# Killing several birds with one stone: A multi-indication population pharmacokinetic model and Bayesian estimator for enteric-coated mycophenolate sodium

Yeleen Fromage, Hamza Sayadi, Kevin Koloskoff, Pierre Marquet, Marc Labriffe, Caroline Monchaud, Jean-baptiste Woillard

## ► To cite this version:

Yeleen Fromage, Hamza Sayadi, Kevin Koloskoff, Pierre Marquet, Marc Labriffe, et al. Killing several birds with one stone: A multi-indication population pharmacokinetic model and Bayesian estimator for enteric-coated mycophenolate sodium. British Journal of Clinical Pharmacology, 2024, 10.1111/bcp.16374. hal-04996512

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Submitted on 19 Mar 2025

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ORIGINAL ARTICLE

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BRITISH
PHARMACOLOGICAL
SOCIETY

# Killing several birds with one stone: A multi-indication population pharmacokinetic model and Bayesian estimator for enteric-coated mycophenolate sodium

Yeleen Fromage<fnref n="1" /> | Hamza Sayadi<fnref n="1" /> | Kevin Koloskoff<fnref n="2" />,<fnref n="3" /> | Pierre Marquet<fnref n="1" />,<fnref n="2" /> ID
Marc Labriffe<fnref n="1" />,<fnref n="2" /> ID | Caroline Monchaud<fnref n="1" />,<fnref n="2" /> | Jean-Baptiste Woillard<fnref n="1" />,<fnref n="2" /> ID

**Correspondence**

Jean-Baptiste Woillard, Univ. Limoges, Inserm U1248 P&T, 2 rue du Pr Descottes, F-87000 Limoges, France.

Email: jean-baptiste.woillard@unilim.fr

**Funding information**

This work is part of the DIGPHAT project which was supported by a grant from the French government, managed by the National Research Agency (ANR), under the France 2030 program, with reference ANR-22-PESN-0017.

**Abstract**

**Aims:** Mycophenolic acid (MPA), the active component of enteric-coated mycophenolate sodium (EC-MPS), exhibits highly variable pharmacokinetics. Only a few population pharmacokinetic (popPK) models and Bayesian estimators (MAP-BE) exist for estimating MPA AUC and all in renal transplantation. This study aimed to develop a popPK model and MAP-BE for MPA AUC estimation using a limited sampling strategy (LSS) in solid organ transplant (SOT), haematopoietic stem cell (HSC) recipients and patients with autoimmune diseases (AID) on EC-MPS.

**Methods:** Full and sparse MPA pharmacokinetic profiles were extracted from our ISBA system, split into development (75%) and validation (25%) sets. An additional extraction was performed after the modelling process for external validation. Pharmacokinetic parameters were estimated using Monolix® (SAEM algorithm). Several absorption models (first order, transit, gamma) were compared. AUC*predicted* by MAP-BE and LSS was compared to the all-sample MAP-BE AUC*reference* using Simulx®.

**Results:** We included 153 PK profiles (863 concentration) from 129 patients (116 SOT and HSC, 13 AID), median [min-max] age 45 years [6-80]. A one-compartment model with double-gamma absorption and first-order elimination best fitted the data. The final model included the EC-MPS indication and inter-occasion variability on gamma rate constants. Main PK parameters (mean ± SD) were CI/F = 4.99 ± 2.22 L/h and Vd/F = 12.60 ± 0.08 L. The optimal LSS at 20 min, 2 h and 4 h post-dose showed good performance in both validation sets (rMPE -2.67% and -4.91%; RMSE 13.55% and 13.47%).

**Conclusions:** The double-gamma absorption model provided an accurate fit. The MAP-BE offers a tool for EC-MPS dose individualization in SOT, HSC and AID patients.

<footnote n="1">¹Department of Pharmacology, Toxicology and Pharmacovigilance, CHU de Limoges, Limoges, France</footnote>

<footnote n="2">²Pharmacology & Transplantation, INSERM U1248, Université de Limoges, Limoges, France</footnote>

<footnote n="3">³ExactCure, Nice, France</footnote>
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### KEYWORDS

haematopoietic stem cell recipients, MAP-BE, mycophenolate sodium, population pharmacokinetics, solid organ transplantation

# 1 | INTRODUCTION

**Mycophenolic acid** (MPA), administered as either mycophenolate mofetil (MMF) or enteric-coated mycophenolate sodium (EC-MPS), has become a cornerstone in the immunosuppressive regimen for organ transplant recipients.¹ Over time, there has been growing recognition of the potential for personalized dosing of this drug in various solid organ and stem cell transplantations, as well as in off-label indications like autoimmune diseases including systemic lupus erythematosus and lupus nephritis.²⁻⁴ Gastrointestinal adverse events are commonly observed with MMF treatment.⁵ In an effort to mitigate these adverse events and enhance clinical outcomes, EC-MPS was developed.⁶ It demonstrates similar efficacy and safety profiles compared to MMF.⁷,⁸ Unlike the rapid release of MPA into the stomach from the MMF prodrug, the enteric coating of EC-MPS enables delayed release of MPA into the small intestine.⁹,¹⁰

Given the substantial inter-individual variability in MPA response to a standard dose and its narrow therapeutic window, therapeutic drug monitoring (TDM) is strongly recommended for MPA.⁴ As clinical outcomes have been linked to the area under the curve (AUC) of MPA, and there is a poor correlation between C₀ and AUC, estimating MPA AUC through TDM is highly recommended. Consequently, limited sampling strategies (LSSs) based on population pharmacokinetic (popPK) models and maximum a posteriori Bayesian estimator (MAP-BE) of individual PK parameters have been developed to facilitate routine estimation of MPA AUC. Therefore, numerous popPK models have been elaborated for the MMF formulation of MPA, using methods such as iterative two-stage Bayesian (IT2B), non-parametric or nonlinear mixed-effect (NLME) approaches.¹¹⁻¹⁶ It is noteworthy that a broad range of indications has been encompassed, including all solid organ transplantations, autoimmune diseases and various adult and paediatric populations.

