Development of a population pharmacokinetic model using combined paediatric and adult data for four pulmonary arterial hypertension drugs

Abstract

Aims

Pulmonary arterial hypertension (PAH) is a syndrome characterized by elevated pulmonary artery pressure. We developed a population pharmacokinetic (PPK) model using combined plasma drug concentration data from Japanese paediatric (<15 years) and adult (≥15 years) patients with PAH to investigate the pharmacokinetic characteristics of PAH treatments (sildenafil, tadalafil, bosentan and ambrisentan).

Methods

PPK analysis was conducted using a nonlinear mixed‐effects modelling approach. A one‐compartment model was selected as the structural model, and an exponential error model was used to describe interindividual variability. Individual patient clearance (CL), adjusted for bioavailability (F) using Bayesian estimation based on the PPK model, was used to estimate the steady‐state plasma concentrations (C_ss) of the drugs in paediatric and adult patients receiving clinical dosages.

Results

PPK analysis was performed on data from 35 paediatric and 16 adult subjects to estimate pharmacokinetic parameters. The population mean CL/F values for sildenafil, tadalafil, bosentan and ambrisentan were estimated at 60.6, 1.76, 8.85 and 0.594 L/h, respectively. Covariates that improved model performance and were incorporated into the final model included the effect of bodyweight on the CL/F of each drug. The estimated C_ss values for all drugs were 26.0%–72.2% lower in paediatric than in adult patients.

Conclusions

This study clarified the pharmacokinetic parameters and their variability for sildenafil, tadalafil, bosentan and ambrisentan using combined data from Japanese paediatric and adult patients with PAH. The results of Bayesian estimation suggest that at current clinical dosages, plasma concentrations of these drugs may be lower in paediatric than adult patients.

What is already known about this subject

• Initial combination therapy with phosphodiesterase‐5 inhibitors and endothelin receptor antagonists is currently recommended for pulmonary arterial hypertension, improving clinical outcomes and increasing 5‐year survival rates from 34.0% to 55.2%.

• Most population pharmacokinetic studies rely on clinical trial data or focus on adult patients receiving a single treatment.

What this study adds

• A population pharmacokinetic model for sildenafil, tadalafil, bosentan and ambrisentan was developed using real‐world data from both paediatric and adult patients with pulmonary arterial hypertension.

• Bayesian estimation indicates that drug exposure in paediatric patients is lower than in adults at current clinical dosing levels.

1. INTRODUCTION

Pulmonary arterial hypertension (PAH) is a chronic and progressive disease characterized by elevated pulmonary arterial pressure and pulmonary vascular resistance, ultimately leading to right‐sided heart failure and death. ¹ PAH occurs across a broad age range from childhood to old age, resulting in considerable variability in the age distribution of patients. The aetiology of PAH is multifactorial and is thought to involve vascular pathologies associated with endothelial dysfunction, including dysregulation of key signalling pathways such as the nitric oxide–soluble guanylate cyclase–cyclic guanosine monophosphate (NO–sGC–cGMP) pathway, the endothelin pathway and the prostacyclin pathway. ² , ³ , ⁴

Current treatment of PAH includes the use of phosphodiesterase‐5 (PDE‐5) inhibitors, soluble guanylate cyclase stimulators, endothelin receptor antagonists, prostacyclin analogues and prostacyclin receptor agonists, all of which are approved for clinical use. In recent years, combination therapy involving PDE‐5 inhibitors and endothelin receptor antagonists has been recommended. ¹ The development of PAH therapies, including the adoption of initial combination therapy, has led to improved patient outcomes, with 5‐year survival rates increasing from 34.0% in the 1980s to 55.2% in recent reports. ⁵ , ⁶

Although several clinical outcomes of PAH drug therapy have been reported, there are limited data on the pharmacokinetic characteristics of these drugs in real‐world patients with PAH, particularly within paediatric populations. One reason for this scarcity of data is that PAH is a rare disease.

