Model-Informed Precision Dosing of Tacrolimus Initial Dosage Optimization in Membranous Nephropathy Patients

Abstract

Objective

Due to the therapeutic window of tacrolimus is narrow and there are significant individual differences in metabolism, a uniform dosage is prone to result in poor efficacy or increased toxic side effects. This study aimed to explore tacrolimus initial dosage optimization in membranous nephropathy (MN) patients based on model-informed precision dosing (MIPD).

Methods

Population pharmacokinetic model, an effective tool of MIPD, was constructed using the non-linear mixed effect modeling approach implemented in NONMEM software, which encompassed a range of patient-related data, including demographic characteristics, physiological and biochemical test results, as well as details regarding concurrent medications.

Results

From the aspect of individualized drug administration, in adult MN patients, the initial dosages of tacrolimus were 0.06 mg/kg, 0.04 mg/kg for patients weighted 50–53 kg, 53–100 kg, respectively. In pediatric MN patients, the initial dosages of tacrolimus were 0.12 mg/kg, 0.10 mg/kg, 0.08 mg/kg, 0.06 mg/kg for patients weighted 10–12.7 kg, 12.7–16.4 kg, 16.4–26.7 kg, 26.7–40 kg, respectively.

Conclusion

This study was the first time to simultaneously recommend the optimal initial dosage of tacrolimus for both adult and pediatric MN patients based on MIPD. Moreover, the dosage required for pediatric MN patients was higher than that for adult MN patients.

Introduction

Membranous nephropathy (MN) can occur in all age groups, which is a glomerular disease characterized by thickening of the glomerular basement membrane and deposition of immune complexes, whose main manifestations are massive proteinuria, edema, hypoproteinemia and hyperlipidemia meanwhile it is one of the most common pathological types of nephrotic syndrome in adults.1–3 The incidence of MN in children is lower compared to that in adult patients.4,5 However, a nationwide 11-year research conducted in China revealed that the prevalence of pediatric MN climbed remarkably, surging from 3% during the initial phase to 7% in the final stage.6 Therefore, MN should be given sufficient attention in both adult and childhood stages.

The treatment of MN should be individualized based on the patient’s risk stratification. The core objective is to reduce proteinuria, control blood pressure, delay the deterioration of renal function, and prevent complications. The drug treatment plan mainly includes glucocorticoids such as prednisone, and immunosuppressants such as cyclosporine or tacrolimus.7–14 Among them, tacrolimus is widely used in MN and is one of the core immunosuppressants for treating patients with intermediate to high-risk membranous nephropathy, especially suitable for those who are dependent on hormones, resistant, or have contraindications.15–19

Tacrolimus reduces the deposition of immune complexes in the glomeruli by inhibiting T-cell activation and reducing the production of autoantibodies, thereby lowering proteinuria, moreover its clinical efficacy is proven to be reliable.20–22 Compared with cyclosporine, tacrolimus has a stronger immunosuppressive effect. Due to the therapeutic window of tacrolimus is narrow and there are significant individual differences in metabolism, a uniform dose is prone to result in poor efficacy or increased toxic side effects.23,24 Clinically, the dosage of tacrolimus must be dynamically adjusted through therapeutic drug monitoring (TDM).25–27 Nevertheless, for the first administration regimen of tacrolimus, there are no available tacrolimus TDM concentration test values for reference. It has brought certain troubles to the formulation of the initial dosage regimen of tacrolimus for MN patients. Furthermore, the in vivo clearance of tacrolimus exhibits significant age-dependent dynamic changes. Children are not “small adults”--the weight-normalized tacrolimus clearance in pediatric populations is markedly higher than that in adults, and it is inappropriate to simply extrapolate adult dosing regimens to children via proportional scaling. Therefore, achieving individualized tacrolimus dosing for both adults and children is of critical clinical importance.

Model-informed precision dosing (MIPD) is a method that dynamically predicts and optimizes individualized treatment regimens based on pharmacokinetic models, patient physiological and pathological characteristics, and TDM data. It has been widely applied in drugs with narrow therapeutic windows.28–32 Traditional TDM is a passive management strategy that relies on post-hoc blood concentration measurement to perform threshold-based dose adjustment after the drug has been administered, which cannot predict future drug exposure in advance. In contrast, MIPD is an active precision dosing paradigm, which can generate prospective dose recommendations before or at the early stage of treatment. The core enabling tool of MIPD is Bayesian forecasting, which can continuously integrate sparse real-world patient data into pre-validated population pharmacokinetic models, to achieve individualized prediction of drug exposure even under non-steady-state conditions.

