Evaluation and Improvement of Specialized Vancomycin Pharmacokinetic Models for Pediatric Cardiovascular Intensive Care Unit and Pediatric Oncology Patients

Abstract

Background and Objective

Dose optimization of vancomycin in distinct pediatric subpopulations is inherently complex due to altered vancomycin pharmacokinetics associated with certain conditions or circumstances, such as cancer or postoperative cardiac surgery. Numerous population pharmacokinetic models have been developed that aim to capture these alterations; however, it is currently unclear whether these specialized models are necessary, or if covariates in a well-specified general model can adequately capture pharmacokinetic variation between special subpopulations. Here, we conduct an external evaluation comparing the predictive performance of published general and specialized population pharmacokinetic models in pediatric oncology and pediatric cardiovascular intensive care unit (CVICU) patients in order to address this question, and guide model selection decisions for model-informed precision dosing of vancomycin in these subpopulations.

Methods

The predictive error, bias, and accuracy of two general, six oncology-supporting, and three CVICU-supporting pharmacokinetic models were compared in two multi-site data sets of pediatric oncology (N = 371, 1392 drug levels, 20 sites) and pediatric CVICU (N = 219, 1136 drug levels, 11 sites) patients, respectively. The best performing model(s) in each subpopulation were refit to evaluate whether predictive performance could be further improved over the published models.

Results

We find that although specialized models performed better than general population models for pediatric CVICU patients, a general model (Colin 2019) performed better than all specialized models for pediatric oncology patients. We additionally report a refit version of the Shimamoto 2024 model for pediatric CVICU patients, which performed better than all published CVICU-supporting models in our data set.

Conclusion

Population pharmacokinetic models developed on distinct pediatric subpopulations are not necessarily more fit-for-purpose than models developed on a general population. Both well-specified general models and specialized models may be capable of achieving suitable clinical performance in these subpopulations, and this assessment of model fit-for-purpose must be made on a case-by-case basis.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40262-026-01623-7.

Key Points

Population pharmacokinetic models developed on distinct subpopulations do not always perform better in those populations than models developed on a general population, underscoring the importance of external evaluation when selecting a suitable model for guiding vancomycin dosing decisions.

For pediatric CVICU patients, specialized models performed better than general population models, with a refit two-compartment model (Shimamoto 2024) performing best.

For pediatric oncology patients, a general model (Colin 2019) performed better than all specialized models.

Introduction

Vancomycin is a glycopeptide antibiotic for the prevention and treatment of infections caused by Gram-positive bacteria, such as methicillin-resistant Staphylococcus aureus (MRSA). Due to high inter-individual (IIV) pharmacokinetic (PK) variability, a risk of increased microbial resistance associated with subtherapeutic exposure, and the risk of nephrotoxicity associated with supratherapeutic exposure [1, 2], it is recommended that an individualized dosing approach be adopted, based on therapeutic drug monitoring (TDM) of vancomycin [3, 4].

Therapeutic drug monitoring-guided dosing in pediatric subpopulations is, however, inherently complex due to physiological changes during normal development [5] as well as reported alterations in pharmacokinetics associated with certain conditions [2]. For example, pediatric oncology patients with hematologic malignancy or neutropenia often have augmented renal clearance compared to the general patient population, which may result in subtherapeutic vancomycin concentrations when following conventional vancomycin dosing guidelines [6]. Similarly, postoperative pediatric cardiac surgery patients have an increased risk of impaired renal function resulting from cardiopulmonary bypass-induced low cardiac output syndrome, requiring a careful dosing strategy to avoid nephrotoxicity [7, 8].

One approach for addressing these complexities is to use TDM in conjunction with model-informed precision dosing (MIPD), wherein doses are individualized through the use of a model, such as a population pharmacokinetic (popPK) model [5]. Population pharmacokinetic models incorporate demographic, anthropomorphic, and biomarker data to partially explain sources of interindividual PK variability, while Bayesian estimation methods informed by TDM samples allow further tailoring of model parameters to predict a patient’s response to a drug. Applying MIPD to clinical practice first requires selecting an appropriate popPK model for the intended patient population [9]. Numerous popPK models have been developed for vancomycin in both the general pediatric population and in several distinct pediatric subpopulations (for reviews, see [2, 10, 11]). Similarities and differences between these general and specialized vancomycin popPK models have been covered in past reviews [2, 10, 11]; however, the value of a specialized model over a well-specified general model in clinical practice is unclear. That is, can model covariates in a well-specified general model capture PK variation between special subpopulations, or are specialized popPK models required for MIPD in subpopulations like pediatric oncology or cardiac surgery patients?

Here, we evaluate the predictive performance of published vancomycin popPK models in two distinct pediatric patient subpopulations—oncology patients (Study 1) and cardiovascular intensive care unit (CVICU) patients (Study 2)—using routine clinical care data collected from multiple sites across the USA. To the best of our knowledge, this work provides the first external evaluations of popPK models in these two difficult-to-study subpopulations, addressing an important research gap identified in previous works [1, 2, 10, 11]. For each study, we first compare model fit-for-purpose based on the a priori and a posteriori predictive performance of each model: meaning their first dose prediction before TDM was performed using popPK parameters, and their subsequent dose predictions after one or more TDM samples were collected using individualized Bayesian estimates of PK parameters, respectively [12]. We then refit the best performing model(s) in each subpopulation as part of the continuous learning approach to MIPD [13–15], evaluating whether predictive performance could be further improved over the published models by adapting and refining these models with new patient data from a broader clinical setting. Together, these studies aim to guide model selection decisions for MIPD of vancomycin in these subpopulations specifically; and more generally, to assess whether models developed on a distinct subpopulation are necessarily more fit-for-purpose than models developed on a general population in this context.

Methods

Literature Review

A literature review was conducted to identify popPK models describing vancomycin PK in pediatric oncology and pediatric CVICU patients using Google Scholar and combinations of the following search terms: pharmacokinetics, vancomycin, pediatric, oncology, CVICU, cardiac, ICU. Models were included for comparison if the following criteria were met: (1) developed on a population closely aligned with either pediatric oncology or CVICU patients; (2) used routinely collected covariates; (3) were parametric; (4) were published after the year 2010 [13]. This final criterion is based on improvements in model development software and solidifying consensus on appropriate model development methods and diagnostics around that year, as well as our own experience evaluating popPK models [16–18].

Independent screening of articles was done by MGM and JHH. A small handful of general pediatric vancomycin models were also selected for comparison based on their good performance and/or use in clinical decision support (CDS) software.

