Clinical covariates that improve the description of high dose methotrexate pharmacokinetics in a diverse population to inform MTXPK.org

Abstract

The MTXPK.org webtool was launched in December 2019 and was developed to facilitate model‐informed supportive care and optimal use of glucarpidase following the administration of high‐dose methotrexate (HDMTX). One limitation identified during the original development of the MTXPK.org tool was the perceived generalizability because the modeled population comprised solely of Nordic pediatric patients receiving 24‐h infusions for the treatment of acute lymphoblastic leukemia. The goal of our study is to describe the pharmacokinetics of HDMTX from a diverse patient population (e.g., races, ethnicity, indications for methotrexate, and variable infusion durations) and identify meaningful factors that account for methotrexate variability and improve the model's performance. To do this, retrospectively analyzed pharmacokinetic and toxicity data from pediatric and adolescent young adult patients who were receiving HDMTX (>0.5 g/m²) for the treatment of a cancer diagnosis from three pediatric medical centers. We performed population pharmacokinetic modeling referencing the original MTXPK.org NONMEM model (includes body surface area and serum creatinine as covariates) on 1668 patients, 7506 administrations of HDMTX, and 30,250 concentrations. Our results support the parameterizations of short infusion duration (<8 h) and the presence of Down syndrome on methotrexate clearance, the parameterization of severe hypoalbuminemia (<2.5 g/dL) on the intercompartmental clearance (Q2 and Q3), and the parameterization of pleural effusion on the volume of distribution (V1 and V2). These novel parameterizations will increase the generalizability of the MTXPK.org model once they are added to the webtool.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

The MTXPK.org webtool was originally developed using a Nordic population of pediatric patients with acute lymphoblastic leukemia. There are many clinical and demographic variables that contribute to the significant interindividual pharmacokinetic variability of high‐dose methotrexate (HDMTX) that may not have been captured by this original population.

• WHAT QUESTION DID THIS STUDY ADDRESS?

The goal of this study was to describe HDMTX pharmacokinetics in a diverse patient cohort and identify meaningful factors that account for methotrexate variability and improve the model's performance.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

Four variables were parameterized, including the novel parameterization of Down syndrome on the clearance of methotrexate and pleural effusion on the volume of distribution of methotrexate. In addition to body surface area and serum creatinine, these new variables will improve the model's performance and increase the generalizability of MTXPK.org.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

The MTXPK.org webtool will continue to facilitate model‐informed clinical decisions regarding supportive care and glucarpidase use for patients receiving HDMTX for the treatment of malignant conditions.

INTRODUCTION

High‐dose methotrexate (HDMTX) is a critical component of many cancer chemotherapy regimens. However, some patients experience delayed methotrexate (MTX) elimination, increasing their risk for severe nephrotoxicity and death. ¹ More than 90% of MTX is eliminated unchanged by the kidneys, so MTX‐induced damage can result in a vicious cycle of slower MTX elimination and increase the risk for MTX toxicity. ¹

This cycle can lead to a significant accumulation of MTX which is often unresponsive to standard supportive care measures like fluid hydration and leucovorin rescue. ¹ , ² For these cases, patients are often eligible for glucarpidase (carboxypeptidase G2), a US Food and Drug Administration‐approved exogenous enzyme that rapidly hydrolyzes MTX into two inactive and non‐nephrotoxic metabolites, 4‐amino‐4‐deoxy‐N(10)‐methylpteroic acid (DAMPA) and glutamic acid. ² These metabolites are rapidly eliminated via non‐renal pathways, thus alleviating the burden on already damaged kidneys. Understanding when to use glucarpidase in the clinical setting has proven to be challenging. The labeled indication states that its use is intended for patients who exhibit delayed MTX clearance (CL), with plasma MTX concentrations that are two standard deviations (SDs) above the mean excretion curve for a specific dose, or who display significantly impaired renal function. ³ Due to the difficulties surrounding the clinical interpretation and implementation of the labeled indication, a glucarpidase consensus guideline was developed. ² An international task force developed this evidence‐based consensus guideline that identifies several actionable concentration‐time thresholds that are associated with significant HDMTX toxicity and warrants the use of glucarpidase. ² Whereas this consensus guideline is a major advancement for glucarpidase use, the static nature of the identified timepoints left some clinical uncertainty regarding sample times that did not align with those in the guideline.

In response to this uncertainty, our group previously developed MTXPK.org, a free, online clinical decision support tool that facilitates model‐informed decisions regarding supportive care and optimized glucarpidase use. ⁴ The MTXPK.org tool uses a nonlinear mixed effects model with Bayesian estimation and real‐time patient data to generate numerical and visual feedback of a patient's HDMTX pharmacokinetics (PKs). The clinical team can leverage many forms of information that this tool provides to make model‐informed decisions about the patient's care. ⁴

The MTXPK.org tool was launched in December 2019 and has seen on average ~700 unique users per month and has been accessed by individuals from more than 100 countries. One limitation identified during the original development of the MTXPK.org tool was the limited perceived generalizability. A rich population PK database with dense therapeutic drug monitoring was used to develop the original model for MTXPK.org; however, the population was limited to Nordic pediatric patients with acute lymphoblastic leukemia (ALL) who received 24‐h infusions. A validity cohort supported the application of the original model for MTXPK.org across ALL, osteosarcoma, and lymphoma protocols but was limited in terms of ancestry. In lieu of these findings, a multisite collaboration consisting of Cincinnati Children's Hospital Medical Center (CCHMC), Children's Healthcare of Atlanta (CHOA), and Texas Children's Hospital (TXCH) was established to investigate the PK and toxicity of HDMTX in pediatric and adolescent young adult (AYA) patients. The objective of this study is to describe the PKs of HDMTX from a diverse patient population (e.g., races, ethnicity, indications for MTX, and variable infusion durations) and identify meaningful factors that account for MTX variability and improve the model's performance.