 Taking tacrolimus as a representative example, the extremely high inter-individual pharmacokinetic variability and narrow therapeutic index of this immunosuppressant make conventional empirical dosing or threshold-only TDM strategies difficult to balance the risk of insufficient immunosuppression and excessive exposure. MIPD can dynamically adjust dosing regimens to maintain drug concentration within the predefined therapeutic window, which significantly improves the rate of target attainment and reduces the occurrence of adverse events.

Thus, this study explored tacrolimus initial dosage optimization in MN patients based on MIPD.

Methods

Enrolled Patients

This study obtained ethical permission from the Research Ethics Committee of the Affiliated Hospital of Xuzhou Medical University (Approval No. XYFY2025-KL599-01), where the requirement for written informed consent could be waived since the data were collected retrospectively without patient identifiers. This study adhered to the Declaration of Helsinki. A retrospective analysis was conducted on patients with MN who received tacrolimus treatment at the aforementioned hospital between May 2022 and September 2025. The study encompassed a range of patient-related data, including demographic characteristics, physiological and biochemical test results, as well as details regarding concurrent medications. Tacrolimus concentration measurement was conducted using Emit^® 2000 Tacrolimus Assay (Enzyme-multiplied immunoassay technique, Siemens Healthcare Diagnostics Inc.,) whose routine test range covered 2 to 30 ng/mL. This study was based on the sparse trough concentration data of TDM, the blood sampling was performed about 30 minutes before the next dose administration. The core modeling logic of population pharmacokinetics is to directly estimate the basic pharmacokinetic parameters at the population level by using nonlinear mixed-effects models, which simultaneously integrate the sparse sampling data from different individuals, without relying on the steady-state assumption.

Modeling

The MIPD, a population pharmacokinetic model, was constructed using the non-linear mixed effect modeling approach implemented in NONMEM (version 7, developed by ICON Development Solutions, Ellicott City, MD, USA). Key pharmacokinetic parameters incorporated into the model including apparent oral clearance (CL/F), volume of distribution (V/F), and the absorption rate constant (Ka), with the latter fixed at 4.48 h⁻¹ based on references.33,34

To quantify inter-individual variability, we employed Equation (I):

(1)

In this formula, B_i corresponded to the individual parameter, TV(B) represented to the typical individual parameter, and ηi signified a symmetrically distributed random effect term.

To quantify random residual variability, we employed Equation (II):

(2)

In this formula, E_i corresponded to the observed concentration, G_i represented the individual predicted concentration. ε₁ signified a symmetrically distributed random effect term.

To quantify relationship between the parameters and weight, we employed Equation (III):

(3)

In this formula, H_i corresponded to the i-th individual parameter, N_i represented the i-th individual weight. N_std signified the standard weight of 70 kg and H_std signified the typical individual parameter. M was the allometric coefficient: 0.75 for the CL/F and 1 for the V/F.35

To quantify continuous or categorical covariates parameters, we employed Equations (IV)-(V):

(4)

(5)

In the two formulas, O_i corresponded to the individual parameter, TV(O) represented the typical individual parameter, Q signified parameter to be estimated, P_i was the covariate of the i-th individual, and P_m denoted population median for the covariate.

This study employed a two-step strategy to construct the covariate model, using alterations in the objective function value (OFV) as the primary metric for variable selection. Concretely, a covariate was incorporated into the model if its inclusion brought about an OFV decrease of more than 3.84 (P < 0.05). Conversely, a covariate was retained in the model if its removal caused an OFV rise exceeding 6.63 (P < 0.01), and was excluded otherwise.

Model Evaluation

The final population pharmacokinetic model of tacrolimus for MN patients was validated through a comprehensive set of methods, including goodness of fit assessments, individual plots, visual predictive checks (VPC), and the bootstrap resampling technique.