However, due to the unpredictable absorption kinetics,¹⁷ developing a feasible limited sampling strategy based on samples in the 4 h post dosing for EC-MPS is challenging.¹⁸ Obtaining a complete AUC from time 0 to 12 h (AUC₀⁻₁₂) is likely necessary to accurately assess MPA exposure in EC-MPS-treated patients, which may limit the feasibility of TDM for this drug.⁶,¹⁷

Based on our current knowledge, there are only two popPK models for EC-MPS, both conducted in a Chinese population of renal transplant recipients.¹⁹,²⁰ Additionally, there is a model established in Caucasian renal transplant patients receiving MMF and EC-MPS.⁶ Thus, there are as yet no validated popPK models in populations with broader indications.

In this context, the aims of this study were (i) to construct a popPK model of EC-MPS in solid organ or stem cell transplant recipients and patients with auto-immune diseases and (ii) to devise a

### What is already known about this subject

* Mycophenolic acid pharmacokinetics are highly variable, requiring therapeutic drug monitoring for optimal dosing.

* Existing population pharmacokinetic (popPK) models and Bayesian estimators (MAP-BE) primarily target mycophenolate mofetil, with limited models for enteric-coated mycophenolate sodium (EC-MPS) in renal transplant patients only.

* EC-MPS's unpredictable absorption poses challenges for accurate popPK model development.

### What this study adds

* This study developed a popPK model and MAP-BE for EC-MPS across solid organ transplant, haematopoietic stem cell transplant and autoimmune disease patients.

* The model addresses MPA pharmacokinetic variability, enabling accurate AUC estimation.

* The MAP-BE and limited sampling strategies provide a tool for individualized EC-MPS dosing across all indications.

MAP-BE for precise estimation of individual pharmacokinetic parameters and EC-MPS exposure indices based on an LSS.

# 2 | METHODS

## 2.1 | Data set and patients

Pseudonymized data were extracted from the Bayesian dosing adaptation platform for immunosuppressants (ISBA) at Limoges University Hospital (abis.chu-limoges.fr). This included all types of indications: renal, hepatic, cardiac, pulmonary and bone marrow transplants, as well as autoimmune diseases (lupus and nephrotic syndrome). When submitting a request on the ISBA ABIS 3.0 platform, the following information is mandatory: patient age, date of immunosuppressive treatment initiation and indication, concomitant immunosuppressive therapies (number and which ones—*cyclosporine*, *tacrolimus*, *sirolimus*, *everolimus* or others with free text), sampling days and times, analytical dosage methods and total concentrations obtained. This study was approved by the ethics committee with approval number 29-2024-05. A second extraction under the same conditions was subsequently
performed after the modelling process to establish an external validation dataset.

## 2.2 | PK modelling

The first dataset was randomly split, based on PK profiles, into a development dataset (75% of the data) and a validation dataset (25% of the data) using R (version 4.3.1). The population PK analysis was performed using a nonlinear mixed-effect approach based on the Stochastic Approximation Expectation-Maximization (SAEM) algorithm in Monolix.²¹ We set a quantification limit at 0.5 mg/L, retaining data below the limit of quantification in the analysis and handling them using the M4 method.²²

### 2.2.1 | Structural model development

Several structural models were tested to fit the data, including one- or two-compartment models with first-order elimination. To describe absorption, models were considered without delay, with a lag time, using transit compartments, double absorptions (combination of lag time and no delay), and finally, gamma absorption models (with single or double absorption described using gamma distributions) as previously described.¹²,²³,²⁴ This latter absorption model has the capacity to depict the double peak concentration curves commonly observed for MPA.

In summary, the absorption rate $V_a$ in a gamma distribution model can be characterized by:

$$V_a = F.D * [r.f_1(t) + (1-r).f_2(t)]$$

with

$$f_i(t) = \frac{b_i^{a_i}}{\Gamma(a_i)} t^{a_i-1} \exp(-b_i t)$$

where F is the bioavailability, D is the dose, r is the fraction of drug absorbed through the faster phase, $\Gamma$ denotes the gamma function, $a_i$ and $b_i$ are the shape and rate parameters of the gamma distribution. It's noteworthy that if $r=1$, a one-compartment model with single gamma absorption is obtained.

The concentration $C(t)$ is subsequently determined by the equation

$$C(t) = C_0 + FAIV.D \left( r \left( \frac{b_1}{b_1 - \lambda} \right)^{a_1} P[a_i(b_1 - \lambda)t] + (1 - r) \left( \frac{b_2}{b_2 - \lambda} \right)^{a_2} P[a_2(b_2 - \lambda)t] \right) \exp(-\lambda t)$$

where P denotes the incomplete gamma function, $C_0$ is the estimated trough concentration at steady state for a reference dose, FAIV is the

disposition coefficient, $a_i$, $b_i$ the shape and rate parameters of the gamma distribution and $\lambda$ is the disposition rate constant.