METHODS

Patient population

This study retrospectively analyzed PK data from pediatric and AYA patients (aged 0.1–32.3 years at the time of MTX administration) who were receiving HDMTX (>0.5 g/m²) for the treatment of a cancer diagnosis (ALL, osteosarcoma, and non‐Hodgkin lymphoma [NHL]) at CHOA, CCHMC, or TXCH between January 2010 and December 2020 (Table 1). The institutional review boards at each medical center approved the retrospective analysis of these data.

TABLE 1.

Demographics.

	All patients n = 1668	Short infusion n = 487	Long infusion n = 1181
Administrations	7506	3087 (41.1%)	4419 (58.9%)
Concentrations	30,250	11,623 (38.4%)	18,627 (61.6%)
Site of treatment
CCHMC	326 (19.5%)	117 (24.0%)	209 (17.7%)
CHOA	630 (37.8%)	231 (47.4%)	399 (33.8%)
TXCH	712 (42.7%)	139 (28.5%)	573 (48.5%)
Age in years (range)	10.9 (0.1–32.3)	13.8 (0.7–31.9)	7.9 (0.1–32.3)
Cancer type
ALL	1106 (66.3%)	0	1106 (93.6%)
LL	63 (3.8%)	11 (2.3%)	52 (4.4%)
NHL	212 (12.7%)	203 (41.7%)	9 (0.8%)
Osteosarcoma	243 (14.6%)	243 (49.9%)	0
Other	44 (2.6%)	30 (6.1%)	14 (1.2%)
Average dose for each administration in g/m2 (range)	5.0 (0.5–18.2)	11.6 (1–18.2)	4.9 (0.5–9.5)
Sex: Male	1012 (60.7%)	326 (66.9%)	686 (58.1%)
Race
Asian	71 (4.3%)	10 (2.1%)	61 (5.2%)
Black	269 (16.1%)	99 (20.3%)	170 (14.4%)
White	1126 (67.5%)	336 (69.0%)	790 (66.9%)
Other a	202 (12.1%)	42 (8.6%)	160 (13.5%)
BMI in kg/m2 (range)	19.7 (10.4–47.3)	18.9 (10–47.3)	17.6 (12–46.8)
Obese	245 (14.7%)	80 (16.4%)	165 (14.0%)
Overweight	242 (14.5%)	68 (14.0%)	174 (14.7%)
Ethnicity: Hispanic	548 (32.9%)	97 (19.9%)	451 (38.2%)
BSA in m2	1.22 (0.24–2.8)	1.49 (0.37–2.7)	0.96 (0.24–2.8)
Baseline SCR in mg/dL (range)	0.4 (0.1–1.9)	0.5 (0.1–1.5)	0.3 (0.1–1.9)
Baseline Alb in g/dL (range) b	3.8 (1.4–5.8)	3.7 (1.7–5.2)	3.8 (1.4–5.8)
Down syndrome c	63 (0.8%)	0	63 (1.4%)
Severe Hypoalbuminemia c	212 (2.8%)	69 (2.2%)	143 (3.2%)
Pleural effusion c	44 (0.5%)	24 (0.8%)	20 (0.45%)

Abbreviations: Alb, albumin; ALL, acute lymphoblastic leukemia; BMI, body mass index; BSA, body surface area; CCHMC, Cincinnati Children's Hospital Medical Center; CHOA, Children's Healthcare of Atlanta; LL, lymphoblastic lymphoma; NHL, non‐Hodgkin's lymphoma; SCR, serum creatinine; TXCH, Texas Children's Hospital.

^a Other, includes American Indian, Middle Eastern, Pacific Islander, multiple, and unknown.

^b Baseline calculated from administrations. Two hundred twenty‐five administrations were missing a baseline albumin.

^c N is administrations.

Data extraction and organization

Deidentified MTX PK, laboratory results, and demographic and clinical treatment data from 1758 patients were extracted or abstracted from the electronic health records. The database was queried using SQLite to obtain PK data relative to each HDMTX administration based on time‐date data. Baseline values (e.g., serum creatinine [SCR], weight, height, serum albumin, and body surface area [BSA]) were obtained closest but up to 7 days before the start time‐date of each HDMTX administration. Time‐varying values (e.g., SCR) were obtained by querying the database for samples collected between the start of the HDMTX administration and the last recorded MTX sample for the administration. Patient charts were reviewed manually using a priori defined algorithms to identify and grade pleural effusion based on Common Terminology Criteria for Adverse Events version 5. ⁵ , ⁶ Patient demographics and incidence of pleural effusion were maintained in a Research Electronic Data Capture (REDcap) database. ⁷ , ⁸

Methotrexate treatment and sample collection

HDMTX was administered as 3‐, 4‐, 24‐, and 36‐h infusions according to the disease and treatment protocol. Infusion durations of 8 h or less were grouped as short infusions (SIs) and infusion durations greater than 8 h were grouped as long infusions (LIs). Dosages ranged from 1 to 18 g/m² in the SI group and from 0.5 to 9.5 g/m² in the LI group. Plasma MTX concentrations were sampled up to 380 h after the start of the HDMTX infusion. MTX concentrations were collected as part of routine care, per the treatment or clinical trial protocol, which often consists of predetermined routine therapeutic drug monitoring at 24, 42, and 48 h after the start of the infusion, and every 6/12/24 h thereafter until the patient's MTX concentration reached the threshold for discharge. Additional sampling was possible at the end of the infusion for SI administrations or at the discretion of the clinical team.

