A Mechanism‐Based Multi‐Level Population PK/PD Model for Potassium‐Competitive Acid Blockers

ABSTRACT

Potassium‐competitive acid blockers (PCABs) are emerging alternatives to proton pump inhibitors for the treatment of acid‐related diseases. However, due to the complex, nonlinear interaction between drug exposure, food intake, and physiological rhythms, optimizing dosing strategies remains challenging. A multi‐leveled population analysis was conducted using published pharmacokinetic and pharmacodynamic data on four representative PCABs: tegoprazan, YH4808, fexuprazan, and vonoprazan. A semi‐mechanistic population PK/PD model was developed to account for food effects, circadian pH rhythms, and pH‐dependent drug absorption. A multi‐level nonlinear mixed‐effects modeling framework was implemented to capture both inter‐drug and inter‐study variability. The model successfully described the time course of plasma concentration and intragastric pH for all four PCABs under various conditions. The model identified differences in pharmacokinetics and pharmacodynamic potency between drugs (with the relative in vitro potency ranked as vonoprazan > fexuprazan > YH4808 > tegoprazan), and simulations demonstrated that both pre‐ and post‐meal administration enhanced pH control in early time period via potentially distinct mechanisms: the pre‐meal effect may arise from temporally separated contributions of food‐ and drug‐induced pH elevation, whereas the post‐meal effect is likely driven by temporally overlapping, additive actions, particularly under low‐dose or non‐steady‐state conditions. Predicted pH profiles and holding times above pH 4 closely matched reported clinical outcomes. The study demonstrates the application of a mechanistic, multi‐level population approach for cross‐drug PK/PD evaluation of PCABs. The findings support drug‐specific dose optimization and highlight the clinical relevance of food–drug interactions. The modeling approach provides a model platform for pharmacotherapy or model‐informed drug development (MIDD).

Study Highlights

• What is the current knowledge on the topic?

  • ○
    Potassium‐competitive acid blockers (PCABs) are increasingly used as alternatives to proton pump inhibitors due to their rapid onset and stable acid suppression. However, existing pharmacometric models often fail to fully integrate the complex bidirectional relationship between drug exposure and intragastric pH, particularly under variable food intake and circadian conditions. Prior models are drug‐specific and typically lack scalability across the class of PCABs.
• What question did this study address?

  • ○
    This study aimed to determine whether a unified, mechanistic population PK/PD model—developed through a multi‐level population approach—could simultaneously describe and compare the pharmacokinetic and pharmacodynamic behavior of multiple PCABs under various clinical conditions, including food intake timing and dosing regimens.
• What does this study add to our knowledge?

  • ○
    The study introduces a novel multi‐level population PK/PD model that incorporates circadian rhythms, food effects, and pH‐dependent absorption within a single framework. By capturing both inter‐drug and inter‐study variability, the model enables quantitative comparison of PCABs and provides mechanistic insight into drug–pH interactions. Simulation results replicate clinical pH profiles and highlight drug‐specific differences in optimal dosing strategies, particularly in the early treatment phase.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    This integrative model offers a scalable platform for model‐informed drug development (MIDD) of current and next‐generation PCABs. It facilitates rational dose optimization by accounting for both physiological and pharmacological contributors to acid suppression. The framework may also inform trial design, improve predictability of food–drug interactions, and enable mechanistic reinterpretation of complex clinical outcomes in gastroenterology.

Schematic overview of a mechanism‐based, multi‐level population model for potassium‐competitive acid blockers.

1. Introduction

Peptic ulcer disease (PUD) is a prevalent gastrointestinal condition characterized by mucosal damage induced by gastric acid, with an estimated global prevalence of approximately 10% [1]. For decades, H2 receptor antagonists (H2RAs) and proton pump inhibitors (PPIs) have served as the standard of treatment for acid suppression. However, potassium‐competitive acid blockers (PCABs) have recently emerged as promising alternatives and are progressively replacing PPIs in clinical practice [2]. Unlike PPIs, which require acid activation and several days to reach maximal efficacy, PCABs exhibit a rapid onset of action and do not require acid activation. Furthermore, whereas PPIs are acid‐labile and require enteric coating to prevent degradation, PCABs provide more consistent acid suppression and are less influenced by meal timing due to their chemical properties [3]. These pharmacological advantages have contributed to the growing adoption of PCABs in the management of acid‐related disorders [4].

Gastric acid secretion is regulated by multiple pathways, including stimulation of H2 receptors via histamine, muscarinic M3 receptors via cholinergic signaling, and CCK‐B receptors via gastrin. These pathways converge on the activation of the H⁺/K⁺ ATPase (proton pump) in parietal cells, facilitating hydrogen ion (H⁺) secretion [5]. This intragastric acidity can be affected by various factors, including disease state, individual tone, food intake, age, circadian rhythm, drug administrations, and so on.

As each of the listed factors has a substantial impact on pH, it is important to clearly distinguish the pure drug effect from intrinsic and extrinsic influences when evaluating the drug's effect on pH. Complicating matters further, anti‐ulcer agents demonstrate a bidirectional relationship between pharmacokinetics (PK) and pharmacodynamics (PD). In particular, pH can influence drug absorption and, conversely, drug exposure can dynamically alter gastric pH [6]. This bidirectional interaction introduces complexity in modeling and necessitates integrative approaches that reflect the interplay of drug physicochemical, physiological, and other clinical factors.