Finally, the traditional PK parameters of mean absorption time (MAT), apparent volume of distribution (V/F) and clearance (CL/F) are derived from the gamma absorption parameters according to the following equations:

$$MAT_i = \frac{a_i}{b_i}$$

$$V/F = \frac{100}{FAIV}$$

$$CL/F = \frac{Dose}{AUC}$$

Additive, proportional and combined residual error models were investigated. Inter-individual and inter-occasion variability was described using an exponential model, except for the parameter r of the double gamma absorption, which followed a logit-normal distribution (values constrained between 0 and 1). Inter-occasion variability (IOV) was studied, based on sequential visits for each patient (visit n + 1, n + 2, etc.). The best structural model and residual error model were selected based on the -2-log likelihood (-2 LL) as well as the precision of the parameters (relative standard error [RSE] < 50%) and the visual inspection of goodness-of-fit plots.

### 2.2.2 | Covariates investigation

The covariates tested on PK parameters included immunosuppressive co-treatments (absence, ciclosporin and others), analytical methods (high-performance liquid chromatography coupled with tandem mass spectrometry and others), indication ((i) renal, hepatic, (ii) cardiac, pulmonary, bone marrow transplants and (iii) autoimmune disease), and sex, treated as qualitative variables. Patient age and time since transplantation were treated as continuous quantitative variables. Scatter plots and Pearson correlation coefficients were drawn between the empirical Bayes estimates and the continuous covariates. Boxplot and analysis of variance (ANOVA) were used for the categorical ones.

Covariates were incorporated individually into the structural model using a forward inclusion and backward elimination approach. Covariates that led to a reduction greater than or equal to 3.84 ($\chi^2$ distribution at 95%) in the -2LL were retained in the structural model.

Categorical covariates were introduced as follows:

$$\theta_j = \theta_{jTPV} * e^{\theta_{COVi} * COVi}$$

where $\theta_j$ is the value of the PK parameter j, $\theta_{jTPV}$ is the mean value of j and $\theta_{COVi}$ is the parameter estimated to represent the effect of the ith covariate (COVi) when its value = 1.

Continuous covariates were investigated using the following equation:
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$$ \theta_j = \theta_{jTPV} * \left( \frac{COVi}{COVi_{median}} \right)^{\theta_{COVi}} $$

where $\theta_j$ is the value of the PK parameter j, $\theta_{jTPV}$ is the mean value of j and $\theta_{COVi}$ is the parameter estimated to represent the effect of deviation from the median for the ith covariate (COVi).

Finally, the set of equations for log or logit-normal parameters and exponential IIV were:

$$ \log(C_0) = \log(C_{0 pop}) + \eta_{C0} $$

$$ \log(b_1) = \log(b_{1 pop}) + \eta_{b_1} + \eta_{OCC} b_1 $$

$$ \log(b_2) = \log(b_{2 pop}) + \beta_{b2\text{cardiac, pulmonary, bone marrow transplantation}} \times [\text{Indication} = \text{cardiac, pulmonary, bone marrow transplantation}] + \beta_{b2\text{autoimmune diseases}} \times [\text{Indication} = \text{autoimmune diseases}] + \eta_{b2} $$

$$ \log(\text{FAIV}) = \log(\text{FAIV}_{\text{pop}}) + \eta_{\text{FAIV}} $$

$$ \log(\alpha) = \log(\alpha_{\text{pop}}) + \eta_{\alpha} $$

$$ \log\left(\frac{r}{1-r}\right) = \log\left(\frac{r_{\text{pop}}}{1-r_{\text{pop}}}\right) $$

### 2.2.3 | Model evaluation

The final model was evaluated using visual inspection of goodness-of-fit plots and the prediction corrected visual predictive check (pcVPC) in the development, validation and external datasets. Additionally, bootstrapping with 500 samples was performed to assess parameter stability, and numerical predictive checks were conducted.

### 2.2.4 | Bayesian estimators

The final model developed was used as a prior to build a MAP-BE allowing estimation of AUC$_{predicted}$ using a three-sample LSS. Several LSSs using samples within the first 8 h post dose were explored in the development set and AUC$_{predicted}$ was compared to the all-sample MAP-BE AUC$_{reference}$ based on relative mean prediction error (rMPE = bias) and root mean square error (RMSE = imprecision).

$$ \text{MPE}(\%) = \frac{1}{N} * \sum_{i=1}^{n} \left( \frac{\text{AUC}_{\text{predicted}} - \text{AUC}_{\text{reference}}}{\text{AUC}_{\text{reference}}} \right) * 100 $$

$$ \text{RMSE}(\%) = \frac{1}{N} * \sqrt{\sum_{i=1}^{n} \left( \frac{\text{AUC}_{\text{predicted}} - \text{AUC}_{\text{reference}}}{\text{AUC}_{\text{reference}}} \right)^2} * 100 $$

To avoid any bias in the AUC$_{reference}$ estimation, we only kept the PK profiles having at least six samples in the validation dataset.

Subsequently, the predictive performance of the MAP-BE based on the best LSS was evaluated in the validation and external datasets by comparing RMSE and rMPE to the AUC$_{reference}$ and the number of patients having an absolute rMPE > 20%. Acceptance criteria were set at ≤ 10% and ≤ 25% for MPE and RMSE, respectively, following the consensus conference guidelines.⁴