Pharmacokinetic modeling

A population PK analysis of HDMTX using nonlinear mixed effects modeling was performed in NONMEM version 7.2.0 (ICON) and was interfaced with Pirana ⁹ and Perl‐Speaks‐NONMEM. ¹⁰ , ¹¹ The original MTXPK.org model used first‐order conditional estimation with interaction and a three‐compartment structural model (ADVAN11 TRANS4) that included BSA and time‐varying SCR as clinical covariates. ⁴ A log‐normal distribution was assumed for the individual PK parameters at each HDMTX administration by using an exponential model to account for the interindividual variability (IIV). The residual unexplained variability was best described using an exponential error model with the log‐transformed both sides approach. The original MTXPK.org model structure and its parameter estimates were used as a reference to estimate the PK parameters (CL, Q2, Q3, V1, V2, and V3), IIV parameters, and residual variability parameter for this new diverse dataset. Results from the initial parameterization for the PK parameters, covariates values, IIV values, and residual variability served as the initial base model for model evaluation. The model‐building process was assessed using the objective function value (OFV). Diagnostic plots included conditional weighted residuals (CWRES) versus time, CWRES versus model‐predicted population concentration (PRED), observation versus PRED, and observation versus model‐predicted individual concentration (IPRED), and visual predictive checks (VPCs).

Covariate analysis

Intrinsic and extrinsic factors of variability were evaluated as potential covariates on the base model. Intrinsic factors include albumin, age, body mass index (BMI), cancer type, administration number, presence of Down syndrome, self‐reported ethnicity, self‐reported race, sex, and presence of pleural effusion. Height and weight queried from the database were used to calculate the BSA (Mosteller equation). BMI was calculated using the Centers for Disease Control and Prevention's (CDC) equation. BMI percentiles and categories for pediatric patients (ages 2–20 years old) were generated using the R package, PAutilities. ¹² Adult patients were categorized following the CDC's definitions for overweight (25 ≤ BMI < 30) and obese (BMI ≥30). Between‐occasion variability was not parameterized; each administration of HDMTX was treated as an independent event, which is consistent with our previous HDMTX model. ⁴ Extrinsic factors include infusion duration and part of the day (morning, afternoon, evening, and night) when the MTX infusion started. Covariate effects of continuous variables were parameterized with a power model and centered to the population's median value (Equation 1). Continuous variables were also analyzed as categorical variables (Equation 2), where categories were developed in collaboration with the clinical team to ensure clinical relevance. Correlation among individual variables was assessed to avoid collinearity. Intrinsic and extrinsic factors were added in a forward stepwise approach. Individual covariates were added in a forward stepwise approach if the covariate reached the statistical significance criteria of p < 0.01 (a reduction of OFV by at least 6.63 with 1 degree of freedom and a reduction of OFV by at least 9.21 with 2 degrees of freedom), decreased the IIV for CL, and if the magnitude of effect was at least 5% of the parameter estimate.

Continuous variable:

$${\theta }_{i,j}={\theta }_{\mathrm{pop}}*{\left(\frac{{\mathrm{COV}}_i}{{\mathrm{COV}}_{\mathrm{pop}}}\right)}^{{\mathrm{Cov}}_{\theta }}*e^{{\eta }_{{\theta }_i}+{\kappa }_{{\theta }_i,j}}$$ (1)

COV _i value of the continuous variable for the ith subject; ${\mathrm{COV}}_{\mathrm{pop}}$, Population median value (centering); ${\mathrm{Cov}}_{\theta }$: Covariate effect on $\theta .$

Categorical variable

$${\theta }_{i,j}={\theta }_{\mathrm{pop}}*{{\text{Category}}_{\theta }}^{{\mathrm{CAT}}_i}*e^{{\eta }_{{\theta }_i}+{\kappa }_{{\theta }_i,j}}$$ (2)

${\text{Category}}_{\theta }$: Covariate effect for a given subcategory; ${\mathrm{CAT}}_i$: Value of 1 or 0 if the ith subject is associated with the subcategory.

Modeling requirements

Standard inputs for population PK (PopPK) modeling for an intravenously administered agent include the patient ID, dose, time of administration, duration or infusion rate, time of sample collection, and drug concentrations. In addition to these standard inputs, the original model for the MTXPK.org webtool includes BSA and SCR as clinical covariates. For a patient to be included in the PopPK analysis, the patient was required to have these standard inputs plus administration‐specific BSA, baseline SCR, and time‐varying SCR because the original model structure was being referenced. When neither height nor weight were reported for that MTX administration, but available for that patient's other administrations, a mean BSA was imputed for the missing administration. The administration was excluded if no imputation was possible (i.e., no height or weight record was recorded for that patient). If a baseline SCR was not available, then the definition of baseline was shifted to include the first sample collected during the infusion. Time‐varying SCR is often collected concurrently with MTX collection times. If the concurrent collection was not available, then imputation was performed for intermediate missing data using the average between previous and posterior values or directly imputing from the nearest reported SCR value (if the previous or posterior value was missing). SCR concentrations below the limit of quantitation were handled as non‐zero values by subtracting 0.01 from the reported lower limit. Baseline albumin was an additional intrinsic factor investigated in this analysis. The parameterization of albumin was dichotomized to quantify the effects of severe hypoalbuminemia (albumin <2.5 g/dL) on MTX PKs and was done so based on feedback from our clinical colleagues. Clinical adjustments to the HDMTX treatment protocol are considered if the patient has severe hypoalbuminemia prior to the start of an HDMTX infusion. If baseline albumin was not available, then it was imputed to a normal value of 3.5 g/dL.