Data Collection

Patient data collected retrospectively or during routine clinical care of pediatric patients treated with intermittent intravenous vancomycin and entered into the InsightRX Nova CDS software tool between January 2018 and April 2025 were de-identified and analyzed retrospectively. Data were collected from multiple sites, including acute care hospitals and academic teaching hospitals distributed across the USA. Because these data were collected during routine health care at contracted health care entities and were de-identified before analysis, this study qualifies for exemption from federal Human Research Subjects regulations under 45 CFR 46.102(f).

These data included patient sex; height and weight; chronological and post-menstrual age at the time of the first dose of vancomycin; serum creatinine measurements; serum vancomycin measurements; the dose amount, timing, and infusion duration of vancomycin administered; treatment course, defined based on the way in which users accessed the CDS tool; cancer type (Study 1); and neutropenia status (Study 1). For treatment courses, when integrated within the electronic health record, new treatment courses were automatically created if the previous dose had taken place at least 7 days before. For users accessing the standalone cloud-based software, new treatment courses were created at the user’s discretion and were limited to 6 months’ duration, after which a user would be required to create a new treatment course.

Patients were included if they were aged < 20 years, had provided at least one serum vancomycin level, and were marked as either an oncology patient (Study 1) or a CVICU patient (Study 2) by the clinician during treatment using a tagging feature available in the InsightRX Nova CDS software tool. Body temperature, which was strictly used to operationalize a binary fever covariate for a single popPK model, was not recorded for any patients; however, for oncology patients with a known diagnosis of febrile neutropenia (also known as neutropenic fever), a body temperature indicating positive fever status was imputed, and for all other patients a negative fever status was assumed [19]. The impact of this assumption was assessed by repeating the analysis with imputed values assuming all patients were with or without fever for the relevant popPK models. Post-menstrual age was available for only a portion of the patients whose chronological age was < 2 years and was imputed as chronological age plus 40 weeks for all other patients.

For both studies, patients were excluded from analysis if they had received hemodialysis (HD), continuous renal replacement therapy (CRRT), extracorporeal membrane oxygenation (ECMO), or were on a ventricular assist device (VAD), or were also tagged as neonatal ICU (NICU) or pediatric ICU (PICU) patients, as these were considered separate populations that do not describe typical oncology or CVICU patients. Prior to analysis, we removed patients with anomalous data, such as patients with apparently inaccurate dosing records (e.g., suspected missing doses), and otherwise suspicious data (e.g., suspiciously high troughs relative to renal function, apparent typos, etc.), identified through graphical checks and manual inspection of important variables. We also removed any treatment courses where large dose gaps were present (> 70 hours), where serum vancomycin concentrations were collected during infusion, or where one or more records had anomalous weights or heights for age based on CDC growth charts (< 0.1 or > 99.9th percentiles). Additionally, we excluded patients who had treatment courses longer than 60 days, since vancomycin models do not typically include inter-occasional variability and PK parameters can be expected to change over such long durations.

Following model-based predictions, patients whose predictions had an absolute conditional weighted residual (CWRES) greater than 4 for any model were considered for removal, since a residual more than four standard deviations larger than the expected residual variability likely indicates erroneous data. This was dealt with on a case-by-case basis, taking into consideration the quality of each patient’s data, the number of records and models where their predictions had an absolute CWRES greater than 4, as well as the general performance of each model. Due to the de-identified nature of the data, chart review was not possible. The analysis pipeline was then repeated with these patients removed for the final results.

An equally-sized control data set was created from our data lake for each subpopulation by including patients who were tagged as neither oncology nor CVICU patients but otherwise met the same inclusion and exclusion criteria. Propensity score matching [20] was used to ensure baseline covariate and TDM sampling distribution parity between control and oncology or CVICU patients.

Propensity Score Matching

Propensity score matching was performed using the MatchIt R package [21]. Propensity scores were estimated using logistic regression of the patient group on the following baseline covariates: sex, post-menstrual age, height, weight, and serum creatinine, as well as the total number of TDM samples for each patient. The matching procedure was iterated upon until we achieved an acceptable covariate balance, as assessed by graphical checks of covariate distributions between the treatment and matched groups. For both studies, we first attempted 1:1 optimal propensity score matching without replacement. For CVICU patients, this specification yielded an excellent balance and was used to create the control data set for this population. For oncology patients, although this model improved covariate balance, graphical checks still showed some systematic differences. Updating the propensity score model to include covariate interactions resulted in better alignment in covariate distribution and was used for propensity score matching in this population.

Pharmacokinetic Analysis

Models identified in the literature review were implemented in NONMEM (version 7.4.4, ICON Development Solutions, Ellicott City, MD, USA). Model prediction performance was evaluated iteratively using the Perl-speaks-NONMEM (PsN; version 5.2.6, [22]) proseval tool. This approach mimics clinical decision making, where model predictions are used to inform dosing decisions without the use of drug levels collected in the future [23]. That is, for each model, popPK parameters were used to predict the first serum vancomycin level of each patient treatment course (i.e., a priori prediction). Subsequent levels were predicted using individualized maximum a posteriori (MAP) Bayesian estimates of PK parameters, obtained by iteratively sub-setting and fitting patients’ historical data within each treatment course (i.e., a posteriori prediction), as illustrated in Fig. 1. For patients with multiple treatment courses, each treatment course was treated as a unique individual in NONMEM. This was deemed reasonable since most patients (Oncology: 62%, CVICU: 67%) had only one treatment course. For oncology patients, treatment courses were typically separated by long lapses of time (median = 47 days, IQR = 18–118 days). For CVICU patients, treatment courses were more closely spaced (CVICU: median = 15 days, IQR = 8–47 days) but due to the rapidly changing condition of these patients, it was expected that individual PK estimates would also differ.

Fig. 1.

Schematic illustrating maximum a posteriori (MAP) Bayesian estimation in a hypothetical patient dosed with 1000 mg vancomycin infused over 2 hours every 12 hours. In this hypothetical scenario, the first level collected (the solid circle at 22 h) was 15 mg/L and was used to inform MAP Bayesian estimation of the individual’s pharmacokinetic (PK) parameters (shown in the overlaid table). These PK parameters were then used to simulate concentration-time curves, and to predict the drug level at 47 h (solid square; 19 mg/L). In real patients, this process was repeated iteratively until a forecast prediction was made for each collected level. Adapted from [23]

The a priori and a posteriori predictive performance of each model was evaluated for prediction error, bias, and accuracy. Prediction error was quantified using root mean square error (RMSE); prediction bias was quantified using relative mean prediction error (MPE), also known as mean percentage error; and prediction accuracy was evaluated by quantifying the proportion of predicted drug concentrations that fell within an absolute error margin of 2.5 mg/L or a relative error margin of 15% of the measured concentrations [5, 23, 24]. These error margins correspond to half the width of a target trough range of 15–20 mg/L, and were determined based on clinical judgment regarding what margin of error may be likely to impact clinical decision making [5, 23, 24].