## 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 2021/22.

# 3 | RESULTS

## 3.1 | Data collection

Information extracted from the ISBA database yielded 153 PK profiles (comprising 863 concentrations) obtained from 129 patients, encompassing 116 individuals with SOT and HSC transplantations and 13 with AID. All patients were receiving Myfortic® (Novartis Pharma AG, Basel, Switzerland). As this study is retrospective and based on real-world data, variability in sampling design, dosing regimen and co-medications was unavoidable, inherent to observational studies outside of controlled clinical trial conditions. For the first extraction, the number of samples per profile ranged from 3 to 11 (Q1 = 3, median = 5, Q3 = 8.5), with EC-MPS doses spanning from 180 to 1440 mg. In the external validation dataset from the second extraction, the sample count per profile ranged from 6 to 9 (Q1 = 6, median = 7, Q3 = 9), with EC-MPS doses between 360 and 720 mg. The number of associated immunosuppressive co-treatments, in addition to EC-MPS were classified as either no co-treatment, ciclosporin (due to its impact on the enterohepatic cycle and the PK of MPA), or other immunosuppressive co-treatments (tacrolimus, everolimus, sirolimus, corticosteroids). The final population characteristics are summarized in Table 1. Note that one patient was excluded due to aberrant MPA concentrations (presented in Table S1 in the Supporting Information) and another because he had only one trough concentration measurement. Ultimately, the spaghetti plot of observed concentrations vs. time for the patients retained in the development dataset is shown in Figure 1, demonstrating the heterogeneity of PK profiles. Regarding the external validation set, one out of 11 patients was excluded because the nine reported blood concentrations were below 2.8 mg/L over a 12-h sampling period. In the initial dataset, 17 patients had more than one occasion, with each patient having between two and five occasions. The intervals between visits were variable, with an average interval of 201 days (range: 2–813 days).
<table><caption>TABLE 1 Demographic characteristics of the profiles used in the different datasets.</caption><thead><tr><th>Variable</th><th>Development data set</th><th>Validation data set</th><th>Validation data set for LSS</th><th>Total</th><th>External data set</th></tr></thead><tbody><tr><td>Number of occasions</td><td>112</td><td>39</td><td>16</td><td>151</td><td>11</td></tr><tr><td>Number of patients</td><td>95</td><td>32</td><td>13</td><td>127</td><td>11</td></tr><tr><td>Number of paediatric patients (age &lt; 18 years old)</td><td>16</td><td>4</td><td>2</td><td>20</td><td>0</td></tr><tr><td>Number of occasions with six or more samples</td><td>46</td><td>16</td><td>16</td><td>62</td><td>11</td></tr><tr><td>Age (years)*</td><td>44 (6–80)</td><td>47 (13–78)</td><td>47.50 (13–78)</td><td>45 (6–80)</td><td>58(18–75)</td></tr><tr><td>Sex (male/female/unknown)* per occasion</td><td>38(34%)/32(29%)/42(37%)</td><td>16(41%)/9(23%)/14(36%)</td><td>5(31%)/3(19%)/8(50%)</td><td>54(36%)/41(27%)/56 (37%)</td><td>5(46%)/2(18%)/4(36%)</td></tr><tr><td>Sex (male/female/unknown) per patient</td><td>34(36%)/28(29%)/33(35%)</td><td>14(44%)/8(25%)/10(31%)</td><td>5(38%)/3(23%)/5(38%)</td><td>48(38%)/36(28%)/43 (34%)</td><td>5(46%)/2(18%)/4(36%)</td></tr><tr><td>Amount (mg) per intake</td><td>360 (180–1440)</td><td>540 (180–720)</td><td>540(180–720)</td><td>360 (180–1440)</td><td>540(360–720)</td></tr><tr><td>Time (days) between EC-MPS initiation and sampling*</td><td>788.50 (6–10 488)</td><td>794 (30–8303)</td><td>808.50(106–8303)</td><td>771 (6–10 488)</td><td>991(82–6332)</td></tr><tr><td>Indication (Renal, hepatic, cardiac, pulmonary, bone marrow transplantations, autoimmune diseases) per occasion*</td><td>64 (57%)/13(11%)/8(7%)/13(12%)/2 (2%)/12(11%)</td><td>28 (72%)/4(10%)/2(5%)/1(3%)/0/4(10%)</td><td>15(94%)/0/0/0/0/1(6%)</td><td>92(61%)/17(11%)/10(7%)/14(9%)/2(1%)/16(11%)</td><td>8(73%)/2(18%)/0/0/0/1(9%)</td></tr><tr><td>Indication (Renal, hepatic, cardiac, pulmonary, bone marrow transplantations, autoimmune diseases) per patient</td><td>54 (57%)/12(13%)/7(7%)/10(11%)/1(1%)/11(11%)</td><td>23 (72%)/4(13%)/2(6%)/1(3%)/0/2(6%)</td><td>12(92%)/0/0/0/0/1(8%)</td><td>77(60%)/16(13%)/9(7%)/11(9%)/1(1%)/13(10%)</td><td>8(73%)/2(18%)/0/0/0/1(9%)</td></tr><tr><td>Immunosuppressive co-treatment: None*</td><td>8</td><td>4</td><td>2</td><td>12</td><td>1</td></tr><tr><td>Immunosuppressive co-treatment: ciclosporin*</td><td>13</td><td>3</td><td>1</td><td>16</td><td>0</td></tr><tr><td>Immunosuppressive co-treatment: others*</td><td>99</td><td>32</td><td>13</td><td>131</td><td>10</td></tr><tr><td>Analytical method *(HPLC/others)</td><td>102(91%)/10(9%)</td><td>33(85%)/6(15%)</td><td>14(88%)/2(12%)</td><td>135(89%)/16(16%)</td><td>11(100%)/0</td></tr></tbody></table>

Note: Data are expressed as median (min-max), effect of covariates with a "***" were investigated on PK parameters.
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<figure><img src="image_7.png" /><figcaption>**FIGURE 1** Spaghetti plot of observed concentration as function of time; blue circles are observed concentration and blue lines are PK profiles for each occasion.</figcaption></figure>

## 3.2 | PK modelling

### 3.2.1 | Structural model

A single-compartment model incorporating first-order elimination and a double gamma distribution absorption best described the data. Among alternative structural PK models, the double absorption model demonstrated superior performance based on –2LL and BIC, as detailed in Table S2 in the Supporting Information. The additive residual error model was preferred for its superior alignment with individual MPA PK profiles. Figure 2 shows nine representative patients, showing the accurate description of individual PK profiles with this model. The complete set of PK profiles from the development dataset is available in Figure S1 in the Supporting Information.