Although previous efforts have applied model‐informed strategies to the development of PCABs, many models have faced challenges in balancing complexity and simplicity when characterizing the mechanistic relationship between pharmacokinetics and pH. For instance, Chung et al. developed a population PK/PD model for YH4808 incorporating circadian effects using multiple trigonometric functions and feedback of increased pH on systemic exposure [6], and Jeong et al. proposed a physiologically based PK/PD model for tegoprazan using a sixth‐order Fourier series and an advanced dissolution, absorption, and metabolism (ADAM) framework [7]. However, both studies incorporated food‐related pH changes primarily through circadian rhythm modeling at the baseline level, without directly modeling the pharmacodynamic effects of food intake, which limits their applicability to diverse clinical dosing scenarios.

The study by Kim et al. presented a physiologically based model for fexuprazan, in which high pH periods in the control group were excluded to isolate drug effects [8]. However, the model did not account for the pH elevation caused by repeated dosing and its subsequent impact on drug absorption. As elevated pH alters the ionization state of PCABs—thereby affecting their solubility and absorption—failure to incorporate this feedback mechanism limits mechanistic interpretability and may ultimately compromise the accuracy of exposure–response predictions.

Despite the increasing clinical relevance of PCABs when considering their applicability, a well‐structured modeling framework that clearly distinguishes external factors (e.g., food intake) from intrinsic drug properties remains underdeveloped. This gap underscores the need for a more mechanistic approach—one that explicitly incorporates the dynamic and bidirectional interactions between drug exposure and intragastric pH. In particular, describing drug–pH's mechanical relationships is expected to play a pivotal role in optimizing combination therapies and interpreting clinical outcomes in acid‐related disorders.

To address these challenges, our study aims to develop a mechanistic, model‐based multi‐level population framework that characterizes both drug‐specific pharmacological properties and physiological pH‐regulating mechanisms. Key known contributors to intragastric pH—such as food intake patterns (meal type and timing), circadian rhythm, and dose‐dependent drug behavior—are incorporated into the model.

Notably, this approach moves beyond the conventional pharmacokinetic‐centered understanding of the “food effect” by acknowledging that food can also influence pharmacodynamic outcomes, particularly in the context of PCABs. However, individual clinical trials often lack the temporal resolution and contextual variability required to disentangle such interdependent factors, largely due to their limited scope and design. To address these limitations, a data‐integrative, multi‐leveled model approach is essential for robust analytic model development.

Leveraging clinical PK/PD data synthesized from the literature, we developed a unified model capable of describing the complex interplay between PCAB exposure and intragastric pH. Simulation studies were further conducted to evaluate the predictive performance and feasibility of the model across a range of dosing scenarios and to explore the impact of food conditions on therapeutic outcomes. Through this model framework, we aim to advance model‐informed drug development for current and upcoming next‐generation PCAB agents.

2. Method

To construct a generalized PK/PD model for the PCAB class, relevant clinical datasets were identified through a comprehensive literature search of PubMed and ClinicalTrials.gov. Studies were included if they provided extractable time–concentration pharmacokinetic profiles of plasma drug levels and corresponding intragastric pH profiles as a pharmacodynamic endpoint. The studies without mealtime information were ruled out. The search employed keywords including “PCAB,” “Potassium‐Competitive Acid Blockers,” “Pharmacokinetics,” and “pH.”

Pharmacokinetic and pharmacodynamic data were digitized using Engauge Digitizer (version 12.1). Studies involving drug–drug interactions, metabolite‐focused analyses, or publications in languages other than English were excluded from the digitization process. Any missing study protocol information was supplemented using data from ClinicalTrials.gov. All included studies and extracted data were independently reviewed by three reviewers to ensure accuracy and consistency.

For each study, the following information was extracted: study reference (author), group identification (within‐study group ID), observed values (plasma drug concentration and pH at each time point), drug administration time, and food intake time. Where available, additional variables were recorded, including meal type (e.g., standard or high‐fat), sex, age (years), and body weight (kg). Placebo or control group data were also collected when provided.

2.1. Model Specification and Development

A semi‐mechanistic PK/PD model was developed to describe the dynamic interaction between plasma drug concentration, intragastric pH, food intake, and physiological circadian rhythms. The pharmacokinetic (PK) model was constructed as a one‐compartment model with first‐order absorption. The pharmacodynamic (PD) model describing pH changes was formulated as an indirect response model by given information in exploratory data analysis (Figure S1) and literature report [6, 7], wherein the rate of pH production (Kin) was influenced by both drug and food effects, as well as circadian variation.

A separate compartment was included to account for the presence and persistence of food in the stomach, allowing the model to incorporate the kinetics of food‐related pH changes. Three key mechanistic drivers were incorporated into the model: (1) the intake effect, representing the combined influence of drug and food; (2) the circadian rhythm, reflecting physiological pH fluctuations over a 24‐h period; and (3) the feedback effect, modeling the pH‐dependent alteration of drug absorption.