The population pharmacokinetic (PPK) approach is a powerful tool for analysing sparse data, identifying factors that influence drug pharmacokinetics and estimating variability. This approach is particularly useful for studying patients who have difficulty providing frequent blood samples, such as paediatric patients, or for research involving limited case numbers, as is common with rare diseases. It is considered valuable for analysing pharmacokinetics in patients with PAH. Indeed, several PPK analyses have been conducted for various PAH treatments. ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ However, many of these reports analyse clinical trial data or focus on adult patients, typically investigating a single PAH treatment. In real‐world clinical settings, performing multiple blood samplings in paediatric patients to evaluate pharmacokinetics is impractical, and there have been few PPK analyses based solely on paediatric data.

In this study, we considered developing a PPK model that integrates data from both paediatric and adult patients. To date, there have been no reports of simultaneous PPK analyses covering all four PAH treatments, nor any analyses combining data from both paediatric and adult populations. This study aimed to develop a PPK model using combined plasma drug concentration data from Japanese paediatric and adult patients with PAH, with the goal of elucidating the pharmacokinetic characteristics of PDE‐5 inhibitors (sildenafil and tadalafil) and endothelin receptor antagonists (bosentan and ambrisentan) in real‐world clinical settings.

2. MATERIALS AND METHODS

2.1. Clinical study

2.1.1. Subjects

The data used for the analysis in this study were collected from patients treated with sildenafil, tadalafil, bosentan or ambrisentan in real‐world clinical settings. Patients receiving PDE‐5 inhibitors (sildenafil and tadalafil) or endothelin receptor antagonists (bosentan and ambrisentan), either as monotherapy or in combination, at Hamamatsu University Hospital (Hamamatsu, Japan) or Seirei Hamamatsu Hospital (Hamamatsu, Japan) were included in the analysis. Medications were prescribed and testing was conducted in accordance with standard medical practice, which was not altered for the purposes of this study. Some of the plasma drug concentration data used in this analysis have been published previously. ¹² , ¹³ In the referenced clinical studies, sildenafil was co‐administered with bosentan for more than 1 year ¹² and with bosentan or ambrisentan for at least 4 weeks before pharmacokinetic evaluation. ¹³ In both studies, pharmacokinetic sampling was performed under steady‐state conditions. These studies were registered with the University Hospital Medical Information Network (UMIN) Clinical Trial Registry (UMIN IDs: 000022593, 000002566 and 000005464). This study was approved by the Ethics Committees of the University of Shizuoka (approval no. 5‐40), Hamamatsu University School of Medicine (approval no. 15‐074) and Seirei Hamamatsu Hospital, Japan (approval no. 2290). All participants provided written informed consent prior to participation.

2.1.2. Collection of analysis data

Plasma drug concentrations of sildenafil, tadalafil, bosentan and ambrisentan were determined using the method described by Tanaka et al. ¹⁴ Patient data were collected, including age, weight, sex, N‐terminal pro‐brain natriuretic peptide, serum creatinine, aspartate aminotransferase and alanine aminotransferase (ALT) levels. Concomitant medications were reviewed using information from medical records and the hospital's medical computer system.

2.2. PPK modelling

2.2.1. PPK model development

PPK analysis was conducted using the nonlinear mixed‐effects modelling programme NONMEM version 7.4.3 (ICON plc, Dublin, Ireland). The NONMEM analyses were performed using the first‐order conditional estimation method with interaction. A one‐compartment model with first‐order absorption and elimination was evaluated to identify the most appropriate structural model for describing the concentration–time data of sildenafil, tadalafil, bosentan and ambrisentan. Interindividual variability of pharmacokinetic parameters in the model was described using an exponential error model, in which the random effects were assumed to follow a normal distribution with a mean of 0 and variance of ω ². Intraindividual variability was estimated using a proportional error model. Candidate covariates included age, weight, sex, N‐terminal pro‐brain natriuretic peptide, creatinine, aspartate aminotransferase and ALT, as well as the presence or absence of sildenafil, tadalafil, bosentan, ambrisentan, beraprost, furosemide, spironolactone and warfarin. Stepwise covariate modelling was used for covariate exploration, along with prediction‐corrected visual predictive check (pc‐VPC) and bootstrap analysis. Perl‐speaks‐NONMEM version 5.2.6 was used to perform the stepwise covariate modelling, pc‐VPC and bootstrap analyses.

