoxicity.

Exposure-response analysis for efficacy.

Instead of AUC_0–48, the predicted AUC over 24 h after the first dose (AUC_0–24) was utilized in the exposure-response analysis for efficacy based on the following: (i) all the patients received daily administration because a limited number of patients with severe renal impairment were enrolled, and (ii) daily AUCs were expected to be similar because there was no substantial change in C_min as well as no appreciable accumulation.

The results (Fig. 6) demonstrated no apparent association between AUC_0–24 and efficacy endpoint on day 5 and at TOC. The exposure-response relationship for efficacy may reach a plateau, given that only one dose level (15 mg/kg daily [QD]) was evaluated.

FIG 6.

Exposure-response analysis for composite response at day 5 (top) and TOC (bottom) in cUTI patients from the phase 3 study. The black points represent the individual AUC_0–24 for patients with composite cure (labeled as 1) or failure (labeled as 0). The solid black line represents the logistic regression fit. The shaded region represents the 95% confidential interval for the fit.

DISCUSSION

In our analysis, nephrotoxicity was defined as an increase in serum creatinine concentration of 0.5 mg/dL or more from baseline. The cutoff was selected to account for the inhibition of the renal transporters MATE1 and MATE2-K by plazomicin. Serum creatinine is primarily filtered through the glomeruli, but a small proportion (∼10% to 20%) undergoes active secretion by the renal proximal tubules. Literature suggests that the increase of serum creatinine caused by the inhibition of the renal transporters (i.e., OCT2, MATE1, and MATE2-K) usually occurs early in therapy, with a prompt return to baseline and with a maximum observed serum creatinine concentration increase of about 0.38 mg/dL. Therefore, the increase in serum creatinine concentration by 0.5 mg/dL may indicate potential nephrotoxicity caused by plazomicin (16, 18).

In the current study, the TDM threshold for plazomicin was evaluated and determined for plazomicin based on PK, efficacy, and safety data, as well as pharmacometrics and statistical approaches. First, our study found appreciable variability for the time to occurrence of nephrotoxicity, ranging from 2 days to 4 weeks after initiation of the plazomicin treatment. It is unclear whether the nephrotoxicity that occurred after 10 days was still drug related, since plazomicin should be completely cleared from the human body after 10 days after the first dose due to the short treatment duration (5 to 7 days) and the short half-life (3.5 h). Second, our study identified a fairly low nephrotoxicity incidence in cUTI patients with normal renal function who were administered plazomicin, suggesting that TDM may not be needed in this population. Action based on this conclusion is expected to improve the efficiency of the TDM strategy as well as reduce the health care burden in cUTI patients receiving plazomicin treatment. Last, our study highlighted the importance of TDM in cUTI patients with renal impairment due to the apparent exposure-dependent nephrotoxicity in cUTI patients with mild or moderate renal impairment. The key question was how to select a TDM threshold for plazomicin that is scientifically justifiable and clinically appropriate.

While the Youden indexes for the thresholds of 2 μg/mL and 3 μg/mL were close, the use of the threshold of 2 μg/mL increases the sensitivity of identifying nephrotoxicity but at the expense of having more patients with potentially unnecessary dose reduction. On the other hand, the use of the threshold of 3 μg/mL results in having fewer patients with an unnecessary dose reduction but at the expense of having more patients with nephrotoxicity. Considering that occurrence of nephrotoxicity in patients whose dose was not adjusted was low overall, regardless of the threshold used, i.e., 1.0% (7/175) for 2 μg/mL and 5.1% (11/216) for 3 μg/mL, and that nephrotoxicity was generally reversible, the use of the threshold of 3 μg/mL may provide an appropriate balance between decreasing the risk of nephrotoxicity and ensuring adequate treatment of the infection, especially in patients with severe infection where treatment failure is a significant concern.

In order to effectively reduce the trough concentration, it is recommended that for subjects with renal impairment who have trough concentrations equal to or higher than 3 μg/mL prior to the second dose, the dosing interval be extended by 1.5-fold (i.e., from every 24 h to every 36 h or from every 48 h to every 72 h) (1). This follows the TDM procedures for other aminoglycosides. Based on our simulation, following administration of the recommended dosage regimen of plazomicin in cUTI patients with mild, moderate, or severe impairment, approximately 87% of subjects would have trough concentrations prior to the second dose below 3 μg/mL, and with use of an extended dosing interval, another 10% subjects would have trough concentrations prior to the third dose below 3 μg/mL. These results revealed that one-time dose adjustment is adequate.

We acknowledge that our study has several limitations. One is that our exposure-response analysis for nephrotoxicity could not provide explanations for the large variability in the time to occurrence of nephrotoxicity. The elevation of serum creatinine several days after stopping plazomicin may not be related to the drug, especially if renal impairment has resolved after discontinuation of plazomicin. It may be explained by the initiation or continuation of other concomitant nephrotoxic medications or underlying kidney diseases. It is also possible that prior episodes of nephrotoxicity may have predisposed patients to repeat episodes by damaging the kidneys. In addition, serum creatinine is not an accurate biomarker for nephrotoxicity, even if it is commonly utilized clinically (19). Further analysis may be worthwhile to explore the impact of confounding factors on the exposure-response relationship for nephrotoxicity. Another limitation is that CART analysis is not a perfect algorithm. The main disadvantage is overfitting and underfitting with a small data set, which may limit the generalizability and robustness of the model (14). To capture the full information, our CART analysis was conducted using all available data from the efficacy and safety studies. No validation process was implemented. Therefore, the TDM threshold for plazomicin may need further verification with additional data.