Dosing strategies and model simulation

The individual model predicted concentrations at 24, 36, 42, 48, 60, and 72 h after the start of the MTX infusion were generated via NONMEM. The mean and two SDs were calculated for current dosing strategies used for the treatment of ALL, osteosarcoma, and NHL.

Software and statistics

PK data obtained from the electronic health records were maintained and queried using SQLite version 3.35.5. PopPK modeling was completed using NONMEM version 7.2.0 (ICON), which was interfaced with Pirana (version 3.0.0) and Perl‐speaks‐NONMEM (version 5.3.0). GraphPad Prism 9.5.0, RStudio version 2022.12.0 + 353, and R 4.2.2 were used to perform statistical tests, generate model statistics, and graph figures. Nonparametric statistical tests were used to compare the differences between the estimated CL or MTX concentrations between different groups. Kruskal‐Wallis analysis of variance (ANOVA) was used for a variable with at least three levels. Dunn's multiple comparisons test was used to compare groups following a statistically significant ANOVA. Mann–Whitney tests were used for a variable with two levels. A p value less than 0.05 was considered statistically significant for comparative analyses.

RESULTS

Overview of the cohort

A total of 1758 patients and 8105 HDMTX administrations were identified during this treatment period. There were 90 (5.1%) patients and 599 (7.4%) HDMTX administrations excluded because they lacked data outlined in the Modeling Requirements section (Figure S1), resulting in a final count of 1668 patients, 7506 HDMTX administrations, and 30,984 concentrations queried from the database. An additional 734 concentrations from 31 administrations were excluded from the PopPK modeling because the samples were collected following the administration of glucarpidase and analyzed by enzyme immunoassays, which cannot differentiate between MTX and DAMPA. Samples collected prior to the administration of glucarpidase were included in the PopPK modeling. The demographics for the modeled population can be found in Table 1.

This dataset comprises a population that had 2445 (32.6%) administrations in non‐White patients, 2210 (29.4%) administrations in Hispanic/Latino patients, and 3363 (44.8%) administrations in non‐ALL patients, which is more diverse compared to the prior analysis of a Nordic pediatric population will ALL that was used to develop the MTXPK.org model. ⁴ Seventeen (1%) patients in the cohort had Down syndrome, all of whom were being treated for ALL. Severe hypoalbuminemia, defined as albumin less than 2.5 g/dL, was considered a clinically meaningful cutoff and was reported in 212 (2%) administrations. Pleural effusion was documented in 44 (0.5%) administrations with similar frequency across infusion durations.

Population PK model development

Description of the data using the new PK parameter estimates with BSA and time‐varying SCR generates a base model OFV of −1831.6 (Table S1). An initial review of the data revealed significant variability in CL estimates (L/h/1.73 m²) across the three medical centers and cancer types (Table S2). Self‐reported race and ethnicity were not uniformly distributed across the three medical centers, where 400 (73%) of the 548 patients who self‐reported as Hispanic/Latino were from TXCH, and 170 (63%) of the 269 patients who self‐reported as Black were from CHOA. Self‐reported race and ethnicity were not associated with initial CL (L/h/1.73 m²) estimates when compared within each institution (Figures S2 and S3). To ensure that additional covariate relationships were not confounded by the treatment location, we explored the inclusion of a categorical “Site of Treatment” parameter to normalize the CLs at CHOA and TXCH to CCHMC. Parameterization of both CHOA and TXCH significantly improved the model's description of the data (ΔOFV = −806.66; Table S2) and served as the new base model's adjusted OFV for subsequent model evaluation.

Covariate modeling

Exploratory analyses investigated the effects of the intrinsic and extrinsic factors of variability on MTX CL and volume of distribution. These analyses identified sex (male), race (Asian, Black), infusion duration (short), cancer type (osteosarcoma), albumin (severe hypoalbuminemia, albumin <2.5 g/dL), pleural effusion, and Down syndrome may be associated with MTX PKs and warranted covariate parameterization. The underlying mechanism for differences between cancer types is likely driven by the effects of infusion duration, supportive care, prior therapies, and the treatment protocol (Table S2). Patients with lymphoblastic lymphoma and NHL had both SI and LI protocols; therefore, infusion duration was selected as the studied variable. The complete forward stepwise inclusion of covariates is presented in Table S1. Parameterization of infusion duration on CL, hypoalbuminemia on the intercompartmental CL, presence of Down syndrome on CL, and pleural effusion on the volume of distribution significantly improved the model's description of the data, with a final OFV of −2825.89 (ΔOFV = −187.59, compared to the adjusted base model). Visual assessment of the GOF plots (Figure 1) and the prediction‐corrected VPC (Figure 2) suggests that the model describes this diverse patient dataset adequately. Final model estimates for this model are available in Table 2 and parameters with updated equations are listed below.

FIGURE 1.

Goodness‐of‐fit plots for the final model on the diverse patient data from Cincinnati Children's Hospital Medical Center, Children's Healthcare of Atlanta, and Texas Children's Hospital. Top left, individual predicted concentration versus the observed methotrexate (MTX) concentration. Top right, population predicted concentration versus the observed MTX concentration. Lower left, conditional weighted residual (CWRES) versus the time after start of MTX infusion. Lower right, the CWRES versus the population predicted concentration. Diagonal line in top graphs represent the line of identity. The red line displays the trend for the data. Dotted lines in lower graphs represent the ±2 CWRES. Solid lines in lower graphs represent the ±5 CWRES.