2.2.2. Model evaluation

The validity of each final model was evaluated using goodness‐of‐fit (GOF) plots and the precision of parameter estimates. The stability of the final model was assessed using the bootstrap method. Predictive performance was evaluated using the pc‐VPC. The observed median, as well as the 2.5th and 97.5th percentiles, were plotted and compared with their respective simulated 95% confidence intervals.

2.2.3. Definition of clinical dosage

The clinical dosage of PDE‐5 inhibitors and endothelin receptor antagonists for PAH was determined based on package inserts and literature. ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ The distinction between paediatric (<15 years) and adult (≥15 years) patients was based on age, as specified in the Japanese prescribing information for prescription drugs. The recommended adult dosages are 60‐mg/day sildenafil, ¹⁵ 40‐mg/day tadalafil, ¹⁶ 250‐mg/day bosentan ¹⁷ and 10‐mg/day ambrisentan. ¹⁸ For paediatric patients, sildenafil is administered at 60 mg/day (≥20 kg, 1–15 years), ¹⁵ 30 mg/day (8–20 kg, 1–15 years) ¹⁵ or 3 mg/kg/day (<8 kg or <1 year). ¹⁹ Tadalafil is given at 1 mg/kg/day (<15 years), ¹⁶ bosentan at 4 mg/kg/day (<15 years) ²⁰ and ambrisentan at 5 mg/day (8–15 years) ¹⁸ or 0.2 mg/kg/day (<8 years). ²¹

2.2.4. Calculation of plasma drug concentration at steady state

The mean steady‐state plasma drug concentration (C_ss) following administration of the clinical dosage was calculated using the following equation:

$$C_{\mathit{ss}}=\mathit{\text{Dose}}/\left(\mathit{CL}/F\right)$$

here, Dose refers to the clinical dosage, and CL/F represents the individual patient's clearance (CL) adjusted for the bioavailability factor (F), estimated using Bayesian estimation based on the developed PPK model. The estimated C _ss values for each PAH treatment were compared between paediatric and adult patients.

2.2.5. Statistical analysis

Statistical analysis was conducted using the software EZR (Saitama Medical Center, Jichi Medical University, Saitama, Japan), which is a graphical user interface for R (www.r-project.org). ²² Data were analysed using the Mann–Whitney U test, with statistical significance set at p < 0.05.

2.3. Nomenclature of targets and ligands

Key protein targets and ligands in this article are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, and are permanently archived in the Concise Guide to PHARMACOLOGY 2023/24 (Alexander et al.). ²³ , ²⁴

3. RESULTS

3.1. Characteristics of the analytical data

Table 1 summarizes the patient characteristics and the number of plasma drug concentrations included in this analysis. Plasma concentrations were obtained as follows: sildenafil, 37 data points from 15 paediatric patients and 260 data points from nine adult patients; tadalafil, 62 data points from 20 paediatric patients and 95 data points from 11 adult patients; bosentan, 19 data points from seven paediatric patients and 170 data points from nine adult patients; and ambrisentan, 66 data points from 18 paediatric patients and 111 data points from 11 adult patients. The relationship between time after administration and plasma drug concentration for each drug is shown in Figure 1. PPK analysis was conducted for PDE‐5 inhibitors and endothelin receptor antagonists using a one‐compartment model as the structural model. Interindividual variability was modelled using an exponential error model, while intraindividual variability was modelled using a proportional error model. The PPK analysis was successfully completed using the analysis software.

TABLE 1.

Characteristics of the patients included in the population pharmacokinetic analysis.