The intake effect, representing the total stimulatory contribution to pH elevation, was modeled as the sum of the drug and food effects:

$$S_{\mathrm{con}}=S_{\mathrm{d}}\times A_{\mathrm{d}}^{\text{Slop}{\mathrm{e}}_{\mathrm{d}}}+S_{\mathrm{f}}\times A_{\mathrm{f}}^{\text{Slop}{\mathrm{e}}_{\mathrm{f}}}$$

where A _d and A _f denote the respective amounts of drug and food in the system, S _d and S _f are their corresponding scaling factors, and Slope_d and Slope_f represent the power‐law exponent shaping their nonlinear contributions depending on the amount of each effect. The resulting value, S _con, is used to calculate the pH stimulus (PHS) according to an activation function as follows [9]:

$$\mathrm{PHS}=\mathrm{p}{\mathrm{H}}_{\max }\times \frac{1}{1+S_{\mathrm{con}}}$$

This function bounds the effect between 0 and pH_max, representing the maximal achievable increase in pH due to a drug or food stimulus. PHS modulates the Kin term in the indirect response model.

The circadian rhythm of intragastric pH was modeled using a cosine function with a fixed period of 24 h:

$$\text{Circadian}=\mathrm{AMP}\times \mathrm{Cos}\left(2\mathrm{\pi }\times \frac{\text{Time}}{N}\right)$$

where AMP is the amplitude of daily pH fluctuation, Time is the hour of the day, and N = 24. This function also modulates Kin, enabling the model to reproduce time‐of‐day–dependent pH changes.

To account for the bidirectional PK–PD relationship specific to PCABs, the feedback effect was implemented using a Gaussian function, describing a bell‐shaped relationship between pH and drug absorption rate:

$$\text{Aborption rate}=K_{\mathrm{a}}\times {\mathrm{e}}^{-\frac{{\left(\mathrm{p}{\mathrm{H}}_{\text{current}}-\text{SCALE}\right)}^2}{\text{SHAP}{\mathrm{E}}^2}}$$

Here, K _a is the typical absorption rate, pH_current is the dynamic pH at a given time, SCALE is the pH level at which absorption is maximal, and SHAPE controls the peak width. This function effectively scales the absorption rate based on current gastric pH, capturing the known pH‐dependent absorption profile of PCABs.

To address inter‐drug and inter‐study variability, a multi‐level modeling approach was introduced using the $LEVEL option in NONMEM version 7.5.1. Drug identity was treated as a super‐level covariate, with study‐specific groups nested within each drug. Simultaneous PK/PD model fitting was performed using the SAEM‐I algorithm (stochastic approximation expectation–maximization with interaction). All random effects were implemented using mu‐referencing to enhance computational efficiency and numerical stability during estimation.

Figure 1 illustrates the schematic relationships between designated compartments and the mixed effect attributes and levels.

FIGURE 1.

Scheme of the mechanistic model and the levels of the random effects in the model (Fixed, fixed effect; NLMEM, nonlinear mixed effect model; Random, random effects).

2.2. Model Diagnostics

Model evaluation was conducted using both numerical and visual diagnostic methods. Numerically, objective function values (OFVs) from the SAEM algorithm were monitored to evaluate the adequacy of the prespecified PK/PD structure and to compare alternative parameterizations within this framework. Model robustness and parameter stability toward individual studies' impact were assessed through nonparametric bootstrapping (500 replicates), comparing the distribution of bootstrapped parameter estimates against the final model estimates.

For visual diagnostics, goodness‐of‐fit (GOF) plots and visual predictive checks (VPC) were employed. GOF assessments included comparisons between observed data and predictions at both the population and individual levels. Specifically, level‐population predictions (LPRED), which incorporate super‐level (drug‐level) ETAs as fixed effects and level‐individual predictions (LIPRED) which include inter‐individual (group) variability to the model prediction, were evaluated alongside individual weighted residuals (IWRES) and conditional weighted residuals (CWRES).

VPCs were performed to assess the model's predictive performance by comparing observed data against simulated prediction intervals. The alignment between observed percentiles and simulated confidence intervals served as a key indicator of model adequacy in capturing variability and central tendencies.

Model adequacy was assessed through evaluation of parameter plausibility and individual post hoc estimates (THETA + ETA), confirming consistency between population and individual levels. To enable cross‐drug comparison of pharmacodynamic strength, we derived a pharmacodynamic potency index (PPI) from the drug‐effect scaling parameter S _d. The index was obtained by taking the reciprocal of S _d to represent the amount required to generate a unit effect, converting this quantity to a concentration scale using the estimated drug‐specific volume of distribution, and then normalizing it by molecular weight to express it on a molar basis. This transformation yields a concentration‐based indicator of pharmacodynamic potency that can be qualitatively compared with known IC₅₀‐level potency information reported for PCABs. Through these diagnostics, we aimed to evaluate and ensure the model's overall validity.

2.3. Simulation Study

A simulation study was conducted on each drug to evaluate whether the model could produce physiologically plausible intragastric pH profiles under a range of dosing scenarios. Response surfaces were generated with drug doses and time of dosing (TOD), where TOD represents the time interval between drug administration and meal intake. The simulation was carried out over 6 days, during which food was administered on Day 0 (baseline), followed by once‐daily drug administration from Day 1 to Day 7. Dose levels ranged from 0 to 100 mg in 10 mg increments, and TOD varied from −2 h (2 h before a meal) to +2 h (2 h after a meal) in 0.5‐h increments. Based on the response surfaces, the simulated profiles were then compared to reported clinical data to confirm the model's predictive power with observed physiological outcomes.