These metrics were calculated by comparing the iteratively predicted drug concentrations ($\mathit{pred}$) relative to the measured concentrations ($\mathit{obs}$) across $N$ concentrations as follows:

$$\text{RMSE=}\sqrt{\frac{{\sum }_{i=1}^N{\left({\text{pred}}_{\text{i}},-,{\text{obs}}_{\text{i}}\right)}^2}{N}},$$

$$\text{MPE=}\frac{1}{N}{\sum }_{i=1}^N\frac{{\text{pred}}_{\text{i}}-{\text{obs}}_{\text{i}}}{{\text{obs}}_{\text{i}}}.$$

For each metric, point and 95% confidence interval (CI) estimates were constructed by bootstrapping samples and computing each error metric across these samples. The resultant intervals showed the estimates most compatible with our data, given the correctness of the set of procedural and statistical assumptions used to compute each interval.

For vancomycin, we considered a model as clinically acceptable if prediction error, bias, and accuracy were within a clinically acceptable range (RMSE < 5, |MPE| < 0.25, and accuracy > 0.60), and the 95% CI of bias included zero. These thresholds were based on the results of previous studies showing that in a general population of patients treated with vancomycin, RMSE was approximately 5 mg/L or less and accuracy was approximately 60% or more for the best models [5]. The threshold for MPE was based on the fact that a 25% bias falls well within a typical PK trough target in the range of 10–25 mg/L [12].

Pharmacokinetic Model Refitting

For both studies, the best performing model(s) were refit using NONMEM on the sample data to evaluate whether predictive performance could be improved over the published models [13], and to gain insight into substantive questions regarding these models. Robustness of the refit models was evaluated by non-parametric bootstrap analysis, where the sample data were resampled 2000 times to estimate the median and 95% CIs of the parameter estimates. For Study 1, the Colin 2019 model was refit on the sample data for oncology patients and matched non-oncology patients to reestimate the effect of cancer status on vancomycin clearance. For Study 2, the best-performing one-compartment (Moffett 2019) and two-compartment (Shimamoto 2024) models were refit on the sample data for CVICU patients, allowing us to evaluate the effect of the number of compartments on describing PK with greater confidence. Any parameters that could not be estimated due to numerical instability were fixed to the published values instead. The final model and covariate structures were not modified from the published models, except for estimating the allometric scaling factor on weight for clearance for the Shimamoto 2024 model.

Software

All computational steps were done in a reproducible pipeline using the open-source programming language R (version 4.3.3, [25]) and the targets R package [26].

Results

Patient Characteristics

For Study 1, there were 371 pediatric oncology patients from a total of 486 eligible patients who met the inclusion criteria (Table 1), treated at 20 healthcare organizations (see Table S1 for exclusions). The majority of oncology patients stemmed from one of three sites: 149 patients (40%) from a single site, followed by 64 patients (17%) from a second site, and 46 patients (12%) from a third site. The remaining sites had anywhere from 1 to 33 patients. For Study 2, there were 219 pediatric CVICU patients treated at 11 healthcare organizations who met the inclusion criteria (Table 1) from a total of 445 eligible patients (see Table S1 for exclusions). The majority of CVICU patients stemmed from one of three sites: 133 patients (61%) from a single site, followed by 53 patients (24%) from a second site, and 31 patients (14%) from a third site. Covariate distributions for both studies showed good agreement with their propensity-score matched controls (Figs S1 and S2).

Table 1.

Summary of vancomycin dosing and baseline patient characteristics for oncology and propensity-score matched non-oncology patients (Study 1), and for CVICU and propensity-score matched non-CVICU patients (Study 2)

Characteristic	Study 1		Study 2
	Oncology	Non-oncology	CVICU	Non-CVICU
Sites, N	20	58	11	25
Patients, N	371	371	219	219
Treatment courses, N	592	502	391	403
Per patient, median (IQR) [range]	1 (1–2) [1–8]	1 (1–1) [1–18]	1 (1–2) [1–14]	1 (1–2) [1–14]
Sex, n (%)
Female	166 (45%)	175 (47%)	101 (46%)	104 (47%)
Male	205 (55%)	196 (53%)	118 (54%)	115 (53%)
Age (years), median (IQR) [range]	7.2 (3.4–13.3) [0.2–20.0]	7.9 (3.9–14.1) [0.3–18.4]	1.1 (0.4–5.2) [0.1–17.8]	1.2 (0.4–5.2) [0.0–17.8]
Post-menstrual age (weeks), median (IQR) [range]	413 (220–735) [51–1081]	454 (245–777) [56–998]	99 (61–310) [46–970]	102 (60–309) [41–970]
Height (cm), median (IQR) [range]	123 (97–154) [58–187]	126 (99–157) [55–195]	73 (61–110) [51–187]	74 (61–109) [50–187]
Weight (kg), median (IQR) [range]	26 (15–51) [5–112]	28 (16–52) [5–124]	9 (6–19) [3–91]	9 (6–19) [3–100]
Serum creatinine (mg/dL), median (IQR) [range]	0.35 (0.24–0.49) [0.06–1.15]	0.34 (0.23–0.50) [0.06–1.08]	0.31 (0.21–0.48) [0.06–2.44]	0.31 (0.22–0.48) [0.06–2.44]
Cancer type, n (%)
Hematological malignancy	304 (82%)	–	–	–
Solid tumor	12 (3.2%)	–	–	–
Unspecified	55 (15%)	–	–	–
Neutropenia, n (%)	48 (13%)	4 (1.1%)	–	–
Vancomycin dosing
Doses, N	7498	6280	4152	4421
Per patient, median (IQR) [range]	12 (7–23) [2–204]	10 (6–18) [1–203]	11 (5–21) [2–178]	10 (6–23) [2–241]
Dose amount (mg/kg), median (IQR) [range]	428 (275–750) [75–1750]	500 (250–800) [25–2500]	125 (90–210) [25–2000]	140 (90–250) [25–2000]
Dosing interval (h), median (IQR) [range]	6.4 (5.9–7.8) [0.1–155.0]	6.5 (5.9–8.0) [0.02–162.0]	7.9 (6.7–8.7) [1.1–151.4]	7.7 (6.3–8.6) [1.2–181.0]
Infusion time (h), median (IQR) [range]	1 (1–1.5) [0.75–4]	1 (1–1.5) [0.5–22]	1 (1–1) [0.5–2]	1 (1–1) [0.5–2]
Vancomycin concentrations
Serum vancomycin concentrations, N	1392	1257	1136	1151
Per patient, median (IQR) [range]	3 (1–5) [1–46]	2 (1–4) [1–40]	3 (2–6) [1–34]	3 (1–6) [1–45]
Sampling time after dose (h), median (IQR) [range]	6.0 (5.4–7.4) [1.4–34.4]	5.9 (5.2–7.5)1.9–61.0]	7.5 (6.6–8.4) [2.2–66.6]	7.4 (6.1–8.4) [2.0–66.6]