	Sildenafil	Tadalafil	Bosentan	Ambrisentan
Demographic data
Number of patients (Paediatric/Adult)	24 (15/9)	31 (20/11)	16 (7/9)	29 (18/11)
Male/Female	8/16	12/19	5/11	11/18
Age (y)	10.8 (0.4–69)	4.6 (0.1–74.2)	26.8 (2.2–69)	4.8 (0.4–69)
Paediatric	5.0 (0.4–14.8)	1.9 (0.1–8.3)	4.8 (2.2–9.2)	1.8 (0.4–8.8)
Adult	47 (38–69)	37.8 (15.5–74.2)	47 (15.6–69)	44.6 (29.4–69)
Bodyweight (kg)	32.3 (6.5–58.7)	14.2 (5.4–73.5)	42.2 (6.9–58.7)	13.4 (7.1–62)
Paediatric	16.5 (6.5–54.9)	10.7 (5.4–23.9)	12 (6.9–54.9)	10.1 (7.1–21.6)
Adult	48.5 (37.4–58.7)	52.3 (32.5–73.5)	48.5 (38.5–58.7)	51.4 (37.4–62)
Dose (mg)	13.3 (1.7–20)	10 (4–40)	62.5 (12–62.5)	2 (0.6–10)
Paediatric	12 (1.7–20)	9 (4–20)	25 (12–62.5)	1 (0.6–5)
Adult	20 (6.7–20)	40 (20–40)	62.5 (62.5–62.5)	10 (5–10)
Number of plasma concentration (paediatric/adult)	297 (37/260)	157 (62/95)	189 (19/170)	177 (66/111)
Laboratory data
NT‐proBNP (pg/mL)	111 (17–1930)	267 (20–5370)	90.5 (18.5–1930)	254 (18.5–1556)
Cre (mg/dL)	0.42 (0.17–1.10)	0.29 (0.18–1.07)	0.50 (0.23–1.10)	0.29 (0.17–1.06)
AST (IU/mL)	27 (15–48)	29 (16–48)	26 (15–48)	26 (15–48)
ALT (IU/mL)	19 (7–52)	14 (5–33)	16.5 (7–50)	15 (5–68)
Concomitant drugs
Sildenafil	‐	‐	11	12
Tadalafil	‐	‐	4	13
Bosentan	11	4	‐	‐
Ambrisentan	5	15	‐	‐
Beraprost	7	4	7	8
Furosemide	9	16	7	14
Spironolactone	7	13	6	11
Warfarin	4	8	2	6

Note: Data are presented as median (range) or n.

Abbreviations: ALT, alanine aminotransferase; AST, aspartate aminotransferase; Cre, serum creatine; NT‐proBNP, N‐terminal pro‐brain natriuretic peptide.

FIGURE 1.

Plasma concentrations of (A) sildenafil, (B) tadalafil, (C) bosentan and (D) ambrisentan vs. time after dosing. Each point represents the plasma concentration of a PAH drug in an individual patient.

3.2. PPK model

3.2.1. PDE‐5 inhibitors (sildenafil and tadalafil): model and validation

In this analysis, reliable estimates of the absorption rate constants (Ka) for both sildenafil and tadalafil could not be obtained from the respective datasets. Consequently, previously reported values were adopted: 4.51 h⁻¹ for sildenafil ²⁵ and 0.84 h⁻¹ for tadalafil. ²⁶ Covariate analysis for sildenafil identified co‐administration of bosentan and bodyweight as significant factors influencing CL/F, while for tadalafil, bodyweight and co‐administration of spironolactone were significant covariates. Figure 2 presents the GOF plots for PDE‐5 inhibitors. For both drugs, the GOF plots showed no conditional weighted residuals (CWRES) exceeding|3|for tadalafil and only one instance for sildenafil. Both models displayed minimal bias in CWRES relative to time after dosing or population predictions, generally aligning along the line of identity (Figure 2E–H). Bootstrap analyses demonstrated high convergence rates—99.95% for sildenafil and 99.7% for tadalafil—with good agreement between parameter estimates and bootstrap medians (Table 2). Additionally, the pc‐VPC confirmed that the 95% confidence intervals of the simulated plasma concentrations for both models largely encompassed the observed percentiles, supporting consistency between simulated and observed data distributions (Figure 4A,B).

FIGURE 2.

Goodness‐of‐fit plots of the final model for (A,B,E,F) sildenafil and (C,D,G,H) tadalafil. (A,C) Observed concentrations vs. population predictions; (B,D) observed concentrations vs. individual predictions; (E,G) conditional weighted residuals (CWRES) vs. time after last dose; (F,H) CWRES vs. population predictions.