### 3.2.2 | Covariate analysis

Due to the high shrinkage observed in some parameters of the empirical Bayesian estimates (EBEs), model evaluation was conducted using the conditional distribution of individual parameters. The indication was identified as a covariate significantly linked to the rate parameter of gamma distribution $b_2$. Incorporating this covariate resulted in a reduction of –2LL by 177 (from 3365 to 3188) and a decrease in BIC by 168 (from 3436 to 3268). Furthermore, including this covariate reduced the interindividual variability $wb_2$ from 1.32 to 0.52. Some

models that considered the impact of other covariates on different parameters exhibited similar –2LL and BIC values. However, the relative error (%) and imprecision were too high for these models to be retained. The PK parameters of the final model with covariates are presented in Table 2; they were all estimated with a good precision (RSE < 48%). Only the impact of the beta _b_2_autoimmune diseases covariate was low and estimated with extreme imprecision (–17% impact with a 188% RSE) indicating a non-significant effect, and thus, can be disregarded.

### 3.2.3 | Model evaluation

The diagnostic plots, depicted in Figure 3, show individual weighted residual against time and individual predictions uniformly and normally distributed around 0 (Figure 3C,D). An excellent correlation was observed between individual predictions and observations (Figure 3B). Additionally, the pcVPCS plot of the final model overlaid with observations from both development, validation and external datasets are presented in Figure 4. The observation percentiles align closely with simulated percentiles from the development dataset. Note that the model can also describe the validation set and the external dataset, showing that this can be transposed and generalized. Numerical predictive checks and distribution plots, displayed as boxplots based on bootstrapping with n = 500 samples, are available in the Figure S2 and S3 in the Supporting Information, respectively.
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<figure><img src="image_9.png" /><figcaption>**FIGURE 2** Typical example of pharmacokinetic profiles; blue circles are observed concentrations and solid purple lines are model predictions.</figcaption></figure>

### 3.2.4 | Bayesian estimators

In the development dataset, the 0.3-2-4 h post-dose LSS demonstrated the best performance and was subsequently chosen for evaluation in the validation dataset (Table 3). This LSS showed excellent performance and accuracy, with an rMPE of -2.67% and an RMSE of 13.55%. The percentage of patients with a bias greater than ±20% was less than 15%.

In the external dataset, the same LSS tested were applied to the 10 profiles having at least six samples, resulting in excellent performance (rMPE of -4.91%, RMSE of 13.47% and 10% of patients with a bias of ±20%). Note that a comparison of different sampling strategies including the patient excluded is available in Table S3 in the Supporting Information. Additionally, the prediction error (%) of AUC for the established model and various LSSs, as well as the performance of all tested LSSs on both the test and external datasets, are provided in Table S4 and Figure S4 in the Supporting Information.

## 4 | DISCUSSION

In this study, we developed a popPK model of EC-MPS describing accurately multiple indications and derived a MAP-BE based on an LSS. The model that best described the data was a double gamma absorption model. While this model had previously been shown to be effective for MMF,²⁴ to our knowledge, it is the first time it has been used for EC-MPS. Our work on EC-MPS confirmed the ability of this model to capture complex absorption and it was better suited than traditional absorption modelling, such as tlag and transit compartments.

The parameters of the final model were accurately estimated using the SAEM algorithm (RSE ≤ 47.1%), as well as the associated inter-individual and inter-occasion variability parameters (RSE ≤ 44.9% and 28.5%, respectively). Although the covariate effect of autoimmune disease showed a low impact and extreme imprecision, indicating a non-significant effect that can be disregarded, we retained it in the model used for pcVPC simulations, as the other two categories
<figure><img src="image_10.png" /></figure>