Simulation

Monte Carlo simulation was utilized to predict tacrolimus concentrations in MN patients. For adult patients with MN, each simulation scenario generated 1,000 virtual MN patients, who were categorized into six weight subgroups (50, 60, 70, 80, 90, and 100 kg) and eight tacrolimus dosage subgroups (0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14 mg/kg). For child patients with MN, each simulation scenario generated 1,000 virtual MN patients, who were categorized into four weight subgroups (10, 20, 30, and 40 kg) and eight tacrolimus dosage subgroups (0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14 mg/kg). All dosages were administered in two equal daily doses. The target therapeutic range for tacrolimus in MN was set at 4–10 ng/mL,17 and the probability of achieving this target concentration was selected as the primary evaluation endpoint.

Results

Patient Information

This study recruited 31 patients diagnosed with MN, of whom 22 were male and 9 were female. The age distribution of the cohort was between 30.00 and 67.00 years, with weights varying from 52.00 to 103.00 kg. Patient demographic data and details of combined drug therapies were summarized separately in Table 1 and Table 2. Drug combination in MN patients included allisartan isoproxil tablet, alprostadil fat emulsiom injection, atorvastatin calcium tablet, bailing capsule, compound sulfamethoxazole tablet, dapagliflozin tablet, dipyridamole tablet, entecavir tablet, fufang shenyan tablet, huangkui capsule, jinshuibao tablet, levothyroxine sodium tablet, papaverine hydrochloride injection, prednisolone acetate tablet, prednisone acetate tablet, rivaroxaban tablet, shenkang injection, tripterygium glycosides tablet.

Table 1.

Demographic Data of Membranous Nephropathy Patients with Tacrolimus

Characteristic	Mean ± SD	Median (Range)
Gender (men/women)	22/9	/
Age (years)	49.35 ± 11.07	55.00 (30.00–67.00)
Weight (kg)	69.65 ± 11.50	67.50 (52.00–103.00)
Albumin (g/L)	34.05 ± 6.79	34.50 (19.00–44.50)
Globulin (g/L)	20.80 ± 2.89	20.95 (14.60–27.70)
Alanine transaminase (IU/L)	23.04 ± 14.46	17.00 (7.00–65.00)
Aspartate transaminase (IU/L)	21.38 ± 7.71	20.00 (13.00–43.00)
Creatinine (μmol/L)	71.64 ± 25.28	68.00 (38.00–154.00)
Urea (mmol/L)	7.19 ± 3.02	6.61 (3.17–14.98)
Total protein (g/L)	54.58 ± 8.34	56.10 (38.00–66.50)
Total cholesterol (mmol/L)	5.87 ± 1.76	5.19 (3.89–9.49)
Triglyceride (mmol/L)	2.85 ± 2.57	2.38 (1.05–13.87)
Direct bilirubin (μmol/L)	3.15 ± 0.92	3.00 (1.60–4.50)
Total bilibrubin (μmol/L)	8.21 ± 3.22	7.10 (3.90–15.60)
Hematocrit (%)	39.20 ± 4.61	39.80 (28.30–47.00)
Hemoglobin (g/L)	128.90 ± 16.68	128.00 (86.00–155.00)
Mean corpuscular hemoglobin (pg)	29.81 ± 2.64	30.30 (20.00–34.60)
Mean corpuscular hemoglobin concentration (g/L)	328.31 ± 10.94	329.00 (303.00–347.00)

Table 2.

Drug Combination in Membranous Nephropathy Patients with Tacrolimus

Drug	Category	N	Drug	Category	N
Allisartan isoproxil tablet	0	23	Huangkui capsule	0	10
	1	8		1	21
Alprostadil fat emulsiom injection	0	26	Jinshuibao tablet	0	25
	1	5		1	6
Atorvastatin calcium tablet	0	18	Levothyroxine sodium tablet	0	27
	1	13		1	4
Bailing capsule	0	12	Papaverine hydrochloride injection	0	17
	1	19		1	14
Compound sulfamethoxazole tablet	0	28	Prednisolone acetate tablet	0	28
	1	3		1	3
Dapagliflozin tablet	0	19	Prednisone acetate tablet	0	22
	1	12		1	9
Dipyridamole tablet	0	28	Rivaroxaban tablet	0	29
	1	3		1	2
Entecavir tablet	0	26	Shenkang injection	0	21
	1	5		1	10
Fufang shenyan tablet	0	26	Tripterygium glycosides tablet	0	27
	1	5		1	4

Notes: Category, 0: without drug, 1: with drug; N: number of patients.