TABLE 2.

Population pharmacokinetic parameters of sildenafil and tadalafil estimated from final model and calculated from bootstrap analysis (PDE‐5 inhibitors).

	Sildenafil				Tadalafil
	Final model		Bootstrap (n = 2000)		Final model		Bootstrap (n = 2000)
	Population mean	95%CI	Bootstrap median	95% CI	Population mean	95% CI	Bootstrap median	95% CI
Pharmacokinetic parameter
Ka (h−1)	4.51 FIX	–	4.51	–	0.84 FIX	–	0.84	–
Vd/F (L)	322	258–387	322	262–471	80.6	38.3–123	76.2	41.7–145
CL/F (L/h)	60.6	44.4–76.8	60.1	44.9–85.4	1.76	1.38–2.14	1.79	1.36–2.41
Effect of BW	0.537	0.196–0.878	0.637	0.367–0.954	0.602	0.408–0.796	0.583	0.278–0.846
Effect of BOS	0.633	0.455–0.811	0.539	0.199–0.841
Effect of SPI					−0.400	−0.542–−0.258	−0.397	−0.544–−0.146
Interindividual variability (%)
Ka	0 FIX	–	0	–	0 FIX	–	0	–
Vd/F	25.5	NA–38.0	24.2	11.0–97.1	67.6	29.8–90.9	68.8	15.6–112
CL/F	56.3	31.2–73.2	53.8	30.1–85.2	37.2	15.9–50.1	34.3	17.4–63.6
Residual error
ε 1 (%)	58.5	51.8–64.5	57.9	51.0–64.2	33.3	28.3–37.7	32.7	27.0–39.8

Note: η‐shrinkage (%): Sildenafil (Vd/F = 43.2%; CL/F = 5.5%), Tadalafil (Vd/F = 42.3%; CL/F = 12.5%).Sildenafil model: CL/F_pop = 60.6 × (BW/BW_median)^0.537 × (1 + 0.633)^Bosentan. Tadalafil model: CL/F_pop = 1.76 × (BW/BW_median)^0.602 × (1–0.400)^{Spironolactone}. CL_pop, predicted population mean of CL/F; Bosentan, indicator variable for concomitant bosentan; BW, bodyweight; Spironolactone, indicator variable for concomitant spironolactone. NA indicates that the lower bound of the 95% CI could not be calculated because the square root of the lower bound for variance parameters (ω ²) was not defined.

Abbreviations: BOS, concomitant use of bosentan; BW, bodyweight; CI, confidence interval; CL/F, apparent total clearance; Ka, absorption rate constant; NA, not applicable; SPI, concomitant use of spironolactone; Vd/F, apparent volume of distribution.

FIGURE 4.

Prediction‐corrected visual predictive checks of the final model for (A) sildenafil, (B) tadalafil, (C) bosentan and (D) ambrisentan. The circles represent the original data. The solid line indicates the 50th percentile of the observed data, and the dashed lines indicate the 2.5th and 97.5th percentiles. The shaded areas represent the corresponding 95% confidence intervals of the 2.5th, 50th and 97.5th percentiles of the predicted data.

3.2.2. Endothelin receptor antagonists (bosentan and ambrisentan): Model and validation

For bosentan, the population estimate of Ka was 2.47 h⁻¹, while for ambrisentan, it was 1.03 h⁻¹, as derived from the current dataset. Covariate analysis identified bodyweight and ALT as significant factors for CL/F in the bosentan model, whereas bodyweight alone was significant in the ambrisentan model. GOF plots for both models demonstrated no bias relative to the line of identity (Figure 3A–D), and CWRES remained below 3, with no discernible bias with respect to time after dosing or population predictions (Figure 3E–H). Bootstrap analyses showed high convergence rates—96.3% for bosentan and 99.9% for ambrisentan—with population estimates consistent with the medians derived from the bootstrap methods (Table 3). In addition, the pc‐VPC confirmed that the 95% confidence intervals of the 2.5th, 50th and 97.5th percentiles for simulated plasma concentrations largely encompassed the observed percentiles for both models, validating the consistency and robustness of the models (Figure 4C,D).