FIGURE 2.

Prediction‐corrected visual predictive check for the final model on the diverse patient data from Cincinnati Children's Hospital Medical Center, Children's Healthcare of Atlanta, and Texas Children's Hospital. Methotrexate (MTX) concentrations are represented by the blue circles. The solid red line represents the median MTX concentration for the simulation. The red dashed lines represent the 5th and 95th percentiles for the simulated data. The red shaded region is the median prediction interval. The blue shaded region are the 5% and 95% confidence intervals for the prediction. The deviation of the median prediction interval from the median observed results from delayed MTX elimination, which is often defined as MTX greater than 0.2 μmol/L at 72 h for short infusions and MTX greater than 0.2 μmol/L at 96 h for long infusions. Clinically, MTX measurements cease after it reaching 0.1 μmol/L. As many patients are below this threshold by 96 h, the data for the patients under the median is missing, thus the measured median and the predicted median are different.

TABLE 2.

Parameter estimates for final model.

Parameter	Value	Relative standard error (%)
Clearance (L/h/1.73 m2)	8.24	1.4
Serum creatinine	−0.26	3.5
Short infusion	1.05	0.8
Down syndrome	0.84	3.2
V1 (L/1.73 m2)	22.1	2.2
Pleural effusion	1.06	9.0
Q2 (L/h/1.73 m2)	0.225	3.0
Hypoalbuminemia	1.17	9.4
V2 (L/1.73 m2)	2.19	2.5
Pleural effusion	1.43	14.9
Q3 (L/h/1.73 m2)	0.0342	8.9
Hypoalbuminemia	1.34	7
V3 (L/1.73 m2)	6.07	21.3

Abbreviations: Q2, intercompartmental clearance between V1 and V2; Q3, intercompartmental clearance between V2 and V3; V1, volume of distribution for central compartment; V2, volume of distribution for peripheral compartment 2; V3, volume of distribution for tertiary compartment 3.

Clearance

$$\begin{array}{c}{\mathrm{CL}}_i=8.24*\left(\frac{{\mathrm{BSA}}_i}{1.73}\right)*{\left(\frac{{\mathrm{SCR}}_i}{40}\right)}^{-0.26}\hfill \\ *{1.05}^{\text{Short Infusion}}*{0.83}^{\text{Down syndrome}}\hfill \end{array}$$ (3)

Central volume of distribution, V ₁

$$V_{1i}=22.1*\left(\frac{{\mathrm{BSA}}_i}{1.73}\right)*{1.06}^{\text{Pleural Effusion}}$$ (4)

Intercompartmental CL, Q₂

$$Q_{2i}=0.225*\left(\frac{{\mathrm{BSA}}_i}{1.73}\right)*{1.17}^{\text{Hypoalbuminemia}}$$ (5)

Peripheral volume of distribution, V ₂

$$V_{2i}=2.19*\left(\frac{{\mathrm{BSA}}_i}{1.73}\right)*{1.43}^{\text{Pleural Effusion}}$$ (6)

Intercompartmental CL, Q ₃

$$Q_{3i}=0.0342*\left(\frac{{\mathrm{BSA}}_i}{1.73}\right)*{1.34}^{\text{Hypoalbuminemia}}$$ (7)

Impact of covariates on HDMTX clearance

The impact of clinical and demographic variables on the final model estimated MTX CL was investigated in both LI (Table 3) and SI (Table 4) cohorts. For LI, results revealed the statistically significant effects of categorical age on MTX CL estimates despite the model's inclusion of both BSA and SCR. The AYA population was found to have a faster MTX CL (CL = 8.65 L/h/1.73 m²) compared to pediatric patients (CL = 8.37 L/h/1.73 m², p < 0.0001). Other statistical findings demonstrated a slower clearance for the first administration number (CL = 8.36 L/h/1.73 m² vs. CL = 8.42 L/h/1.73 m², p = 0.046), altered clearance by part of the day (p < 0.0001), and faster clearance for self‐reported race as Black (CL = 8.56 L/h/1.73 m²) compared to self‐reported race as White (CL = 8.38 L/h/1.73 m², p = 0.03); however, it is unlikely that these statistical differences would have significant clinical effects. Conversely, the presence of Down syndrome and pleural effusion were associated with significantly slower clearances (p < 0.0001, p = 0.013; respectively) and would be expected to have clinical implications. Additionally, the inclusion of these variables in the model significantly improved the model's description of the data and is why these variables will be added to the MTXPK.org equation.

TABLE 3.

Impact of variables on final methotrexate clearance estimates in long infusion administrations, N = 4419.

Variables	Total administrations		Clearance (L/h/1.73 m2)
	N	%	Median	p value
Albumin (g/dL)				0.23
>2.6	4276	96.8	8.41
≤2.5	143	3.2	8.39
Age, years
≤2	307	6.9	8.23	0.11
2–15	3419	77.4	8.37	Ref.
>15	693	15.7	8.65	< 0.0001
Admin. number				0.046
1	1156	26.2	8.36
≥2	3263	73.8	8.42
BMI
Healthy	2507	56.7	8.42	Ref.
Overweight	704	15.9	8.38	0.89
Obese	658	14.9	8.53	0.16
Down syndrome a				< 0.0001
Yes	63	1.4	7.15
No	4356	98.6	8.40
Ethnicity				0.41
Hispanic	1661	37.6	8.37
Not Hispanic	2758	62.4	8.43
Part of the day				< 0.0001
Morning	203	4.6	8.31
Afternoon	1187	26.8	8.67
Evening	1161	26.3	8.47
Night	1868	42.3	8.19
Pleural effusion				0.013
Yes	20	0.4	7.84
No	4373	99.6	8.41
Race
White	2980	67.4	8.38	Ref.
Black	646	14.6	8.56	0.003
Other b	793	18.0	8.37	> 0.999
Sex				0.85
Male	2542	57.5	8.41
Female	1877	42.5	8.41

Note: A variable with two groups was analyzed using a Mann–Whitney test. A variable with three or more groups was analyzed using a Kruskal‐Wallis test followed by a Dunn's Multiple Comparisons test to the reference group. A statistically significant p‐value is shown in bold.