Modelling

Equations (VI) and (VII) defined the final tacrolimus population pharmacokinetic model established for MN patients:

(6)

(7)

Model Evaluation

Goodness of fit assessments, individual plots were presented in Figures 1–2, where the predicted values had a good match with the measured values. The result of VPC was shown in Figure 3, where the majority of the concentration points fall within the 95% confidence interval of the model. The bootstrap was presented in Table 3, where the bias from CL/F, V/F were less than 5%. Collectively, these findings confirmed the reliability and robustness of the tacrolimus population pharmacokinetic model developed for MN patients.

Figure 1.

Goodness of fit. (A) Observations vs population predictions. (B) Observations vs individual predictions. (C) Conditional weighted residuals (WRES) vs individual predictions. (D) Conditional WRES vs time.

Figure 2.

Individual plots.

Abbreviations: ID, patient ID number; DV, measured concentration value; IPRED, individual predictive value; PRED, population predictive value.

Figure 3.

Visual predictive check (VPC) of model.

Abbreviation: CI, confidence interval.

Table 3.

Parameter Estimates of Tacrolimus Final Model and Bootstrap Validation in Membranous Nephropathy Patients

Parameter	Estimate	Bootstrap			Bias (%)
		Median		95% Confidence Interval
CL/F (L/h)	9.54	9.66		[1.13, 13.75]	1.26
V/F (L)	76.3	78.9		[3.0, 214.0]	3.41
Ka (h−1)	4.48 (fixed)	––		––	––
ωCL/F	0.172	0.094		[0.003, 0.381]	−45.35
σ1	2.504	2.601		[0.010, 3.508]	3.87

Notes: 95% confidential interval was displayed as the 2.5th, 97.5th percentile of bootstrap estimates. CL/F, apparent oral clearance (L/h); V/F, apparent volume of distribution (L); Ka, absorption rate constant (h⁻¹); ω_CL/F, inter-individual variability of CL/F; σ₁, residual variability, additive error; Bias, prediction error, Bias = (Median-Estimate) / Estimate×100%.

Dosage Recommendation

The simulated tacrolimus concentrations of adult patients with MN and the probability to achieve therapeutic window were shown in Figures 4–5, respectively. Additionally, the simulated tacrolimus concentrations of child patients with MN and the probability to achieve therapeutic window were shown in Figures 6–7, respectively. In adult MN patients, the initial dosages of tacrolimus were 0.06 mg/kg, 0.04 mg/kg for patients weighted 50–53 kg, 53–100 kg, respectively. In pediatric MN patients, the initial dosages of tacrolimus were 0.12 mg/kg, 0.10 mg/kg, 0.08 mg/kg, 0.06 mg/kg for patients weighted 10–12.7 kg, 12.7–16.4 kg, 16.4–26.7 kg, 26.7–40 kg, respectively.

Figure 4.

Simulated tacrolimus concentrations of adult patients with MN. (A) 50 kg MN patients. (B) 60 kg MN patients. (C) 70 kg MN patients. (D) 80 kg MN patients. (E) 90 kg MN patients. (F) 100 kg MN patients.

Figure 5.

Probability to achieve therapeutic window in adult patients with MN.

Figure 6.

Simulated tacrolimus concentrations of child patients with MN. (A) 10 kg MN patients. (B) 20 kg MN patients. (C) 30 kg MN patients. (D) 40 kg MN patients.

Figure 7.

Probability to achieve therapeutic window in child patients with MN.

These recommended dosages were shown in Table 4.

Table 4.