FIGURE 3.

Goodness‐of‐fit plots of the final model for (A,B,E,F) bosentan and (C,D,G,H) ambrisentan. (A,C) Observed concentrations vs. population predictions; (B,D) observed concentrations vs. individual predictions; (E,G) conditional weighted residuals (CWRES) vs. time after last dose; (F,H) CWRES vs. population predictions.

TABLE 3.

Population pharmacokinetic parameters of bosentan and ambrisentan estimated from the final model and calculated from bootstrap analysis (endothelin receptor antagonists).

	Bosentan				Ambrisentan
	Final model		Bootstrap (n = 2000)		Final model		Bootstrap (n = 2000)
	Population mean	95%CI	Bootstrap median	95%CI	Population mean	95%CI	Bootstrap median	95%CI
Pharmacokinetic parameter
Ka (h−1)	2.47	1.25–3.70	2.43	1.33–4.74	1.03	0.638–1.46	1.06	0.579–1.91
Vd/F (L)	41.0	30.5–51.5	40.2	30.7–60.9	12.4	9.26–15.5	12.2	8.04–16.0
CL/F (L/h)	8.85	6.81–10.9	8.81	6.81–10.9	0.594	0.432–0.756	0.603	0.424–0.818
Effect of BW	0.472	0.192–0.752	0.476	0.335–0.838	0.561	0.247–0.875	0.550	0.225–0.900
Effect of ALT	−0.203	−0.341–−0.065	−0.214	−0.572–−0.015
Absorption lag time (h)	0.379	0.309–0.449	0.388	0.155–0.700
Interindividual variability (%)
Ka	0 FIX	–	0	–	0 FIX	–	0	–
Vd/F	29.7	NA–47.7	29.1	7.52–61.5	39.2	2.7–55.4	38.7	8.33–63.2
CL/F	32.9	8.63–45.7	31.2	13.1–50.2	60.8	38.3–77.0	58.0	34.7–73.2
Residual error
ε 1 (%)	59.0	50.3–66.5	57.2	49.0–63.2	35.8	30.9–40.1	35.4	30.2–40.3

Note: η‐shrinkage (%): Bosentan (Vd/F = 33.4%; CL/F = 6.8%), Ambrisentan (Vd/F = 36.3%; CL/F = 4.6%).

Bosentan model: CL/F_pop = 8.85 × (BW/BW_median)^0.472 × (ALT/ALT_median)^−0.203. Ambrisentan model: CL/F_pop = 0.594 × (BW/BW_median)^0.561. CL_pop, predicted population mean of CL/F; BW, bodyweight; ALT, value of alanine aminotransferase. NA indicates that the lower bound of the 95% CI could not be calculated because the square root of the lower bound for variance parameters (ω ²) was not defined.

Abbreviations: ALT, value of alanine aminotransferase; BW, bodyweight; CI, confidence interval; CL/F, apparent total clearance; Ka, absorption rate constant; NA, not applicable; Vd/F, apparent volume of distribution.

3.3. Evaluation of predicted plasma concentrations in paediatric and adult patients after administration of clinical doses

The estimated C_ss values for each drug in paediatric and adult patients are presented in Figure 5. For sildenafil, the median (range) C_ss in paediatric patients was 25.4 (4.95–83.4) ng/mL, compared with 34.3 (17.1–95.0) ng/mL in adult patients. The C_ss of sildenafil in paediatric patients was 26.0% lower than that in adult patients (p = 0.064). For tadalafil, the median C_ss among paediatric patients was 461 (201–982) ng/mL, while that in adult patients was 768 (320–998) ng/mL—a significant reduction of 40.0% in paediatric patients compared with adults (p < 0.001). In the case of bosentan, paediatric patients exhibited a median C_ss of 339 (257–583) ng/mL, markedly lower than the 1221 (732–2904) ng/mL observed in adult patients (p < 0.001). The median C_ss of ambrisentan was 164 (60.0–433) ng/mL in paediatric patients, representing a 45.0% decrease compared with 298 (74.2–504) ng/mL in adults (p = 0.003).