3. Results

3.1. Data Collection and Data Processing

A total of four potassium‐competitive acid blockers (PCABs)—YH4808 [6], fexuprazan [10], vonoprazan [11, 12], and tegoprazan [13, 14, 15, 16, 17, 18, 19, 20, 21]—were included in the final dataset. These drugs were selected based on the availability of time‐concentration pharmacokinetic (PK) profiles and corresponding intragastric pH data, extracted from published literature. Each digitized study arm was treated as a distinct group‐level individual for modeling purposes.

In total, the dataset includes a range of doses for each drug, regimens (single vs. multiple dosing), and feeding conditions (fasted vs. fed). Tegoprazan dose data ranging from 50 to 400 mg, YH4808 from 30 to 600 mg, fexuprazan from 10 to 320 mg, and vonoprazan up to 120 mg. All the drug datasets include single and multiple doses, with each study arm including drug concentration and pH data. Table 1 summarizes the studies included for each drug, detailing the number of subjects, dose levels, and the number of observations per arm. Optional covariates such as meal type (standard vs. high‐fat), age, sex, and body weight were collected when available. However, due to incomplete reporting across studies, these variables were not incorporated as statistical covariates in the current analysis.

TABLE 1.

The summary of collected drug observations.

Drug	Author	Type	Design	Dose (N group)	No. observation
					Total	PK	PD
YH4808	Tae Kyu Chung (2022)	PK, PD	Single	30 (2)	62	17	45
				50 (2)	67	22	45
				100 (2)	65	21	44
				200 (2)	67	23	44
				400 (2)	69	23	46
				600 (2)	66	21	45
			Multiple	100 (4)	138	44	94
				200 (4)	94	46	48
				400 (4)	134	39	95
Fexuprazan	J. Sunwoo (2018)	PK, PD	Single	10 (8)	40	16	24
				20 (8)	41	17	24
				40 (8)	41	17	24
				80 (8)	41	17	24
				160 (8)	58	34	24
				320 (8)	41	17	24
			Multiple	20 (8)	54	30	24
				40 (8)	54	30	24
				80 (8)	54	30	24
				160 (8)	54	30	24
Vonoprazan	Yuuichi Sakurai (2015)	PK, PD	Single	1 (11)	74	26	48
				5 (15)	82	34	48
				10 (14)	82	34	48
				15 (6)	41	17	24
				20 (13)	82	34	48
				30 (6)	41	17	24
				40 (15)	82	34	48
				80 (7)	41	17	24
				120 (8)	41	17	24
	H. Jenkins (2015)	PK, PD	Multiple	10 (18)	123	27	96
				15 (9)	62	14	48
				20 (18)	123	27	96
				30 (18)	123	27	96
				40 (18)	123	27	96
Tegoprazan	Sungpil Han (2019)	PK, PD	Single	50 (6)	37	11	26
				100 (6)	35	10	25
				200 (6)	37	11	26
				400 (6)	37	12	25
			Multiple	100 (6)	75	25	50
				200 (6)	75	25	50
	Jun Gi Hwang (2019)	PK	Single	100 (12)	11	11	0
	Jong‐Lyul Ghim (2021)	PK, PD	Multiple	100 (20)	9	9	0
	Jinjie He (2021)	PK	Single	50 (10)	11	11	0
				100 (10)	12	12	0
				200 (10)	12	12	0
			Multiple	100 (10)	20	20	0
	Deok Y. Yoon (2021)	PK	Single	50 (36)	34	34	0
	Ji‐Young Jeon (2021)	PK	Multiple	50 (11)	13	13	0
	Sungpil Han (2021)	PK, PD	Single	200 (48)	74	24	50
	Jung Sunwoo (2020)	PD	Multiple	50 (8)	51	0	51
	Eunsol Yang (2022)	PD	Single	50 (16)	13	0	13

Instead, the model was formulated within an indirect‐response framework in which key physiological modifiers, such as food effects and circadian rhythms, were incorporated as structural, mechanistic components influencing the system's input and regulatory processes. This approach allowed the model to capture the major determinants of pH dynamics while maintaining a flexible structure that can accommodate additional covariates in future analyses as more complete datasets become available.

The dataset supports hierarchical modeling of inter‐drug variability and within‐drug consistency across doses and feeding states through numeric drug ID (1: tegoprazan, 2: YH4808, 3: fexuprazan, 4: vonoprazan).

As individual‐level data were unavailable, digitized mean profiles from each study arm were treated as pseudo‐individuals. Accordingly, η‐variability reflects inter‐group or inter‐study differences rather than true subject‐level inter‐individual variability.

3.2. Model Development

Using the suggested model structure, which integrates circadian pH rhythms, food and drug contributions, and pH‐dependent absorption kinetics, a simultaneous PK/PD model successfully described all four PCAB agents. A multi‐level analysis framework was implemented, with drug identity specified as a super‐level variable and individual study groups nested within each drug. This structure allowed the model to capture both inter‐individual (group) variability (e.g., across doses or conditions) and between‐drug variability (e.g., in absorption rate, clearance, potency, and peak absorption pH level).

Model parameters were estimated using the SAEM‐I algorithm, and all variability components were specified with mu‐referencing to improve numerical stability during estimation. The final model demonstrated successful convergence and yielded parameter estimates with acceptable relative standard errors (RSE), indicating overall estimation precision (Table 2).

TABLE 2.

Estimated model parameters.