CVICU cardiovascular intensive care unit, IQR interquartile range

Literature Review

A literature review identified six suitable vancomycin models for pediatric oncology patients [19, 27–31], and three suitable vancomycin models for pediatric CVICU patients [32–34]. One additional oncology-supporting model developed on patients receiving continuous vancomycin was identified but excluded given the availability of covariates in our data set [35]. Two general pediatric vancomycin models were also selected based on their good performance and/or use in MIPD clinical routines via the InsightRX Nova precision dosing platform [36, 37]. The model by Le et al is a general model developed exclusively on pediatric patients. The model by Colin et al was developed on 14 pooled data sets, which included patients across the age spectrum from both general populations as well as specialized subpopulations. One of these specialized populations included adults with hematological malignancy, and this model therefore included an effect of this condition on clearance. We chose to evaluate this model both with and without this covariate effect, which we denote as “Colin 2019 (Onc)” and “Colin 2019”. The selected models differed in the covariates used as predictors of vancomycin pharmacokinetics (Table 2) as well as model structure (Tables S2–S4).

Table 2.

Covariates used as predictors of vancomycin pharmacokinetics for each population pharmacokinetic model included in the analyses

Model	AGE	PMA	WT	CR	CRCL	BT	CANC
General vancomycin models
Colin 2019a	–	X	X	X	–	–	–
Le 2014	X	–	X	X	–	–	–
Oncology-supporting vancomycin models
Chuphan 2022	–	–	X	–	Xc	–	–
Colin 2019 (Onc)a	–	X	X	X	–	–	X
Hadi 2015	–	–	X	–	–	–	–
Lv 2020	–	–	X	–	–	–	–
Shimamoto 2021	–	X	X	–	Xc	X	–
Wang 2020	–	–	X	–	Xb	–	–
Zhao 2014	–	–	X	–	Xc	–	–
CVICU-supporting vancomycin models
Kamp 2024	–	–	X	–	Xb	–	–
Moffett 2019	–	X	X	–	Xb	–	–
Shimamoto 2024	–	X	X	–	Xc	–	–

AGE age (y), BT body temperature (BT ≥ 38.0 °C, flag 1; BT < 38.0 °C, flag 0), CANC cancer status, CR serum creatinine (mg/dL), CRCL creatinine clearance (L/h or L/h/1.73m²), PMA post-menstrual age (wk), WT weight (kg)

^aThe Colin 2019 model also has a heel-prick status covariate, which we set to zero for all patients because it was not collected in our data set

^bCRCL calculated using the Schwartz equation [38]

^cCRCL calculated using the revised "bedside" Schwartz equation [39]

For both studies, the distribution of patient characteristics in our samples (Figs S3 and S4) were generally similar to the development populations of the oncology-supporting and CVICU-supporting vancomycin models, respectively (Table 3). The development population for the Colin 2019 meta-model included older adult patients, and children and adolescents were the smallest cohort in this study (118/2554, 4.6%), leading to higher physical measurements and postnatal ages relative to both our samples; and the development population for the Le 2014 model skewed towards older children, leading to higher physical measurements and postnatal ages relative to our Study 2 sample of pediatric CVICU patients.

Table 3.

Sample size and patient characteristics of the pharmacokinetic models included in the analysis

Model	N	AGE	PMA	HT	WT	CR
General vancomycin models
Colin 2019	2554	[0.00–101.00]	[23.5–5266.43]	[26–202]	[0.42–160.0]	[0.15–9.75]
Le 2014	138	6.10 (2.20–12.20)	–	–	22.2 (13.2–37.9)	0.37 (0.30–0.50)
Oncology-supporting vancomycin models
Chuphan 2022	212	3.5 (0.9–10.9)	–	95.5 (65–136)	14.0 (7.2–30.4)	0.38 (0.25–0.59)
Hadi 2015	95	6 (2.46)	–	113.98 (15.6)	19.6 (6.95)	0.406 (0.118)
Lv 2020	53	8.62 (4.13)	–	125.6 (25.1)	28.12 (14.67)	0.33 (0.15)
Shimamoto 2021	165	[0.25–18.00]	–	–	20.7 (13.5–46.5)	0.34 (0.25–0.45)
Wang 2020	92	7.0 [0.4–17.1]	–	124.0 [62.0–180.0]	24.3 [7.0–70.0]	0.48 [0.28–1.44]
Zhao 2014	70	5.6 [0.3–17.7]	–	–	20.2 [5.6–71.0]	0.34 [0.11–1.59]
CVICU-supporting vancomycin models
Kamp 2024	133	0.24 (0.08–0.55) [0.00–17.18]	51 (43–69) [35–933]	57 (52–68) [43–175]	4.5 (3.5–7.0) [2–70]	0.32 (0.23–0.50) [0.11–2.00]
Moffett 2019	261	0.31 (0.07–0.77)	54.6 (42.6–76.9)	58 (51.5–67.1)	4.8 (3.4–7.4)	0.32 (0.25–0.41)
Shimamoto 2024	152	0.33 (0.09–1.31) [0.01–13.53]	55.2 (43.5–107.1) [37.9–744.7]	57.5 (48.5–72.3) [41.0–153.0]	4.6 (3.1–7.9) [1.8–38.7]	0.32 (0.25–0.39) [0.11–1.06]

Values are median (IQR) [range] for all models except the Hadi 2015 and Lv 2020 models, which are mean (SD)

AGE age (y), CR serum creatinine (mg/dL), HT height (cm), PMA post-menstrual age (wk), WT weight (kg)

Study 1: Comparison of Literature Model Predictive Performance in Oncology Patients

Of the nine identified general and oncology-supporting popPK models, model prediction error (Fig. 2A) was best for pediatric oncology patients using the Shimamoto 2021 model a priori. However, there was a substantial overlap in the RMSE estimates most compatible with our data between the Shimamoto 2021 model and the Colin 2019 model for a priori predictions; these were the only models whose RMSE estimates fell inside our chosen clinically acceptable range (RMSE < 5), although neither model’s CIs fell exclusively inside this range. For a posteriori predictions, the Colin 2019 and Shimamoto 2021 models performed the best, and the Colin 2019 (Onc) and Le 2014 models also had RMSE estimates that fell inside our chosen clinically acceptable range, although again, no model fell exclusively inside this range.