FIGURE 5.

Predicted plasma concentrations of (A) sildenafil, (B) tadalafil, (C) bosentan and (D) ambrisentan in paediatric and adult patients receiving clinical doses. The upper and lower whiskers represent the 90th and 10th percentiles, respectively. Outliers are shown as circles. All p‐values were calculated using the Mann–Whitney U test.

4. DISCUSSION

This study aimed to develop a PPK model using combined plasma drug concentration data from paediatric and adult patients with PAH, with the goal of elucidating the pharmacokinetic characteristics of PAH treatments in real‐world clinical settings. Based on the results, a PPK model incorporating real‐world data from both paediatric and adult patients was successfully developed, allowing for characterization of the pharmacokinetics of PDE‐5 inhibitors (sildenafil and tadalafil) and endothelin receptor antagonists (bosentan and ambrisentan). Furthermore, the model enabled the prediction of C_ss for sildenafil, tadalafil, bosentan and ambrisentan in both adult and paediatric patients with PAH.

In this analysis, the simplest and most accurate model was achieved using a one‐compartment model with first‐order absorption as the structural model, an exponential error model for interindividual variability and a proportional error model for intraindividual variability. The small number of patients with PAH and limited data availability made it difficult to construct more complex models. Based on the time course plasma drug concentration data for all drugs (Figure 1), a one‐compartment model with a single elimination phase was deemed appropriate as the structural model. Previous PPK studies of several PAH drugs have also frequently employed a one‐compartment model. ⁸ , ¹⁰ , ²⁷ , ²⁸

In the covariate analysis, bodyweight was identified as a significant covariate for CL/F in sildenafil, consistent with previous reports. ⁸ , ²³ For sildenafil, the inclusion of concomitant bosentan use as a covariate resulted in a 1.63‐fold increase in CL/F. Several pharmacokinetic studies have demonstrated a significant drug–drug interaction between sildenafil and bosentan, which reduces sildenafil concentrations. ²⁹ , ³⁰ , ³¹ This interaction is attributed to bosentan's induction of cytochrome P450 3A4 (CYP3A4) expression in the liver and intestinal wall via activation of the pregnane X receptor. ³² The population mean estimate of CL/F for sildenafil in this study was 60.6 L/h, which is close to previously reported values (70.5–73.7 L/h). ³³ For tadalafil, concomitant use of spironolactone was included as a covariate. This is considered a consequence of the progression of right heart failure in patients receiving spironolactone because worsening right heart function could lead to reduced hepatic perfusion and congestive hepatopathy, potentially resulting in reduced tadalafil CL/F. ³⁴ Additionally, the population mean estimates of Vd/F and CL/F for tadalafil obtained in this analysis were consistent with a previous report. ¹⁰ Although earlier studies have included bosentan use as a covariate for tadalafil CL/F, only four of 31 patients (12.9%) in this analysis were receiving concomitant bosentan therapy, which may have been insufficient for its inclusion as a covariate. The results for both sildenafil and tadalafil in this study are consistent with PPK analyses involving non‐Japanese populations, suggesting no significant differences in pharmacokinetic characteristics between Japanese and non‐Japanese patients. ¹⁰ , ²⁵

For bosentan, ALT was identified as a covariate for CL/F, reflecting its metabolism in the liver and the potential influence of liver function on drug clearance. ³⁵ However, the extent to which ALT accurately reflects liver dysfunction remains uncertain, highlighting the need for further investigation. In this study, the estimated CL/F for bosentan was 8.85 L/h, which is consistent with a previously reported value of 5.48 L/h in Japanese patients, thereby supporting the reliability of the constructed model. ²⁸ There are limited reports on bosentan PPK models; thus, this study provides valuable insights in this field. While previous PPK analyses of ambrisentan in non‐Japanese patients with PAH have employed a two‐compartment model, this study used a one‐compartment model. Despite this difference, the CL/F for ambrisentan estimated in this study was consistent with previous findings, ⁷ suggesting minimal variability in CL/F between Japanese and non‐Japanese patients.