Class	No.	Parameter (unit)	Estimates (RSE%)	IIV, CV% (RSE%) [Shr%]	IDV, CV% (RSE%) [Shr%]
Error	1	Prop err (PK)	0.545 (4.5)	—	—
	2	Add err (PD)	0.880 (4.2)	—	—
Physio	3	Kin (1/h)	0.435 (20.9)	98.28% (42.9) [15]	—
	4	Base	1.090 (3.2)	7.75% (150.5) [15]	—
	5	pHMax	5.570 (3.2)	—	—
	6	K g (1/h)	1.820 (20.1)	—	—
	7	AMP	0.704 (13.8)	60.05% (40.5) [26]	—
Feed	8	SCALE	4.080 (6.7)	29.23% (31.8) [17]	10.98% (58.2) [0]
	9	SHAPE	2.660 (8.9)	—	—
Drug	10	K a (1/h)	0.156 (7.4)	20.45% (38.3) [35]	31.56% (124.3) [1]
	11	CL (1/h)	98.700 (5.9)	29.60% (30.3) [20]	161.14% (9.5) [0]
	12	V d (L)	56.600 (17.8)	28.29% (42.3) [56]	89.36% (50.6) [0]
Effect	13	S f	0.043 (51.1)	—	—
	14	Slopef	1 (fixed)	—	—
	15	S d (1/mg)	0.693 (18.3)	54.96% (39.4) [23]	31.56% (66.7) [0]
	16	Sloped	0.572 (15.2)	—	—

Note: pH scale reated parameter's unit (Base, pHMax, AMP, Additive error, SCALE) is pH level. Dimensionless: Proportional error, SHAPE, S _f, Slope_f, and Slope_d.

Abbreviations: Add. err, additive error (as standard deviation); AMP, amplitude of pH fluctuation in circadian rhythm; Base, baseline level of pH; CL, drug clearance; IDV, inter‐drug variability; IIV, inter‐individual variability; K _a, drug absorption rate; K _g, gastric emptying rate; Kin, production rate of pH; pHMax, maximum achievable pH level; Prop. err, proportional error (as standard deviation); RSE, relative standard error (calculated by non‐parametric method); SCALE, Scaling parameter for peak function; S _d, scaling factor for drug effect; S _f, scaling factor for food effect; SHAPE, shaping parameter for peak function; Shr, Shrinkage; V _d, drug volume of distribution.

Notably, the physiological parameters such as Kin (pH production rate), Base (baseline pH), AMP (amplitude of circadian variation), and pHmax (maximum achievable pH) were consistently estimated across drugs. The model also captured inter‐drug variability in PK parameters, particularly in clearance (CL) and volume of distribution (V _d), as well as in the drug‐specific effect parameters S _drug and S _slope, which together govern the extent and sensitivity of intragastric pH elevation. These parameters were estimated consistently, enabling the model to differentiate how each drug modulates the pH response profile, with the remaining inter‐individual (study group) variability plausibly reflecting differences across study arms included in the analysis.

The food effect scaling parameter (S _food) was also estimated, albeit with larger uncertainty (RSE ~59%), possibly due to variability in meal types and incomplete meal timing information across studies. Still, its inclusion improved the model's ability to separate food‐driven and drug‐driven components of pH modulation.

Collectively, the successful optimization and estimation of super‐level parameters support the feasibility and extensibility of the model structure. The resulting parameter estimates serve as a quantitative foundation for subsequent simulations, including those evaluating dosing strategies and food effects across different clinical conditions.

3.3. Model Diagnostics

Model performance was evaluated through both visual and numerical diagnostics. The goodness‐of‐fit (GOF) plots demonstrated strong agreement between observed and predicted values at both the population and individual levels (Figure 2, Figures S2 and S3). Leveled predictions—incorporating inter‐drug variability as fixed effects—successfully captured the central trend of the data, indicating that the hierarchical structure of the model appropriately accommodated between‐drug differences. Conditional weighted residuals (CWRES) were symmetrically distributed around zero, with the majority of values falling within ±3, suggesting an absence of systemic bias in the residuals. The individual prediction plots adequately captured the trends across both plasma and pH levels for each drug (Figures S4–S7).

FIGURE 2.

Goodness of Fit (GOF) for PCABs. (A) Observations versus population prediction. (B) Observations versus individual prediction. (C) Individual weighted residuals versus individual predictions. (D) Conditional weighted residuals versus time.

Visual predictive checks (VPCs) further confirmed the adequacy of the model in representing both central tendency and variability across the full range of observations (Figure 3). The observed percentiles aligned well with the corresponding prediction intervals, indicating that the model successfully captured the dynamic pH and concentration profiles across drugs, dose levels, and timing of drug and food administration.

FIGURE 3.

Visual Predictive Checks (VPCs) of PCABs. Left 4 panes (A) are VPC for plasma drug concentration, right 4 panes (B) for pH. The areas are confidence intervals of prediction (blue for 5, 95th percentile, red for median prediction), and the lines are observations (blue for 5, 95th percentile, red for median observation).

Numerical evaluation of model robustness was conducted through nonparametric bootstrapping with 500 replicates. Of these, 449 runs converged successfully, and the final parameter estimates consistently fell within the 95% confidence intervals of the bootstrapped distributions (Figure S8). Most estimates were also within ±1 standard deviation of the bootstrap mean, further confirming model stability and reliability. The high bootstrap success rate and low relative standard errors (RSE) across parameters support the robustness and generalizability of the model structure.