<table><caption>TABLE 2 Final estimated parameters of the double gamma absorption model.</caption><thead><tr><th rowspan="2">Parameters</th><th rowspan="2">Final model estimate (%RSE)</th><th rowspan="2">Shrinkage of conditional distribution (%)</th><th colspan="5">Bootstrap (n = 500)</th></tr><tr><th>Mean</th><th>P2.5</th><th>Median</th><th>P97.5</th><th>Bias(%)</th></tr></thead><tbody><tr><td>C<sub>0</sub> (mg/L)</td><td>2.21 (6.50)</td><td>-5.76</td><td>2.24</td><td>1.92</td><td>2.24</td><td>2.6</td><td>1.55</td></tr><tr><td>a<sub>1</sub></td><td>1280.97 (0.25)</td><td></td><td>1319.06</td><td>633.19</td><td>1234.08</td><td>2488.69</td><td>2.97</td></tr><tr><td>b<sub>1</sub> (h<sup>-1</sup>)</td><td>418.42 (18.90)</td><td>4.54</td><td>360.16</td><td>131.23</td><td>320.3</td><td>769.85</td><td>-13.92</td></tr><tr><td>a<sub>2</sub></td><td>395.34 (2.30)</td><td></td><td>371.58</td><td>173.71</td><td>343.92</td><td>767.52</td><td>-6.01</td></tr><tr><td>b<sub>2</sub> (h<sup>-1</sup>)</td><td>95.69 (14.40)</td><td>-1.61</td><td>98.52</td><td>32.94</td><td>91.79</td><td>202.53</td><td>2.96</td></tr><tr><td>FAIV (mg/L)</td><td>7.87 (3.35)</td><td>-83.6</td><td>8.55</td><td>6.64</td><td>8.6</td><td>10.61</td><td>8.65</td></tr><tr><td>λ (h<sup>-1</sup>)</td><td>1.81 (7.48)</td><td>4.95</td><td>1.86</td><td>1.39</td><td>1.83</td><td>2.5</td><td>2.83</td></tr><tr><td>r</td><td>0.79 (2.14)</td><td></td><td>0.69</td><td>0.46</td><td>0.69</td><td>0.87</td><td>-13.09</td></tr><tr><td>beta<sub>2</sub> cardiac, pulmonary, bone marrow transplantations</td><td>0.59 (47.1)</td><td></td><td>0.41</td><td>-1.29</td><td>0.5</td><td>1.53</td><td>-31.43</td></tr><tr><td>beta<sub>2</sub> autoimmune diseases</td><td>-0.17 (188)</td><td></td><td>-0.33</td><td>-2.11</td><td>-0.25</td><td>1.33</td><td>99.61</td></tr><tr><td>Residual additive error σ</td><td>1.38 (3.47)</td><td></td><td>1.49</td><td>1.32</td><td>1.46</td><td>1.84</td><td>7.76</td></tr><tr><td colspan="8">Inter-individual variability (%RSE)</td></tr><tr><td>C<sub>0</sub></td><td>0.49 (10.80)</td><td></td><td>0.5</td><td>0.35</td><td>0.49</td><td>0.67</td><td>1.62</td></tr><tr><td>b<sub>1</sub></td><td>0.92 (44.9)</td><td></td><td>0.87</td><td>0.21</td><td>0.89</td><td>1.5</td><td>-6.15</td></tr><tr><td>b<sub>2</sub></td><td>0.52 (16.1)</td><td></td><td>0.68</td><td>0.28</td><td>0.66</td><td>1.12</td><td>32.04</td></tr><tr><td>FAIV</td><td>0.12 (11.00)</td><td></td><td>0.26</td><td>0.1</td><td>0.25</td><td>0.5</td><td>114.39</td></tr><tr><td>λ</td><td>0.44 (14.20)</td><td></td><td>0.52</td><td>0.2</td><td>0.47</td><td>1.1</td><td>18.97</td></tr><tr><td colspan="8">Inter-occasion variability (%RSE)</td></tr><tr><td>b<sub>1</sub></td><td>1.08 (28.50)</td><td></td><td>0.99</td><td>0.38</td><td>1.01</td><td>1.55</td><td>-8.09</td></tr></tbody></table>

Abbreviations: C₀, estimated trough concentration at steady state for a reference dose; a₁ and b₁, shape and rate parameters of the gamma distribution; FAIV, the disposition coefficient; λ, the disposition rate constant; r, fraction of drug absorbed through the faster phase; beta<sub>2</sub>_X, effect of factor X on PK parameters b₂, IIV and IOV are expressed as SD.

displayed significant effects. It is challenging to compare the results of this study with previous works, as this double gamma absorption has only been used for MMF. Briefly, the literature reports values for a₁ ranging from 4.44²⁴ to 21.20,²⁵ b₁ from 3.91²⁴ to 7.90,²⁵ a₂ from 15.38¹² to 54.70,²⁴ b₂ from 5.46¹² to 73.80,²⁴ FAIV from 4.41²⁴ to 8.87¹⁴ and r from 0.30²⁵ to 0.59.¹² The values found in this study are either in the upper range of the interval (e.g., FAIV at 7.87) or highly above these observed intervals (e.g., a₁ at 1280.97 compared to the upper limit of 21.2). This could be attributed to the different formulation of EC-MPS and the fact that this study includes a comprehensive range of transplants and autoimmune diseases, encompassing patients from paediatric to elderly and extremely wide post-transplantation periods, whereas previous studies were highly targeted.

The trend lines in the residual plots show no significant trend overall, with only a slight deviation at higher concentrations, which remains minimal given the small number of high-concentration data points. While we acknowledge some bias in the observed concentrations vs. population predictions, the primary purpose of our model is to estimate AUC via Bayesian estimation, rather than for simulation. Regarding the pcVPC, although two outliers appear in both the development and external datasets at later sampling times (~9 h post-dose), these represent a small subset of data points. For the critical absorption phase within the first 6 h, empirical percentiles are

generally consistent with predicted percentiles, with deviations mainly occurring at high concentrations in the external dataset. Despite this, these points fall within the prediction confidence intervals.

In terms of literature specific to EC-MPS, our structural model is a single-compartmental one, similar to that proposed by Wang et al.,¹⁹ whereas those of de Winter et al.⁶ and Chen et al.²⁰ are two-compartmental. The absorption models include double extravascular absorption for Wang et al., and first-order absorption with a lag time for Chen et al. and de Winter et al. Notably, de Winter et al. explored a gamma distribution for absorption, which did not improve the model fit according to their objective function, unlike Chen and Wang, whose models did not include gamma absorption. In our study, however, the gamma absorption model provided a better fit. Our estimated values of CL/F (4.99 L/h) and Vd/F (12.60 L) are within the range reported in the literature: apparent clearance ranging from 4.28 L/h¹⁹ to 16 L/h⁶ and volume of distribution from 3.73 L¹⁹ to 611 L.²⁰

IOV was defined based on sequential visits for each patient (visit n + 1, n + 2, etc.). However, in the dataset, we observed substantial variation in the time intervals between visits across patients. We acknowledge that this heterogeneity in visit intervals may have introduced bias into the IOV estimation.