Model diagnostics using GOF plots for all drugs in the final models indicated that the models provided an adequate fit. We developed PPK models for sildenafil, tadalafil, bosentan and ambrisentan, demonstrating adequacy in parameter estimation accuracy, model stability and predictive performance for plasma drug concentrations, thereby supporting their overall suitability.

Using the developed models, we estimated the C_ss of sildenafil, tadalafil, bosentan and ambrisentan in both adult and paediatric PAH patient populations. The results indicated that the median C_ss values for all drugs were lower in the paediatric group than in the adult group. The estimated C_ss values reflect plasma concentrations in paediatric and adult patients under real‐world conditions following clinical dosing regimens as outlined in package inserts and clinical guidelines. Previous studies have also indicated that plasma concentrations of PAH drugs tend to be lower in paediatric patients than in adults. ⁷ , ¹⁰ , ²⁵ , ³⁶ Lower plasma drug concentrations may suggest reduced therapeutic efficacy. However, in the case of sildenafil, therapeutic effects have been observed even at standard paediatric doses in children with PAH. ³⁷ , ³⁸ This raises the possibility that paediatric patients may be more sensitive to the therapeutic effects of these drugs, allowing sufficient efficacy to be achieved at lower plasma concentrations. To date, the optimal plasma concentrations of PAH drugs for treating paediatric patients have not been established. In the future, investigating the relationship between plasma drug concentrations and therapeutic effects in paediatric patients may help advance the development of personalized treatment strategies for this population.

The models developed in this study have several limitations that should be considered. Notably, patients with significantly impaired hepatic or renal function were not included, indicating that these models may not be applicable to such individuals. In addition, although weight was included as a covariate in all models, patients with severe obesity were not represented. Therefore, caution should be exercised when applying these models to patients whose bodyweight falls outside the range observed in this study. During covariate model construction, the shrinkage of Vd/F exceeded 30% for all drugs examined. According to US Food and Drug Administration guidelines for PPK analysis, shrinkage values between 20% and 30% are considered high. ³⁹ As a result, covariate exploration in this analysis was performed only for CL/F, and not for Vd/F. Furthermore, it was difficult to estimate Ka and account for its interindividual variability. The high shrinkage of Vd/F and the challenges in estimating Ka are likely attributable to the sampling schedule. The data used in this analysis were derived from routine clinical laboratory tests, which included relatively few time course blood samples following drug administration. Consequently, most samples were obtained during the elimination phase, with limited data available from the absorption and distribution phases—factors that may have hindered accurate estimation of Ka and Vd/F. Finally, this study did not assess the relationship between plasma drug concentrations and therapeutic efficacy or adverse effects.

This study characterized the pharmacokinetic parameters and their variability for sildenafil, tadalafil, bosentan and ambrisentan by integrating real‐world data from Japanese paediatric and adult patients with PAH. The results of Bayesian estimation suggested that, at currently used clinical doses, plasma concentrations of these drugs tend to be lower in paediatric patients than in adults. The findings of this study are expected to contribute to the optimisation of pharmacotherapy for patients with PAH.

AUTHOR CONTRIBUTIONS

Motoyasu Miura, Shimako Tanaka, Yasumi Nakashima, Noriyuki Namiki, Naoki Inui, Hiroshi Watanabe and Shinya Uchida were involved in the conception and trial design. Yasumi Nakashima, Mariko Tatsuguchi, Keiichi Odagiri, Naoki Inui and Hiroshi Watanabe were responsible for patient care and clinical specimen collection. Motoyasu Miura, Shimako Tanaka, Yasuharu Kashiwagura, Noriyuki Namiki and Shinya Uchida performed data analysis, interpretation and statistical analysis. Motoyasu Miura and Shinya Uchida wrote the manuscript with input from all authors.

CONFLICTS OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Miura M, Tanaka S, Aihara R, et al. Development of a population pharmacokinetic model using combined paediatric and adult data for four pulmonary arterial hypertension drugs. Br J Clin Pharmacol. 2026;92(10):3611‐3621. doi: 10.1002/bcp.70676

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.