Abbreviations: BMI, body mass index; N, number of administrations; Ref., reference group in analysis; %, percentage of total administrations.

Morning was defined as 05:00–12:00; afternoon was 12:00–17:00; evening was 17:00–21:00; and night was 21:00–05:00.

^a Estimated clearance values are prior to NONMEM parameterization.

^b Other, includes American Indian, Asian, Middle Eastern, Pacific Islander, Multiple selected, and did not disclose.

TABLE 4.

Impact of variables on final methotrexate clearance estimates in short infusion administrations, N = 3087.

Variables	Total administrations		Clearance (L/h/1.73 m2)
	N	%	Median	p value
Albumin (g/dL)				0.35
>2.6	3018	97.8	8.33
≤2.5	69	2.2	8.49
Age, years
≤2	37	1.2	7.84	0.01
2–15	1908	61.8	8.37	Ref.
>15	1142	37.0	8.29	0.69
Admin. number				< 0.0001
1	479	15.5	8.17
≥2	2608	84.5	8.37
BMI
Healthy	1815	58.8	8.38	Ref.
Overweight	396	12.8	8.41	0.42
Obese	461	14.9	8.29	0.81
Ethnicity				< 0.0001
Hispanic	549	17.8	8.66
Not Hispanic	2538	82.2	8.27
Part of the day				0.018
Morning	180	5.8	8.29
Afternoon	558	18.1	8.44
Evening	1133	36.7	8.31
Night	1216	39.4	8.31
Pleural effusion				0.013
Yes	24	0.8	8.48
No	3059	99.2	8.33
Race
White	2082	67.4	8.30	Ref.
Black	694	22.5	8.34	0.49
Other a	311	10.1	8.61	< 0.0001
Sex				< 0.0001
Male	1980	64.1	8.43
Female	1107	35.9	8.20

Note: A variable with two groups was analyzed using a Mann–Whitney test. A variable with three or more groups was analyzed using a Kruskal‐Wallis test followed by a Dunn's Multiple Comparisons test to the reference group. A statistically significant p‐value is shown in bold.

Abbreviations: BMI, body mass index; N, number of administrations; %, percentage of total administrations.

Morning was defined as 05:00–12:00; afternoon was 12:00–17:00; evening was 17:00–21:00; and night was 21:00–05:00.

^a Other, includes American Indian, Asian, Middle Eastern, Pacific Islander, Multiple selected, and did not disclose.

Analysis of the SI data revealed several statistical findings with differences in estimated CL less than 5%. However, infants treated with SI protocols displayed slower MTX CL (CL = 7.84 L/h/1.73 m²) when compared to pediatric patients (CL = 8.37 L/h/1.73 m², p = 0.01). However, these findings likely reflect the effect of cancer type and treatment protocol rather than a true reduction in CL.

Simulated MTX concentrations following current dosing strategies

The mean and two SD from the model predicted concentrations at 24, 36, 42, 48, 60, and 72 h after the start of the HDMTX infusion are reported for current dosing strategies used for the treatments of ALL, osteosarcoma, and NHL (Table 5). Importantly, the two SDs above each of the means at the 24‐, 36‐, 42‐, and 48‐h timepoints provides concentrations that are much lower than the concentrations at corresponding timepoints in the current glucarpidase consensus guideline, ² which are defined as greater than 120 μM (>50 μM for SI) at 24‐h, greater than 30 μM at 36‐h, greater than 10 μM at 42‐h, and greater than or equal to 5 μM at 48‐h.

TABLE 5.

Simulated MTX concentrations following current dosing strategies.

Dosing strategy	Total administrations		24‐h (μM)		36‐h (μM)		42‐h (μM)		48‐h (μM)		60‐h (μM)		72‐h (μM)
	N	%	Mean	2SD	Mean	2SD	Mean	2SD	Mean	2SD	Mean	2SD	Mean	2SD
All
5 g/m2 over 24 h	3193	42.5	84.8	127.3	2.46	10.08	0.96	5.34	0.48	2.63	0.19	1.07	0.09	0.54
1 g/m2 over 36 h	100	1.3	10.15	14.5	10.08	14.44	1.15	2.87	0.26	0.75	0.05	0.14	0.02	0.06
Lymphoma
3 g/m2 over 3 h	644	8.6	1.08	6.30	0.31	1.71	0.19	1.02	0.13	0.68	0.07	0.37	0.05	0.24
8 g/m2 over 4 h	127	1.7	2.87	14.11	0.76	3.49	0.45	1.97	0.29	1.20	0.14	0.55	0.09	0.31
Osteosarcoma
12 g/m2 over 4 h	1128	15.0	5.71	17.67	1.21	3.94	0.66	2.19	0.39	1.31	0.18	0.59	0.12	0.33
10 g/m2 over 4 h	151	2.0	7.64	20.86	1.45	4.26	0.75	2.21	0.42	1.24	0.19	0.50	0.12	0.27

Abbreviations: 2SD, two standard deviations above the mean; %, percentage of total administrations; ALL, acute lymphoblastic leukemia; g/m², grams per squared meter; MTX, methotrexate; N, number of administrations.