Together, the diagnostic results demonstrate that the model provides an adequate fit to the observed data, appropriately characterizes variability across multiple levels (within and between drugs), and is suitable for simulation‐based applications in drug development and dosing strategy evaluation.

3.4. Simulation

The simulations aimed to evaluate whether the final model could accurately reproduce intragastric pH behavior under steady‐state conditions and diverse meal timing schedules. A summary of the simulation results in a typical dose of drug and response surface is presented below (Table 3, Figure 4).

TABLE 3.

Statistical summary of simulated drug pharmacodynamics at typical doses, derived from the final model and comparison between simulation and observed levels of pH 4 ≥ HTR (holding time ratio).

Drug		Tegoprazan	YH4808	Fexuprazan	Vonoprazan
Dose (mg)		50	100	40	20
Day 1	pH level	4.1 ± 1.59	3.42 ± 1.57	4.19 ± 1.55	4.42 ± 1.65
	pH 4 ≥ duration (h)	12.69 ± 4.94	8.71 ± 4.17	13.32 ± 5.74	14.72 ± 5.91
	pH 4 ≥ HTR	53.43 ± 20.82	36.68 ± 17.54	56.09 ± 24.17	62.00 ± 24.87
Day 7	pH level	4.38 ± 1.62	3.64 ± 1.64	4.74 ± 1.53	5.03 ± 1.61
	pH 4 ≥ duration (h)	14.56 ± 5.5	10.2 ± 4.95	16.7 ± 5.76	18.15 ± 5.53
	pH 4 ≥ HTR	60.66 ± 22.93	42.5 ± 20.64	69.6 ± 23.98	75.63 ± 23.06
Reported pH 4 > HTRs		52%–68%	43%	55%–70%	83%–96%

Note: Each drug was given orally once a day for 7 days (q.d.). pH 4 ≥ duration (h): Cumulative time (in hours) during which intragastric pH ≥ 4 within a 24‐h period. HTR: pH ≥ 4 holding time ratio in a day (%), Reported value is mean ± standard deviation.

FIGURE 4.

Population prediction‐based percentages of the gastric pH maintained above 4 depending on the dose of tegoprazan and time of dosing (TOD). TOD is the time difference between meal and drug administration. The negative TOD is when a drug is given earlier than the meal, while the positive TOD means the drug was given after the meal.

4. Discussion

This study presents a population PK/PD model for PCABs, developed through a multi‐level population framework [22]. By integrating clinical data across drugs, studies, and dosing regimens, the model captures both drug‐specific pharmacology and physiological drivers of intragastric pH. This multi‐leveled mixed‐effect population approach facilitated the integration of published and internal data, enabling quantitative insights that would be difficult to achieve through individual studies alone.

The model incorporates physiological rhythms, food effects, and the feedback effect, enabling a robust and mechanistic understanding of the interactions between drug action and gastric pH. The circadian component, modeled using cosine functions, successfully captured the diurnal variation in gastric pH, characterized by lower levels during the daytime and a rise at night, which is consistent with established clinical findings. Pharmacokinetic parameters such as absorption rate (Ka), clearance (CL), and volume of distribution (V _d) were estimated within expected ranges and showed consistency across different PCABs, supporting the structural validity of the model.

The feedback mechanism was modeled with a Gaussian function, reflecting the known pH‐dependent solubility and absorption behavior of PCABs. The estimated pH range for maximal absorption was consistent with published data on PCAB bioavailability. For example, in the case of fexuprazan, optimal absorption was observed around pH 4, with reduced solubility reported at both low (pH 1.2) and high (pH 6.8) pH levels [23]. This pattern supports the physiological plausibility of a bell‐shaped absorption profile and reinforces the relevance of our model structure.

While previous models—such as those developed by Jeong et al. and Kim et al.—have effectively described PK/PD relationships, they did not explicitly incorporate dynamic feedback between pH and drug absorption. Compared to the approach proposed by Chung et al., our model introduces a more refined feedback mechanism, allowing for a more detailed representation of the bidirectional interaction between intragastric pH and PCAB bioavailability. This refinement may enhance the model's ability to capture nuanced absorption behaviors across varying gastric environments.

Comparison with existing models, such as Jeong et al. for tegoprazan and Kim et al. for fexuprazan, suggests that our approach may offer improved predictive performance. While previous models employed Fourier‐ or ADAM‐based frameworks and placed less emphasis on explicitly modeling food–pH–drug interactions, we sought to complement these efforts by incorporating such interactions directly through a scaling term. This allowed us to separate the respective contributions of food and drugs to pH modulation, supporting clearer clinical interpretation.