In conclusion, the application of population PK modeling, exposure-response analysis, and CART analysis allowed the evaluation of a dosage regimen and TDM strategy for plazomicin in cUTI patients with renal impairment. A simple and efficient individualized dosing strategy could reduce the risk of side effects and improve the benefit/risk profile for plazomicin. Our study demonstrated the utility of pharmacometrics and statistical approaches to inform the dosage regimen and TDM strategy for drugs with narrow therapeutic windows.

MATERIALS AND METHODS

Dose evaluation using a population PK model.

The population PK model for plazomicin was previously developed and submitted to the FDA by Achaogen. The details of model development and validation have been published (15). Briefly, a three-compartment PK model with zero-order input and first-order elimination was established based on the pooled plazomicin concentration data from healthy subjects, subjects with different degrees of renal impairment and cUTI patients. Overall, the population PK model reasonably characterized the PK profiles of plazomicin in healthy subjects, subjects with different degrees of renal impairment, and cUTI patients.

The population PK model was used to simulate the plazomicin concentrations over 48 h in cUTI patients with normal renal function and mild, moderate, or severe renal impairment. A hypothetical cohort of 3,000 patients was generated with the demographic information (except renal function) randomly selected from the phase 3 study (ClinicalTrials.gov identifier NCT02486627) (10). The body weight range was 40.5 to 135 kg, the age range was 18 to 90 years, the height range was 142 to 194 cm, and the body surface area range was 1.29 to 2.43 m². Thereafter, a random estimated glomerular filtration rate (eGFR) value was assigned to each patient using a uniform distribution between 15 and 120 mL/min based on a previous reported approach (20). The dose was 15 mg/kg daily for patients with normal renal function or mild renal impairment, 10 mg/kg daily for patients with moderate renal impairment, and 10 mg/kg every other day for patients with severe renal impairment. The simulation was performed 100 times. The AUC over 48 h (AUC_0–48) was estimated for each patient. AUC instead of C_max was selected as the PK metric to indicate efficacy, because the half-life was prolonged in patients with renal impairment, while C_max values did not change significantly.

Exposure-response analysis for nephrotoxicity.

In the phase 2 and phase 3 studies, the assessment of nephrotoxicity was conducted up to 4 to 6 weeks. Considering the short treatment duration (5 to 7 days) and the short half-life (3.5 h), plazomicin was expected be completely cleared from the human body within 10 days after the first dose. Any nephrotoxicity that occurred after 10 days after the first dose may not be explained by a direct mechanism-based PK/pharmacodynamic (PD) model. Thus, an exposure-response analysis for nephrotoxicity was conducted in cUTI patients from the phase 2 study (ClinicalTrials.gov identifier NCT01096849) (11) and the phase 3 study (ClinicalTrials.gov identifier NCT02486627) (10). Nephrotoxicity was defined as an increase in serum creatinine concentration of 0.5 mg/dL or more from baseline. C_min was used in the exposure-response analysis for nephrotoxicity. The time course of C_min over the treatment duration was assessed prior to conducting the exposure-response analysis for nephrotoxicity. Other covariates (for instance, treatment duration and CL_CR at baseline) for the exposure-response relationship for nephrotoxicity were also evaluated.

CART analysis.

CART analysis was utilized to determine the TDM threshold for plazomicin in cUTI patients to reduce the nephrotoxicity incidence. The sensitivity and specificity of two different TDM thresholds were evaluated. The Youden index was calculated and the receiver operating characteristics (ROC) analysis was performed to compare the two TDM thresholds. The Youden index is a statistic that captures the performance of a dichotomous diagnostic test, used for setting optimal thresholds. The larger the Youden index, the better the performance at a given threshold.

Exposure-response analysis for efficacy.

Considering that the efficacy endpoints in phase 2 and phase 3 studies were different, an exposure-response analysis for efficacy was conducted in cUTI patients from the phase 3 study only (ClinicalTrials.gov identifier NCT02486627) (10). Two efficacy endpoints were assessed: (i) composite microbiology and clinical response on day 5 and (ii) composite microbiology and clinical response at TOC. Both of these measures were the primary endpoint for the study. AUC was selected as the key PK metric based on available information from plazomicin animal and microbiology studies. A total of 189 cUTI patients with evaluable efficacy and available PK information were included in the exposure-response analysis for efficacy.

Software.

Population PK analysis and simulations were performed by nonlinear mixed effects modeling approach using NONMEM 7.3 (Icon Development Solutions, Ellicott City, MD, USA). Dose evaluation in patients with renal impairment, exposure-response analysis, CART analysis, and ROC analysis were handled using R (version 4.0.3).