Regarding the different covariates contributing to the heterogeneity of PK profiles, previous studies have identified body
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**FIGURE 3** Diagnostic plots for the model of population predictions and individual predictions vs. observed MPA concentrations (A, B), weighted residuals as a function of time (h) (C) or individual prediction (D) in the development population. Yellow lines are trend lines.</figcaption></figure>

weight,²⁰,²⁶ albumin level²⁷⁻²⁹ and creatinine clearance²⁰ as the most frequently influential factors on MPA clearance. Since our dataset did not include this information, we were unable to assess

their impact, which may represent a partial limitation of this study. Previous studies²⁹ have reported a positive correlation between the coadministration of CsA and MPA CL/F, attributing this effect to
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>FIGURE 4 Prediction-corrected visual predictive check (pcVPC) of the model with the observations (mg/L) of the development (A), validation (B) and external (C) dataset vs. time (h). Prediction interval (10th and 90th percentile): coloured area; predicted percentiles: dotted line; empirical percentile: blue line; observed data: blue dot.</figcaption></figure>

<table><caption>TABLE 3 Comparison of the different limited sampling strategy in (A) the validation set (n = 16) and (B) external set (n = 10).</caption><thead><tr><th colspan="4">A</th></tr><tr><th>Sampling time (h post-dosing)</th><th>rMPE (%)</th><th>Relative RMSE (%)</th><th>Percentage of patients with a rMPEgreater than ± 20%</th></tr></thead><tbody><tr><td>0.3-2-4</td><td>-2.67</td><td>13.55</td><td>12.5</td></tr><tr><td>0.3-3-6</td><td>-8.73</td><td>18.87</td><td>37.5</td></tr><tr><td>1.5-4-6</td><td>1.47</td><td>17.76</td><td>37.5</td></tr></tbody><thead><tr><th colspan="4">B</th></tr><tr><th>Sampling time (h)</th><th>rMPE (%)</th><th>Relative RMSE (%)</th><th>Percentage of patients with a rMPEgreater than ± 20%</th></tr></thead><tbody><tr><td>0.3-2-4</td><td>-4.91</td><td>13.47</td><td>10</td></tr><tr><td>0.3-3-6</td><td>-3.33</td><td>16.4</td><td>30</td></tr><tr><td>1.5-4-6</td><td>-5.36</td><td>12.5</td><td>0</td></tr></tbody></table>

Abbreviations: rMPE, relative mean prediction error (bias); RMSE, root mean square error (imprecision).
CsA's inhibition of the enterohepatic recirculation of MPA.³⁰ In contrast to these studies, where CsA use was prevalent (52%–87% of patients), only 16/151 (11%) of our patients were on CsA, reflecting the shift in immunosuppressive protocols favouring tacrolimus with MPA. Specifically, cyclosporine inhibits the transport of MPAG from hepatocytes into the bile, thus reducing EHC.³¹ In contrast, tacrolimus does not notably affect MPA pharmacokinetics, as demonstrated in a study by van Gelder et al.³² In our study, however, we identified the treatment indication as a significant covariate, while co-treatment with cyclosporine was not retained. This is consistent with the gamma MMF model previously implemented by Koloskoff et al.,²⁴ which also did not find co-treatment to be a significant covariate.

The indication covariate was the only factor found to explain part of the inter-individual variability in $b_2$, leading to its reduction. Our study is unique in encompassing all indications for the molecule, making direct comparisons with other studies difficult. Even if we acknowledge as an important limitation the physiological and pharmacokinetic differences between the various transplant types and autoimmune diseases included in our study, the decision to gather the different indications into (i) renal and hepatic transplants, (ii) pulmonary and cardiac transplants and bone marrow transplants, and (iii) autoimmune diseases was based on convergence reasons. We initially attempted to develop the model without grouping the six indications, but the analysis could not converge, largely due to the limited sample sizes within certain subgroups. Subsequently, we attempted various clinically and biologically logical groupings, beginning with (i) kidney-liver transplants, (ii) lung-heart transplants, (iii) bone marrow transplants and (iv) autoimmune diseases. However, this approach did not yield satisfactory model stability or reliable parameter estimates. In an effort to improve convergence, we tested additional groupings to balance sample sizes more effectively: (i) kidney-liver transplants, (ii) lung-heart transplants and (iii) a combined group for bone marrow transplants and autoimmune diseases. Unfortunately, this configuration also failed to stabilize the model. Our final attempt involved testing combinations such as (i) kidney transplant, (ii) liver transplant, (iii) heart-lung transplant, (iv) bone marrow transplant and (v) autoimmune disease, including a variation that combined bone marrow and autoimmune diseases. Each of these options proved inadequate for achieving robust parameter estimation. Ultimately, we arrived at the grouping reported in this study: (i) kidney-liver, (ii) heart-lung-bone marrow and (iii) autoimmune disease. While we acknowledge that combining heart-lung and bone marrow transplants may not align precisely with clinical or biological rationale, this approach provided the best model stability and an acceptable level of predictive accuracy.