The drug‐effect scaling parameter S _d was further summarized as a pharmacodynamic potency index (PPI), as defined in the Methods, to facilitate cross‐drug comparison on a concentration scale. Using this index, the relative pharmacodynamic potency of the four PCABs was ranked as vonoprazan (24.2 nM) > fexuprazan (45.6 nM) > YH4808 (80.7 nM) > tegoprazan (286 nM). This ordering closely paralleled the available in vitro IC₅₀ values for H⁺/K⁺‐ATPase inhibition (vonoprazan: 19 nM [24], fexuprazan: 25 nM [8], YH4808: unknown, tegoprazan: 520 nM [25]), indicating that the model‐derived PPI recapitulates known potency differences across the class. Although the PPI is not an in vitro binding constant and inevitably reflects clinical context (e.g., dose range, study design, and PK–PD nonlinearity), its close numerical alignment with IC₅₀‐level information supports the mechanistic plausibility of the model and underscores that the estimated drug‐effect scaling parameters capture clinically relevant differences in pharmacodynamic strength. In addition, the SCALE parameter, which defines the pH level associated with maximal absorption in the feedback function, showed a trend that was broadly consistent with known pKa values for the PCABs. The Empirical Bayes estimates for SCALE followed the order vonoprazan (0.147), fexuprazan (0.0585), YH4808 (−0.0766), and tegoprazan (−0.129), which is directionally aligned with the reported pKa values (vonoprazan: 9.06, fexuprazan: 8.4, tegoprazan: 5.1; no pKa information available for YH4808). While this relationship is not expected to be one‐to‐one due to differences in formulation, study design, and gastric physiology, the concordant ordering suggests that the model‐estimated SCALE parameter captures a mechanistically reasonable shift in the optimal pH window for absorption across drugs, complementing the potency ranking provided by the PPI.

The diagnostics demonstrated sufficient model performance. The VPCs confirmed that observed values were well‐captured within the model's prediction intervals. Bootstrap analysis further validated parameter robustness, with final estimates consistently falling within the z‐score ±1 in each resampled parameter's distributions. All parameters were contained within the interquartile range (25th to 75th percentiles), suggesting that stable and reliable parameter estimates were sustained.

Nonetheless, some parameters should be interpreted with caution given the literature‐based, digitized nature of the dataset. For K _a, reliance on log‐scale concentration–time profiles with relatively sparse sampling in the absorption phase likely inflated RSEs and limited the precision of inferences regarding very early (e.g., first‐hour) PK behavior. For the baseline pH parameter (Base), aggregation of study‐level means across heterogeneous sites, populations, and assay conditions implies that unresolved between‐study differences are absorbed into this term rather than captured by explicit covariates.

In addition to these data‐driven limitations, a discrepancy observed in the YH4808 goodness‐of‐fit plots may stem from model simplification: while previous studies have characterized YH4808 using a two‐compartment structure, a single‐compartment model was adopted here to standardize comparisons across drugs. For drug‐specific analysis, however, adopting a two‐compartment structure may yield improved precision and a more accurate representation of the drug's pharmacokinetic behavior.

The simulation results closely reproduced the meal timing‐dependent pH profiles observed by Deok Y. Yoon et al. (2021) with similar settings, demonstrating strong agreement between model prediction and clinical data [26]. A single dose of tegoprazan produced a marked elevation in gastric pH within a few hours—an effect well captured by the model and consistent with clinical findings [4, 27]. Overall, the correspondence between our model outputs and literature reports builds confidence in the validity of the analysis.

In addition, the simulation also produced a calculation of high variation in intragastric pH under the same conditions. The predicted variability was not sufficient to yield statistically significant differences between dosing regimens. This observation was further supported by simulations incorporating inter‐individual variability and residual error, in which the differences between pre‐ and post‐meal administration became minimal and clinically indistinguishable (Figures S9–S12).

At steady state, the predicted mean percentage of time with intragastric pH maintained above 4 in steady‐state was 60% for tegoprazan 50 mg, 42% for YH4808 100 mg, 69% for fexuprazan 40 mg, and 75% for vonoprazan 20 mg. These values are consistent with the simulated Day 7 holding‐time ratios summarized in Table 3, and they closely aligned with the reported clinical ranges for each drug: tegoprazan (52%–68% [28, 29, 30]), YH4808 (43% [31]), fexuprazan (55%–70% [30, 32]), and vonoprazan (83%–96% [30, 33]). This concordance supports the model's capacity to accurately represent and differentiate the pharmacodynamic profiles of multiple PCABs under unified conditions.

The simulation study with a response surface analysis provided further insight into the relationship between dosing timing and pharmacodynamic outcomes. In tegoprazan, both pre‐ and post‐meal administration of PCABs generally appeared more effective than administration during meals in maintaining intragastric pH. Notably, post‐meal dosing showed a more favorable profile at higher doses over 50 mg, and this trend became more pronounced under steady‐state conditions. This reflects not only the drug's inherent pharmacological, physicochemical properties but also the transient pH‐elevating effect of food intake. Model‐based predictions reflected the known difference between PPIs and PCABs regarding food interaction. While PPIs are sensitive to food effects due to delayed absorption and suboptimal synchronization with proton pump activity [34], the simulations indicated that PCABs, which are acid‐stable and rapidly absorbed, are less influenced by food intake.

Furthermore, each PCAB exhibited distinct dosing strategies to sustain high pH holding time ratios (HTRs) during the non‐steady state period, due to their unique behavior within the gastric pH environment and intrinsic ADME characteristics. These differences, however, tended to diminish as the steady state was achieved. This suggests that even within the same PCAB class, drug‐specific factors, such as pKa values and absorption or metabolic profiles, may interact in a nonlinear manner to influence therapeutic outcomes. Consequently, different administration strategies may be required during the initial treatment phase depending on the specific properties of each drug. For example, although avoiding drug administration during meals may contribute to maintaining higher pH levels, the preferable timing of administration can differ between drugs such as tegoprazan and fexuprazan, particularly during the early treatment period, due to their distinct pharmacokinetic and pharmacodynamic properties (Figures S9–S12).