Fig. 2.

Predictive performance of published pharmacokinetic models for pediatric oncology patients dosed with vancomycin, assessed by root mean square error (RMSE), relative mean prediction error (MPE), and accuracy. Error bars represent the point and 95% confidence interval estimate for each model. For RMSE and accuracy, the dotted lines represent the upper and lower limits of the clinically acceptable range, respectively. For MPE, the dotted lines represent the lower and upper limits of the clinically acceptable range, and the solid line represents a target value of zero bias

The Hadi 2015 model produced the least biased predictions a priori, and the Lv 2020, Colin 2019, and Shimamoto 2021 models produced the least biased predictions a posteriori (Fig. 2B), with CIs overlapping zero. The Colin 2019, Wang 2020, and Zhao 2014 models also met our chosen thresholds for a priori predictions (|MPE| < 0.25), and all models but Zhao 2014 fell exclusively in this range for a posteriori predictions.

Model prediction accuracy (Fig. 2C) was best for pediatric oncology patients using the Hadi 2015 and Colin 2019 models a priori, and the Colin 2019 model a posteriori. In the latter case, this was the only model whose accuracy estimates overlapped with our chosen clinically acceptable range (accuracy > 0.60)—although barely. Otherwise, for both a priori and a posteriori predictions, accuracy estimates for all models fell exclusively outside our chosen clinically acceptable range.

On balance, the Colin 2019 model had the best performance across a priori and a posteriori predictions for pediatric oncology patients and was the only model close to satisfying all our criteria for clinical acceptability a posteriori. In matched non-oncology patients, the Colin 2019 model also had the best overall performance across a priori and a posteriori predictions. However, relative to oncology patients, predictive performance was similar or worse across all metrics, with the exception of a priori predictive bias. In general, this pattern held true across all models (Fig. S5). When examining these results across the three largest sites in our sample, the Colin 2019 model continued to show competitive predictive performance, but other models such as the Shimamoto 2021 model had the best overall performance for some sites (Fig. S6). Goodness-of-fit plots for each of the models are shown in Figures S7–S14.

We also investigated the impact of our imputation process for the Shimamoto 2021 model, which takes the presence of a fever as a predictor for clearance. If instead of relying on user-entered tags for febrile neutropenia we imputed the presence or absence of a fever for all patients, there was minimal impact on RMSE and accuracy, with similar a priori and a posteriori predictive performance regardless of the imputed values (Fig. S15). However, assuming all patients had a fever, we saw improved prediction bias a priori, but worsened bias a posteriori.

Study 1: popPK Model Refitting in Oncology Patients

The re-estimated Colin 2019 (Onc) model parameters and bootstrap validation results are shown in Table 4. In general, the re-estimated parameters were similar in our sample compared to the published values; however, the effect of cancer status on vancomycin clearance was considerably lower with a value overlapping zero, indicating that with the information in our sample we could not distinguish a significant difference in clearance between oncology and non-oncology patients. The refit model did not improve predictive performance (Fig. S16).

Table 4.

Model parameters from the published and refit Colin 2019 (Onc) models and bootstrap validation (n = 2000)

Parameter	Colin 2019 (Onc)		Colin 2019 (Onc) refit		Bootstrap replication, n = 2000
	Estimate	SE	Estimate	SE	Median	2.5th	97.5th
θCL	1.67	0.03	1.51	0.02	1.52	1.43	1.57
θVD1	3.75	0.07	3.57	0.03	3.69	3.12	3.85
θVD2	3.73	0.13	3.91	0.06	3.96	3.29	4.40
θQ2	1.17	0.08	0.81	0.13	0.84	0.64	1.19
θCANC	0.29	0.03	0.06	0.40	0.09	0.04	0.13
θPROP	0.21	0.01	0.22	0.04	0.22	0.19	0.24
θADD	1.23	0.12	0.81	0.14	0.75	0.39	1.19
ωCL (IIV)	0.27	0.01	0.26	0.08	0.25	0.04	0.29
ωVD1 (IIV)	0.27	0.03	0.41	0.13	0.47	0.37	0.62
ωVD2 (IIV)	0.83	0.05	0.93	0.07	0.94	0.77	1.07

ADD additive error (%), CANC cancer status, CL clearance (L/h), IIV interindividual variability (%), PROP proportional error (%), Q intercompartmental clearance (L/h), SE standard error, VD volume of distribution (L)

Study 2: Comparison of Literature Model Predictive Performance in CVICU Patients

Of the five identified general and CVICU-supporting popPK models, model prediction error (Fig. 3A) was best using the Moffett 2019 model a priori and the Kamp 2024, Moffett 2019, and Shimamoto 2024 models a posteriori, which all had similar estimates. Additionally, for a priori predictions, all models but Colin 2019 and Kamp 2024 had RMSE estimates that fell inside our chosen clinically acceptable range (RMSE < 5)—although no model fell exclusively inside this range. For a posteriori predictions, all models but Colin 2019 and Le 2014 models had RMSE estimates that fell exclusively inside our chosen clinically acceptable range.

Fig. 3.

Predictive performance of published and refit pharmacokinetic models for pediatric cardiovascular intensive care unit (CVICU) patients dosed with vancomycin, assessed by root mean square error (RMSE), relative mean prediction error (MPE), and accuracy. Error bars represent the point and the 95% confidence interval estimate for each model. For RMSE and accuracy, the dotted lines represent the upper and lower limits of the clinically acceptable range, respectively. For MPE, the dotted lines represent the lower and upper limits of the clinically acceptable range, and the solid line represents a target value of zero bias

The Moffett 2019 model produced the least biased predictions a priori, and the Colin 2019 model produced the leased biased predictions a posteriori (Fig. 3B). In both cases, these were the only models whose MPE estimates included zero. However, for a priori predictions, the Le 2014 model fell exclusively within our chosen clinically acceptable range (|MPE| < 0.25); and for a posteriori predictions, all models fell exclusively in this range.