DISCUSSION

The purpose of this project was to describe the PKs of HDMTX from a diverse patient population (e.g., races, ethnicity, indications for MTX, and variable infusion durations) and identify meaningful factors that account for MTX variability and improve the model's performance. Although the MTXPK.org model adequately describes HDMTX PK data, ⁴ we sought to explore the many intrinsic and extrinsic factors available to us in these 1668 demographically and clinically diverse patients that were not available in the previous dataset. Using these data, we were able to (1) quantify the impact of infusion duration, Down syndrome, pleural effusion, and severe hypoalbuminemia on MTX PKs; (2) identify populations of interest for further investigations; and (3) provide concentration‐time profiles from real patient data for several common dosing strategies used to treat ALL, NHL, and osteosarcoma.

Our covariate modeling parameterized infusion duration, severe hypoalbuminemia, Down syndrome, and pleural effusion on MTX PKs. Depending on the cancer type and treatment protocol, HDMTX will either be administered as SI (3–8 h) or a LI (24 or 36 h). The original pediatric cohort used to develop the MTXPK.org model consisted of only LI treatment protocols for treating ALL, so it was unable to estimate the effect of infusion duration on MTX PKs. However, external validation using SI treatment protocols supported the original model's use in this population and was therefore incorporated into the MTXPK.org webtool. The current dataset provided 487 patients, 3087 administrations, and 11,883 concentrations from SI treatment protocols that enabled parameterization of SI on MTX PKs (Table 1). The parameterization for SI on clearance results in an estimated 5% faster MTX CL (L/h/1.73 m²) compared to LI CL estimates (Table 2) and is similar to the previously reported value from the Guardian Research Network. ¹³ Although this estimate is less than the previously reported between‐occasion variability of 20%, ¹⁴ , ¹⁵ the inclusion of the SI parameterization improves the model's description of the data and will further improve MTXPK.org's ability to accurately forecast MTX concentrations in patients receiving SI treatment protocols.

Severe hypoalbuminemia (albumin <2.5 g/dL) was also identified as an important variable on MTX PKs. Albumin is a circulating protein found in the plasma and has a reference range of 3.5 to 5 g/dL in a healthy human subject. ¹⁶ Circulating MTX is 50%–60% bound to albumin, ¹⁷ which suggests that a decrease in serum albumin would increase the amount of free (unbound) MTX. Several reports have linked the effects of albumin and hypoalbuminemia to altered MTX PKs. ¹³ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ Mainly, these reports support the reduction of MTX CL with decreasing albumin. Our parameterization for severe hypoalbuminemia on MTX CL resulted in an estimated ~2% reduction in MTX clearance (Table S1), and did not significantly improve the description of the data. Investigation of severe hypoalbuminemia on MTX CL did not reveal a significant reduction to MTX clearance in our LI or SI cohorts (Tables 3 and 4). However, these clearance estimates were generated using the final model, which includes the parameterization of severe hypoalbuminemia on intercompartmental clearance. Results found considerable increases in the estimated intercompartmental clearance for both the Q ₂ and Q ₃ for patients with severe hypoalbuminemia (Table 2). This parameterization is recapitulated by the pathophysiology of severe hypoalbuminemia. A lack of circulating albumin increases the amount of free (unbound) MTX, which would increase its availability to diffuse into peripheral compartments (i.e., the liver, target tissues, or less vascular tissues). This would then generate faster k ₁₂ or k ₁₃ values but unaltered k ₂₁ or k ₃₁ values, yielding faster intercompartmental clearance. Nonetheless, parameterization of severe hypoalbuminemia on intercompartmental clearance improves the model's description of the data (Table S1) and will enable MTXPK.org to adequately describe patients with severe hypoalbuminemia.

Our data also supported the novel parameterization of Down syndrome on clearance. Down syndrome is a congenital chromosome abnormality that has an estimated 30× greater risk of developing ALL, and comprises 5% of the pediatric patients with ALL. ²² , ²³ Patients with Down syndrome are at a greater risk for toxicity, ²⁴ which has led to protocols using a lower dose of MTX in this population. ²² Prior work on the effect of Down syndrome on MTX CL determined that patients with Down syndrome demonstrate a 20% slower CL compared to patients without Down syndrome, ²⁵ which can be attributed to the additional copy of the reduced folate carrier 1 found on chromosome 21. To the author's knowledge, this is the first parameterization of Down syndrome on MTX CL using a PopPK approach. The parameterization of Down syndrome on clearance results in an estimated decrease in MTX clearance by 17% (Table 3 , Table S1), which is consistent with these prior findings. The inclusion of Down syndrome improves the model's description of the data (Table S1) and enables MTXPK.org the ability to adjust the Bayesian forecasted concentrations based on the presence of Down syndrome.