These results suggest that gapping time between food intake may actually enhance PCAB therapy by further elevating intragastric pH during the early hours, particularly during the initial stage of therapeutics and under low‐dose conditions (e.g., < 50 mg for tegoprazan), but mostly ignored due to the high variability in PK‐PD (pH) problem. The synergy highlights the importance of considering both pharmacologic and physiologic contributors to acid suppression when designing treatment regimens. As we have confirmed in the simulation study, several clinical studies have also suggested that meal‐induced buffering can enhance pH control in early time period, reinforcing the potential value of coordinated drug–meal timing during initial therapy [35, 36].

The hierarchical structure of our model, which incorporates drug‐specific parameters at a super‐level, provides a scalable and flexible framework that accommodates inter‐drug and inter‐study variability. This enables robust evaluation of drug‐specific differences and simulation of pharmacological behavior across diverse clinical settings. Furthermore, by capturing high‐variability and mechanistically complex PK–PD dynamics in a unified framework, the model facilitates more refined statistical interpretations. This quantitatively trained structure may offer a basis for revisiting previously or potentially inconclusive findings in complex gastro‐pharmacological problems by providing enhanced mechanistic clarity [5, 37].

While the current analysis was limited to datasets from healthy subjects, the structure of the model is readily adaptable for future evaluation in patient populations when such data become available.

In summary, this study demonstrates that a physiologically rational, multi‐level population PK/PD model that can effectively capture the complex interplay between drug effects, food intake, and circadian rhythms in intragastric pH regulation. The model supports quantitative comparisons across PCABs, facilitates rational dose optimization, and informs the design of future trials. Utilizing the integrated (multi‐level) model of the four drugs, it will be possible to derive the target product profile (TPP) and differentiating factors for a new PCAB from a PK/PD perspective. Moving forward, this framework may be extended to other acid‐related indications and further refined by incorporating additional mechanistic elements such as dissolution kinetics, patient‐specific covariates, and the integration of intragastric pH dynamics with drug–drug interaction mechanisms to expand the scope of interaction prediction. Ultimately, this work illustrates the value of combining mechanistic pharmacology with meta‐analytic modeling techniques to support model‐informed drug development (MIDD) for next‐generation acid suppressants.

5. Conclusion

This study presents a physiologically and mechanistically informed population PK/PD model for potassium‐competitive acid blockers (PCABs), developed through multi‐level population analysis across multiple drugs and clinical datasets. By incorporating circadian rhythm, food effects, and pH‐dependent absorption, the model effectively disentangles physiological and pharmacological drivers of intragastric pH modulation.

The model reproduced observed PK/PD profiles and yielded interpretable parameters, while simulations highlighted the potential synergy between drug effect and meal‐induced buffering, particularly in the early, non‐steady‐state phase. These results support the model's application in optimizing medication strategies and evaluating drug‐meal interactions.

With its multilevel structure and strong diagnostic performance, the model offers a scalable platform to inform the development and refinement of both current and next‐generation PCAB therapies within a model‐informed drug development (MIDD) framework.

Author Contributions

W.J. and J.L. wrote the manuscript. W.J. and J.L. designed research. W.J., J.L., T.S., and H.J. performed the research. W.J., J.L., H.J., H.Y., S.L., and J.C. analyzed the data. H.Y., S.L., and J.C. contributed to funding acquisition and supervision.

Funding

This study was supported by Chungnam National University, Institute of Information & Communications Technology Planning Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS‐2022‐00155857, Artificial Intelligence Convergence Innovation Human Resources Development [Chungnam National University]), National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT; No. RS‐2023‐00278597, RS‐2022‐NR069643, RS‐2022‐NR070856, Senior Health Convergence Research Center based on Life Cycle [Chungnam National University]), Korea Environmental Industry & Technology Institute (KEITI) through Core Technology Development Project for Environmental Diseases Prevention and Management (RS‐2021‐KE001333), funded by the Korea Ministry of Environment (MOE), a grant of the Korea Machine Learning Ledger Orchestration for Drug Discovery Project (K‐MELLODDY), funded by the Ministry of Health & Welfare and Ministry of Science and ICT, Republic of Korea (grant number: RS‐2024‐00460694), the Korea Institute of Toxicology (KIT) Research Program (no. 2710008763, KK‐2401‐01), Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI) grant funded by the Ministry of Health & Welfare, Republic of Korea (grant number: RS‐2024‐00336984, RS‐2025‐02306055), supported by the Ministry of Trade, Industry, and Energy (MOTIE), Korea, under the “Infrastructure program for industrial innovation” supervised by the Korea Institute for Advancement of Technology (KIAT) (RS‐2024‐00434342). This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS‐2025‐25397599).

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1: psp470181‐sup‐0001‐DataS1.docx.

Data S2: psp470181‐sup‐0002‐DataS2.docx.

Data S3: psp470181‐sup‐0003‐DataS3.docx.

Jung W., Lee J., Jeon H., et al., “A Mechanism‐Based Multi‐Level Population PK/PD Model for Potassium‐Competitive Acid Blockers,” CPT: Pharmacometrics & Systems Pharmacology 15, no. 1 (2026): e70181, 10.1002/psp4.70181.