Model prediction accuracy (Fig. 3C) for pediatric CVICU patients was best using the Moffett 2019 model a priori, and the Shimamoto 2024 model a posteriori. In addition, for a posteriori predictions, all models with the exception of Le 2014 had accuracy estimates that were compatible with our chosen clinically acceptable range (accuracy > 0.60). For a priori predictions, accuracy estimates for all models fell exclusively outside this range.

On balance, the Moffett 2019 model had the best performance across a priori and a posteriori predictions, followed by the Shimamoto 2024 model, which had comparable a posteriori performance but worse a priori performance. In general, this pattern held true when examining these results across the three largest sites in our sample (Fig. S17). In matched non-CVICU patients, predictive performance was highly similar to that of CVICU patients across all models (Fig. S18). Goodness-of-fit plots for each of the models are shown in Figures S19–S26.

Study 2: popPK Model Refitting in CVICU Patients

The models with the best predictive performance were re-estimated and the resulting model parameters and bootstrap validation results are shown in Tables 5 and 6. For the Moffett 2019 model, re-estimated parameters for the volume of distribution (VD) and IIV on clearance and in the VD were all higher in our sample compared to the published values, while the effect of post-menstrual age and creatinine clearance on vancomycin clearance were all lower. For the Shimamoto 2024 model, re-estimated parameters for the effect of creatinine clearance on vancomycin clearance and IIV on clearance and in the peripheral VD were all higher in our sample compared to the published values; clearance, the central VD, the effect of weight on vancomycin clearance, and additive error were all lower. For both models, the remaining re-estimated parameters were similar to the published values. Together, this indicates that less of the IIV could be explained by patient covariates.

Table 5.

Model parameters from the published and refit Moffett 2019 models and bootstrap validation (n = 2000)

Parameter	Moffett 2019		Moffett 2019 (refit)		Bootstrap replications, n = 2000
	Estimate	SE	Estimate	SE	Median	2.5th	97.5th
θCL	7.86	0.16	7.50	0.03	7.49	7.10	7.92
θVD	63.60	3.23	70.44	0.08	70.07	60.48	82.11
θPMA	− 0.28	0.09	− 0.17	0.37	− 0.17	− 0.30	− 0.05
θCRCL	0.90	0.05	0.77	0.08	0.77	0.66	0.88
θPROP	0.20	0.02	0.24	0.03	0.24	0.22	0.25
ωCL (IIV)	0.17	0.03	0.32	0.06	0.32	0.28	0.36
ωVD (IIV)	0.26	0.09	0.35	0.12	0.35	0.26	0.44

CL clearance (L/h), CRCL creatinine clearance (mL/min/1.73m²), IIV interindividual variability (%), PMA post-menstrual age (wk), PROP proportional error (%), SE standard error, VD volume of distribution (L)

Table 6.

Model parameters from the published and refit Shimamoto 2024 models and bootstrap validation (n = 2000)

Parameter	Shimamoto 2024				Shimamoto 2024 (refit)				Bootstrap replications, n = 2000
	Estimate		SE		Estimate		SE		Median	2.5th		97.5th
θCL	4.88	0.38		3.56		0.10		3.56			3.05		4.63
θVD1	21.60	2.05		12.72		0.31		12.82			7.86		28.95
θQ	2.95	0.46		–		–		–			–		–
θVD2	21.70	1.74		26.72		0.08		26.84			22.94		33.98
θWT	0.75	–		0.56		0.05		0.56			0.50		0.62
θCRCL	0.55	0.04		0.63		0.07		0.64			0.55		0.74
θHILL	1.73	0.52		–		–		–			–		–
θT50	36.90	3.43		–		–		–			–		–
θPROP	0.24	0.01		0.21		0.06		0.21			0.18		0.23
θADD	0.97	0.24		0.89		0.23		0.88			0.56		1.17
ωCL (IIV)	0.23	0.05		0.26		0.05		0.26			0.23		0.29
ωVD2 (IIV)	0.41	0.10		0.47		0.15		0.47			0.33		0.79

Blank estimates were fixed to the value of the published estimates

CL clearance (L/h), CRCL creatinine clearance (mL/min/1.73m²), HILL Hill coefficient, IIV interindividual variability (%), PROP proportional error (%), Q intercompartmental clearance (L/h), T50 postmenstrual age at which 50% of adult clearance is reached (weeks), VD volume of distribution (L), WT weight (kg)

Predictive performance was improved a priori and a posteriori for the refit Shimamoto 2024 model but only improved a posteriori for the refit Moffett 2019 model (Fig. 3). Comparing predictive performance between the refit and published models, the refit Shimamoto 2024 model had the best predictive error a priori and a posteriori (Fig. 3A); similar (absolute) predictive bias to the best-performing Colin 2019 model a posteriori, followed closely by the refit Moffett 2019 model, whose MPE estimates also included zero (Fig. 3B); and the best predictive accuracy a posteriori along with the refit Moffett 2019 model (Fig. 3C). Thus, on balance, the refit Shimamoto 2024 model had the best performance across a priori and a posteriori predictions and was the only model aside from the refit Moffett 2019 model that was close to satisfying all our criteria for clinical acceptability a posteriori. However, the a priori performance came short of satisfying these criteria – additionally losing out to the published Moffett 2019 model, which had similar prediction error and accuracy but less bias.

Discussion

Population pharmacokinetic models and Bayesian forecasting can account for inter-patient variability in pharmacokinetics, and so hold particular promise for addressing the inherent complexities of vancomycin dosing in pediatric subpopulations with known alterations in vancomycin pharmacokinetics [5]. Here, we evaluated the predictive performance of two general and several specialized popPK models for vancomycin in large multi-site samples of 371 pediatric oncology patients (Study 1) and 219 pediatric CVICU patients (Study 2). We also refit the best performing models to evaluate if predictive performance could be improved further. A strength of our approach is that predictive performance was evaluated iteratively, where each serum vancomycin level was predicted using Bayesian estimates informed by previous levels. This approach mimics clinical decision making with MIPD in practice—where model predictions are used to inform dosing decisions without knowing future lab results—providing the best translation of model fit-for-purpose for clinical performance [12].