Similarly, the data also supported the novel parameterization of pleural effusion on volume of distribution. Pleural effusion is the accumulation of fluid in between the parietal and visceral pleura, called the pleural cavity, and is normally around 0.1 to 0.3 mL/kg. ²⁶ During the presence of a pleural effusion, the fluid volume in the pleural cavity increases, creating a third space effect, ²⁶ which increases the fluid volume for a patient. There has been limited work investigating the impact of pleural effusion on HDMTX PKs. ²⁶ , ²⁷ A previous study showed that the presence of pleural effusion during HDMTX treatment results in elongated half‐life and slowed intercompartment distribution rate constants. ²⁷ Parameterization of pleural effusion demonstrates the increase in estimated volume of distribution in both V ₁ and V ₂ compared to patients without pleural effusion (Table 2). These increases are consistent with the pathophysiology of pleural effusion and further improve the model's ability to describe diverse patient populations and facilitate model‐informed supportive care and glucarpidase use upon implementation into the MTXPK.org webtool.

In addition to these parameterizations, we investigated the effects of age, administration number, BMI, ethnicity, part of the day, race, and sex on MTX CL in our LI (Table 3) and SI (Table 4) cohorts. Our data shows that the first administration of HDMTX is associated with statistically slower MTX CL for both LI and SI, which is consistent with previous findings. ¹ Whereas this difference is statistically significant, the difference is marginal and is unlikely to impact clinical outcomes. However, it has been hypothesized that the induction therapy for ALL consists of many immunomodulating agents that can increase the risk for prior infection. ²⁸ , ²⁹ Subsequently, the effects of infection and prior antibiotic use augments the clearance of MTX during these first administrations, through the likely mechanisms of altered albumin and impaired renal function, ²⁸ , ³⁰ which increases the frequency of glucarpidase use. ³⁰ Another interesting variable to note was the part of the day that corresponded to the start of the HDMTX administration. This is a statistical finding that has many factors that could confound these results, but it is interesting to note that the morning (05:00–12:00) and night administrations (21:00–05:00) in the LI cohort were associated with slower MTX clearance compared to the afternoon (12:00–17:00) and evening (17:00–21:00) administrations (Table 3). These results are consistent with the circadian effects on metabolic activity and renal function. ³¹ , ³² On the contrary, a previous study that investigated the effects of circadian rhythm on 400 mg/m² of MTX over 30 min in NHL found no significant difference between an 06:00 and 18:00 administration. ³³

Last, using real patient data, we compiled the mean model predicted concentration and two SDs above the mean for MTX concentrations at 24, 36, 42, 48, 60, and 72 h after the start of MTX infusion for common dosing strategies used to treat ALL, NHL, and osteosarcoma (Table 5). This table serves as a reference guide for “normal” MTX concentrations at static timepoints in lieu of using the MTXPK.org webtool. Future investigations will determine the concentration thresholds associated with MTX‐induced toxicities following common dosing strategies.

Although this collaboration yielded the largest patient database for HDMTX PK, there is still PK variability that we were not able to explain. The parameterization of TXCH and CHOA was not anticipated during the initial data analysis plan; these findings were identified during data exploration prior to the covariate model building process. Initially, the effects of TXCH and CHOA were believed to be driven by the increase in patient diversity, with more Hispanic patients at TXCH and non‐White patients at CHOA. Preliminary findings revealed that neither self‐reported ethnicity nor race affected MTX CL at either site of treatment (Figures S1 and S2). Given the large number of treatment protocols used across all three sites, it was not feasible to parameterize the protocol number. In response to this finding, there are ongoing efforts to confirm the amounts and rates of fluid hydration and sodium bicarbonate that patients received, as these have been shown to alter MTX clearance. ³⁴ , ³⁵ , ³⁶ Genotype data are also being acquired and future studies will investigate the effects of known polymorphisms on MTX CL. ³⁷

With these novel parameterizations, the perceived generalizability of the MTXPK.org model will be increased now that it can describe more diverse patient data, and continue to facilitate model‐informed supportive care and glucarpidase use across all ages, races, ethnicities, treatment protocols, and malignancies.

AUTHOR CONTRIBUTIONS

Z.L.T., T.P.M., E.A.P., N.P.D., L.P., S.G.B., N.A., M.B.B., E.S.S., M.M.O., S.M.C., and L.B.R. wrote the manuscript. T.P.M., S.M.C., M.B.B., E.S.S., M.M.O., and L.B.R. designed the research. Z.L.T., E.A.P., S.G.B., N.A., T.P.M., N.P.D., O.A., N.U., V.J., M.B.B., and A.C. performed the research. Z.L.T., T.P.M., N.P.D., M.B.B., and L.B.R. analyzed the data.

FUNDING INFORMATION

Z.L.T. was supported by the National Institute of Child Health and Development T32 Cincinnati Pediatric Clinical Pharmacology Training Program (T32HD069054) during the analysis for this manuscript. L.B.R. received research funding for this study from BTG International. M.B.B. was supported by the National Cancer Institute (K08 CA263482). The funders had no role in the design, collection, analysis, or publication of this manuscript.

CONFLICT OF INTEREST STATEMENT

L.B.R. consulted for and received research funding from BTG, International. M.M.O. received honoraria from Pfizer, consulted for Jazz Pharmaceuticals, and research funding from AbbVie, Amgen, and Pfizer. M.B.B. has received compensation as a member of a scientific advisory board for BTG, International, research funding from Bristol Myers Squibb, Celgene, and consulted for Jazz Pharmaceuticals. T.P.M. has stock and other ownership interests in AbbVie, Gilead Sciences, Thermo Fisher Scientific, and United Health Group. All other authors declared no competing interests for this work.

Supporting information

Figures S1–S3

Tables S1‐S2

Taylor ZL, Miller TP, Poweleit EA, et al. Clinical covariates that improve the description of high dose methotrexate pharmacokinetics in a diverse population to inform MTXPK.org. Clin Transl Sci. 2023;16:2130‐2143. doi: 10.1111/cts.13600