Initial Dosage Recommendation of Tacrolimus in Membranous Nephropathy Patients

Adult Patients			Child Patients
Body Weight (kg)	Dosage (mg/kg/day)	Probability of Achieving the Target Concentrations (%)	Body Weight (kg)	Dosage (mg/kg/day)	Probability of Achieving the Target Concentrations (%)
[50–53)	0.06	74.5–76.0	[10–12.7)	0.12	66.0–69.8
[53–100]	0.04	74.5–84.3	[12.7–16.4)	0.10	66.0–68.0
			[16.4–26.7)	0.08	68.0–76.5
			[26.7–40]	0.06	74.0–78.7

Discussion

MIPD is a clinical strategy based on mathematical models and individual patient characteristics to optimize drug dosages, aiming to achieve individualized treatment, improve efficacy, and reduce adverse reactions. This method integrates TDM data, pharmacokinetic/pharmacodynamic models, and patient-specific factors, uses computer simulations to predict the optimal dosage regimen, and supports dosage adjustment decisions.36–43 Some studies have explored individualized administration regimens of tacrolimus based on MIPD. For example, multiple studies have validated MIPD as a reliable tacrolimus individualized dosing strategy across kidney, liver and heart transplant populations.44–48 Therefore, this study explored tacrolimus initial dosage optimization in MN patients based on MIPD.

The final model analysis revealed that the above medications used by the patients did not show any significant drug-drug interaction that affected the tacrolimus clearance rate of MN patients. Furthermore, based on Monte Carlo simulation, we recommended the optimal initial dosage of tacrolimus for MN patients. The Monte Carlo method is a numerical calculation approach based on random sampling and probability statistics, which approximates the solutions to complex problems through a large number of random simulations. It plays a crucial role in the formulation of individualized tacrolimus dosage. For instance, Liao et al reported tacrolimus population pharmacokinetic model in adult Chinese patients with nephrotic syndrome and dosing regimen identification using Monte Carlo simulations.49 Wang et al reported optimization of initial dose regimen of tacrolimus in paediatric lung transplant recipients based on Monte Carlo simulation.50 Stefanović et al reported effect of the interrelation between CYP3A5 genotype, concentration/dose ratio and intrapatient variability of tacrolimus on kidney graft function: Monte Carlo simulation approach.51

In this study, we simulated and recommended the optimal initial dosage of tacrolimus for adult MN based on the Monte Carlo method. In adult MN patients, the initial dosages of tacrolimus were 0.06 mg/kg, 0.04 mg/kg for patients weighted 50–53 kg, 53–100 kg, respectively. Meanwhile, based on the adult MIPD model of this study, we made a moderate model extrapolation and provided an initial dosage regimen for tacrolimus in children with MN. In pediatric MN patients, the initial dosages of tacrolimus were 0.12 mg/kg, 0.10 mg/kg, 0.08 mg/kg, 0.06 mg/kg for patients weighted 10–12.7 kg, 12.7–16.4 kg, 16.4–26.7 kg, 26.7–40 kg, respectively.

Although this work relied on the NONMEM as its core tool, its methodology naturally extended to research on artificial intelligence (AI) models. Indeed, AI had recently made impressive strides in medical research, diagnosis, and treatment-for example, through AI models52 and large language models.53 On the one hand, the current model could be further integrated with machine learning algorithms to utilize real-world electronic health record data for real-time prediction and dynamic updating of individualized drug exposure, thereby enhancing the adaptability of dosage recommendations. On the other hand, the dose simulation framework established in this study (Monte Carlo simulation and probability-of-achievement assessment) could be fully integrated with deep reinforcement learning models to build an adaptive medication decision-making system based on real-time patient feedback, achieving a leap from static rule-based recommendations to dynamic strategy optimization.

Of course, this study had certain limitations. First of all, since genetic polymorphisms were not routinely used as a testing method in clinical diagnosis and treatment, we did not obtain information on drug genetic polymorphisms during the data collection process. Therefore, in the model for dose recommendation, there was no module for genetic polymorphisms, which also making our MIPD model more in line with the real clinical scenario of tacrolimus use. Secondly, this study was based on retrospective data from a single center. In the future, a multi-center prospective study would need to verify our conclusions.

Conclusion

This study was the first time to simultaneously recommend the optimal initial dosage of tacrolimus for both adult and pediatric MN patients based on MIPD. Moreover, the dosage required for pediatric MN patients was higher than that for adult MN patients.

Funding Statement

This work was supported by The Suzhou Applied Basic Research Science and Technology Innovation Project (No. SYWD2024258), Jiangsu Key Laboratory of New Drug Research and Clinical Pharmacy Project (No. 25KF06).

Data Sharing Statement

The datasets used and/or analyzed during the current study are available from the corresponding author (Dongdong Wang) on reasonable request.

Disclosure

The authors report no conflicts of interest in this work.