In pediatric CVICU patients we found that models developed on this patient population performed better than general population models, with the refit Shimamoto 2024 model performing best (Fig. 3). In contrast, we found that for pediatric oncology patients, a general popPK model (Colin 2019) outperformed purpose-built models (Fig. 2). Moreover, re-estimating the effect of cancer status on clearance for the Colin 2019 (Onc) model resulted in an estimate statistically indistinguishable from zero, suggesting that cancer status was not predictive of patient PK in this data set (Table 4). Interestingly, both general popPK models (Colin 2019, Le 2014) also performed better in the oncology patients than in matched non-oncology patients (Fig. S5). Together, these results suggest that both well-specified general models and specialized models can achieve suitable clinical performance in distinct pediatric subpopulations, and that this assessment must be made on a case-by-case basis.

Pediatric CVICU patients in our data set tended to be young, with an interquartile post-menstrual age (PMA) of 61–310 weeks and an interquartile chronological age of 0.4–5.2 years (Table 1). Renal function matures rapidly in these early months of life—reaching 90% of adult glomerular filtration rate (GFR) by age 1 and 98% by age 2 in full-term neonates [40]—and varies as a function of both gestational age (GA) at birth and postnatal age, with birth-related differences in GFR between pre-term and full-term neonates with the same PMA becoming negligible beyond 65 weeks [41]. Of the three specialized CVICU models in Study 2, one model (Kamp 2024) lacked a term for GA (Table 2), despite more than a quarter of their patients being under the age of 1 month, with a maximum age of 17 years (Table 3). This model instead relied only on body size (weight) and creatinine clearance (a derived covariate that incorporates age) to scale PK parameters, and it is possible that the lack of maturation function resulted in its relatively poor performance in our data set. The other two CVICU models incorporated PMA as a covariate, as well as weight and creatinine clearance, perhaps allowing them to better capture changes in drug clearance as a function of maturation, serum creatinine, and body size. The oncology patient population was generally older, with 75% of patients having a PMA of 220 weeks or more; however, here too, the best performing models [19, 36] included PMA as a covariate.

All models that included a maturation effect incorporated this effect only on clearance; however, body water composition also varies in newborns and infants compared to older children [42]. Since vancomycin is a hydrophilic drug, it is possible that VD also varies with age. However, we did not observe a relationship between age and volume, and it is possible this effect size is small relative to other sources of variability.

Notably, GA was missing and imputed to a typical full-term birth value of 40 weeks for 362 (97.6%) oncology patients in Study 1, and 174 (79.5%) CVICU patients in Study 2. Previous work has shown that imputing a fixed value for GA can be a reasonable approach when the information needed for more sophisticated methods is unavailable, with the caveat that the true GA may be substantially different from the imputed GA when the same fixed value is used for full-term or pre-term births [43]. For patients with missing GA, we also lacked information on full-term or pre-term birth status, and thus we could only use a single fixed value typical of full-term births; therefore, PMA may have been erroneously estimated for an unknown number of patients in either study. However, in a more general infant population, we found that imputing a GA of 40 weeks had minimal impact on vancomycin model performance for patients over 37 weeks of PMA [5], which was true of all patients in both studies (Table 1), and the present results suggest that selecting a popPK model that accounts for maturation may be preferable to those that do not, even when GA is unknown. In cases where other information such as birth weight or term status are available, more accurate imputation strategies can be used for missing GA [43].

It should also not be taken for granted that a model tailored to a patient population will outperform a literature model. For the CVICU population, re-estimation of model parameters improved predictive performance, while no improvement was observed after re-estimation of the best-performing model for oncology patients.

In the case of the Colin 2019 (Onc) model, the cancer status covariate was a study-specific parameter that came from adult oncology patients who had significantly higher clearance relative to patients from other studies in their meta-analysis [36, 44]. Although previous studies have reported higher clearance in adult [45, 46] and pediatric [31, 47] oncology patients, we are unaware of any published popPK models that have directly estimated the magnitude of additional clearance attributable to cancer status in this population. Instead, these reported differences have been based on either mean differences between oncology and non-oncology patients [45–47] or nominal comparisons between studies [31].

Pediatric popPK studies that have tested the effect of cancer status [27], type of hematological disease [30, 31], or primary diagnosis [19] on vancomycin clearance, all discarded these covariates from their final model, suggesting that cancer itself may not be an independent risk factor for augmented renal clearance or altered vancomycin PK. This assertion is supported by Hirai and colleagues [48], who found that febrile neutropenia—but not cancer, other critical illnesses, or surgery—significantly increased the risk of augmented renal clearance in pediatric patients, indirectly influencing vancomycin clearance. Therefore, it is likely that the reported effect of cancer status on vancomycin clearance in the published Colin 2019 (Onc) model was either age-specific or a batch effect (i.e., related to that particular data set and not the underlying biology). Future research should explore covariates that might better explain augmented renal clearance in pediatric oncology patients, such as body temperature [19] or neutropenia status.

In pediatric CVICU patients, the general-purpose Colin 2019 model had adequate predictive performance but was outperformed by all three specialized models a posteriori on all metrics except bias, and this slight edge was eliminated after refitting the Shimamoto 2024 model (Fig. 3). It is interesting that the refit Shimamoto 2024 model, a two-compartment model, outperformed the refit Moffett 2019 model, given that the vast majority of published pediatric vancomycin models use one compartment [2, 10, 11]. However, in contrast to the general pediatric population and other subpopulations, two-compartment models are more often the best structural models in critically ill children [10], and a previous PK analysis of vancomycin in infants undergoing open-heart surgery with cardiopulmonary bypass also found that a two-compartment model performed best in their sample [49]. Together, these findings suggest that an appropriately specified two-compartment vancomycin model may be beneficial in pediatric CVICU patients, as it is in other subpopulations.

Additionally, as in previous studies, we found that MAP Bayesian estimates of individual PK parameters improved predictive performance and attenuated the differences in predictive performance between models [5]. Therefore, clinicians could collect earlier drug levels to improve dose optimization in cases where a pharmacokinetic model appears to be a poor fit for a patient, or uncertainty in covariate values is suspected. For models that continue to fit poorly, selecting another model that better reflects patient covariates or subpopulation, or using clinical judgment to adjust dosing from model predictions, may improve dose optimization for an individual patient [13].

Because both our studies used routine clinical care data, our approach has several limitations related to data quality and availability. These limitations stem from the scope of retrospective data not originally collected for research purposes, which may have a higher risk of incorrect or missing data that can introduce bias. Where possible, we reduced the risk of this bias by maintaining strict inclusion criteria and exclusion criteria for the data used in both studies; however, we were limited in our ability to address bias associated with several forms of uncaptured data.