Although the gamma absorption model effectively describes pharmacokinetic profiles due to its mathematical flexibility, it complicates the assessment of covariate impact as it diverges from physiological processes. The parameters $b_2$ are 95.69 $h^{-1}$, 172.62 $h^{-1}$ and 80.73 $h^{-1}$ for the three different indication groups, resulting in $MAT_2$ (mean absorption time) of the second absorption peak of 4.09 h, 2.29 h and 4.90 h, respectively. The impact of group (iii) with AID is

unclear due to the high imprecision of estimation (188%). Therefore, it can be concluded that $MAT_2$ is almost halved in group (ii) compared to the reference group of renal and hepatic transplants.

The various LSS tested led to the selection of the times 0.3 h, 2 h and 4 h. These times differ from the LSS 0.3 h, 1 h and 3 h used in the MMF consensus,⁴ highlighting the delayed absorption of EC-MPS compared to MMF. Chen et al. reported an LSS for EC-MPS at times of 1.5 h, 2 h, 4 h, and 1.5 h, 2 h, 4 h, 6 h, further demonstrating the need for later sampling times compared to MMF. Their LSS was determined by multiple regression analysis and a Bayesian approach, yielding similar results, leading to a prediction error for three sampling times of –7.57 ± 24% and a mean root square error of 20.3 ± 20.5%. Therefore, our LSS demonstrated strong performances relative to other LSS.

Regarding the external dataset, we chose not to merge it with the validation set to form a single large test set for two reasons. Firstly, to respect the temporal sequence of events, this dataset was constructed subsequently to the modelling process, once the final model and LSS had already been developed and tested on the development and validation sets. Secondly, since these datasets were obtained by a 75%:25% data splitting from an original dataset, it would have been challenging to merge the validation dataset with an additional dataset extracted later.

This study has some limitations. The dataset was built from extractions from our ISBA site, resulting in a multicentre study (139 PK profile from Europe and 12 from outside geographical Europe). While this allows for broader generalization, it also introduces variability in PK profiles and data sparsity due to different treatment protocols. Inconsistencies in analytical methods over time remain a significant issue. Reliable extrapolation of MPA concentrations measured by immunoassays to chromatographically determined concentrations is not possible and cannot be recommended, which highlights the potential influence of the measurement method on residual error. Additionally, to calculate the reference AUC, we integrated the concentration profile over the dosing interval. This was done using only rich kinetics (six or more sampling points), which led to a loss of PK profiles. Nevertheless, we deliberately avoided influencing the data-splitting process and the inclusion of patients having at least six samples in the validation set would have biased the random data-splitting process. Indeed, all the rich profiles would have been in the validation set. Unlike de Winter et al.,⁶ we did not investigate the difference between morning and evening PK profiles, as all blood samples in our study were collected in the morning. The extended lag time in EC-MPS absorption could be attributed to the enteric-coated formulation and the enterohepatic circulation of MPA. Variations in gastrointestinal motility and environmental conditions between morning and evening might explain differences in absorption.³³ To better understand potential diurnal variations in absorption or the impact of EHC, future studies should include sampling after the evening dose as well.

An important limitation is the absence of heart or lung transplant recipients in both the validation and external datasets, which may affect the model's generalizability. Furthermore, the small sample size
<figure><img src="image_15.png" /></figure>

in certain subgroups limits the development of an LSS specific to these populations, and subgroup analyses, though valuable, are currently constrained by sample size. It is also important to highlight that our dataset was limited to immunosuppressive co-treatments only, and we did not have access to information on other concurrent medications that patients might have been prescribed. This absence of data on non-immunosuppressive co-medications represents a limitation, as other drug classes could potentially influence MPA metabolism or enterohepatic cycling, contributing to unaccounted pharmacokinetic variability in EC-MPS. Lastly, the most important limitation is the assumption of steady-state for all PK profiles, as the double gamma absorption model presumes that the parameter C₀ represents the trough concentration at steady-state.

5 | CONCLUSION

This study is the first to develop a popPK model for EC-MPS using a double gamma distribution absorption model implemented with an NLME approach. It is also the first study based on a population of multiple SOT and patients with AID, facilitating its generalization. The resulting model demonstrated correct performance in terms of individual estimation and prediction accuracy, enabling the derivation of an LSS using MAP-BE to predict AUC. These three samples taken within the first 4 h post-dose can be used in TDM, enhancing patient management and will soon be implemented on our ISBA website (https://abis.chu-limoges.fr/).

AUTHOR CONTRIBUTIONS

Y.F. developed the population pharmacokinetic model. Y.F., H.S., K.K. and J.B.W. conceptualized and designed the study and performed data analysis and interpretation. Y.F., C.M., M.L., P.M. and J.B.W. collected and/or curated clinical and pharmacokinetic data and supervised the study. Y.F., K.K. and J.B.W. drafted the manuscript. All the authors revised the manuscript critically for important intellectual content and approved the final version of the manuscript.

ACKNOWLEDGEMENTS

The authors thank Helene Roussel-Vachat for her efforts leading to the favourable opinion from the ethics committee. This work is part of the DIGPHAT project which was supported by a grant from the French government, managed by the National Research Agency (ANR), under the France 2030 program, with reference ANR-22-PESN-0017.

CONFLICT OF INTEREST STATEMENT

No conflicts of interest to declare.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on reasonable request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

ORCID

Pierre Marquet https://orcid.org/0000-0001-7698-0760

Marc Labriffe https://orcid.org/0000-0001-5840-8904

Jean-Baptiste Woillard https://orcid.org/0000-0003-1695-0695

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## SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.

**How to cite this article:** Fromage Y, Sayadi H, Koloskoff K, et al. Killing several birds with one stone: A multi-indication population pharmacokinetic model and Bayesian estimator for enteric-coated mycophenolate sodium. *Br J Clin Pharmacol*. 2024;1-13. doi:10.1111/bcp.16374