First, inclusion criteria for either study required manual tagging of patients as an oncology patient (Study 1) or a CVICU patient (Study 2) by the clinician during treatment. This is an optional feature in the InsightRX Nova CDS software tool that uses a free text field, meaning that cancer types were not always known and that patients in the “general” population may also have been oncology or CVICU patients but untagged. Second, body temperature was not recorded for any oncology patients in our sample and had to be imputed/assumed based on other information—specifically, whether or not patients were diagnosed with febrile neutropenia. This diagnosis was also entered using the optional manual tagging feature in the InsightRX Nova CDS software tool, therefore, it is possible that there were additional patients in our sample with febrile neutropenia who were not tagged. Indeed, the improved a priori predictive bias for the Shimamoto 2021 model when assuming all patients had a fever suggests that a positive neutropenia diagnosis may not have been tagged in many cases (Fig. S15). Third, we did not have access to the assays used to measure serum vancomycin concentrations, as this information is not recorded in the InsightRX Nova CDS software tool; although inter-assay and inter-batch variability in vancomycin assays may impact the accuracy of serum vancomycin concentration measurements, these are relatively limited compared to the overall residual error magnitude, so we did not expect a major influence of this factor. Fourth, one oncology-supporting model identified in our literature review (Guilhaumou 2016) was excluded from evaluation, given that it included covariates unavailable in the InsightRX Nova CDS software tool. To the best of our knowledge, both studies otherwise included all relevant oncology-supporting and CVICU-supporting models. Finally, our study only included patients whose data were entered into the InsightRX Nova CDS software tool. Individual sites may have had protocols that dictate alternative approaches for vancomycin therapy management for certain subsets of patients, representing an unknown type of bias.

A further limitation of both our studies is that we excluded certain patient categories from analysis (patients on HD, CRRT, ECMO, and VAD or who were tagged as NICU or PICU patients), as these patient populations were considered pharmacokinetically distinct from our target cohorts of typical oncology and CVICU patients. Specifically, both renal replacement therapy and mechanical circulatory support can further increase the variability of vancomycin PK in critically ill patients [50–53], adding an additional layer of complexity to MIPD that may not be captured by conventional PK models [52, 54, 55]. Likewise, whereas typical oncology and CVICU patients have predictable PK alterations associated with their conditions [6–8], patients admitted to the NICU or PICU present with heterogeneous critical illnesses (e.g., sepsis, trauma, respiratory failure, prematurity, etc.) that introduce fundamentally different pathophysiological states. The varied hemodynamic profiles, organ perfusion patterns, and disease processes in these patients would introduce substantial heterogeneity that would limit the generalizability of our findings to the primary populations of interest. In our data set, ward location was determined based on clinical use of an optional tagging feature and applied to an entire treatment course. It is likely that patients tagged with both CVICU as well as a second ICU tag were moved from one ward to another, suggesting different patterns of care or comorbidities, or reflecting different disease progressions relative to patients tagged CVICU only.

The decision to exclude these patient categories largely reflected the exclusion criteria of the models considered in our comparisons: patients receiving extracorporeal organ support were excluded from the development population of all models, with the exception of the Kamp 2024 model that included a small number of patients on ECMO. General ICU patients were only included in the development populations of the Colin 2019, Hadi 2015, Le 2014, and Kamp 2024 models. Therefore, we caution against generalizing the results of our studies to these patient groups. Development and external evaluation of models that can adequately capture vancomycin PK for oncology and CVICU patients receiving extracorporeal organ support or presenting with concurrent critical illnesses is still needed, and it is unclear whether, for example, a general PK model for patients receiving renal replacement therapy would have better predictive performance than the best performing models identified here. Until then, we recommend performing intensified PK monitoring of vancomycin when applying MIPD to oncology and CVICU patients who are receiving extracorporeal organ support or are admitted to the NICU or PICU to prevent inadequate treatment outcomes, regardless of the chosen model.

Finally, without dense sampling, we were unable to assess the ability of the models to accurately estimate the true area under the concentration–time curve (AUC) experienced by a patient. Although this is the primary drug exposure metric of clinical interest in vancomycin [4], we have previously shown that the ability to accurately predict the next vancomycin serum level in sparsely sampled routine clinical data correlates well with the ability to adequately estimate AUC [14].

Conclusion

Overall, this research addresses a growing need for external evaluations comparing the predictive performance of popPK models in specific pediatric subpopulations [10]—providing guidance for model selection decisions for MIPD of vancomycin in pediatric oncology and pediatric CVICU patient populations. We find that the general Colin 2019 model performed best in pediatric oncology patients (Study 1) and that the refit Shimamoto 2024 model performed best in pediatric CVICU patients (Study 2), indicating that popPK models developed on distinct subpopulations are not necessarily more fit-for-purpose than models developed on a general population. Instead, it appears that both well-specified general models and specialized models can achieve suitable predictive performance in distinct pediatric subpopulations, and that this assessment of model fit-for-purpose must be made on a case-by-case basis.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

The authors received no funding for this work. Data reported in these analyses were collected as part of the routine operation of InsightRX.

Declarations

Author contributions

Conceptualization: MGM, JHH, RJK; Methodology: MGM, JHH, RJK; Software: MGM; Data curation: MGM, JHH, RJK; Formal analysis and investigation: MGM; Visualization: MGM; Writing – original draft preparation: MGM; Writing – review and editing: MGM, JHH, RJK; Project administration: MGM, JHH; Supervision: JHH, RJK. All authors have read and agreed to the published version of the manuscript.

Data availability

Due to its proprietary nature, supporting data cannot be made available.

Code availability

Due to its proprietary nature, supporting code cannot be made available. NONMEM model files are available as supplementary information.

Ethics approval

Data forming the basis of this analysis were collected as part of routine health care operations at contracted health care entities and not specifically for this study. These data were de-identified prior to analysis. These data are retrospective, and their use poses a minimal risk to patients. No study team member has access to subject identifiers linking data to specific individuals. Therefore, this study is exempt from federal Human Research Subjects regulations as defined in the US federal regulations 45 CFR 46.102(f).

Informed consent

The requirement for patient consent was waived since this is a retrospective review of de-identified data collected during routine clinical care, involving minimal risk to subjects.

Consent to participate

Not applicable. The data underlying this work were collected as part of routine clinical care and de-identified prior to analysis.

Consent to publish

Not applicable.

Competing interests

MGM, JHH, and RJK are employees of InsightRX. MGM, JHH, and RJK hold stock options with InsightRX, and RJK is a stockholder of InsightRX.