Pharmacokinetic Model Selection for Personalized Infliximab Dosing in IBD

ABSTRACT

Infliximab, a monoclonal antibody used for immune‐mediated diseases, shows high interpatient pharmacokinetic variability. Prolonged exposure increases the risk of adverse effects and costs, making dose personalization essential to balance safety, efficacy, and cost‐effectiveness. Population pharmacokinetic models support individualized dosing, but different models may predict varying drug exposure for the same patient. This study aims to identify compatible models for each patient and assess the impact of model selection on dosing. This retrospective study included adult Crohn's disease patients receiving infliximab. Published pharmacokinetic models were screened. Model‐patient compatibility was evaluated using Multivariate Exact Discrepancy through 100,000 Monte Carlo simulations. The Metropolis‐Hastings algorithm generated individual parameter distributions. For each model‐patient pair, the median and 90% confidence interval of the dose required to achieve a target exposure of 2079 mg*day/L were computed. Sixteen models were tested. No model was compatible with all patients. Dosing was calculated only for compatible pairs. The average median dose was 9.25 mg/kg, with an average imprecision of 6.63 mg/kg. The highest median dose reached 23.21 mg/kg, reflecting inter‐model differences, while the greatest imprecision (25.69 mg/kg) stemmed from patient variability. This concentration‐based method personalizes dosing via pharmacokinetic profiling. Patients can be classified into three groups: (1) those for whom all models provide similar recommendations, indicating high reliability across models; (2) those incompatible with all models, for whom the posology recommended by the manufacturer should be prioritized; and (3) those for whom some models are compatible but intensified therapeutic drug monitoring is required.

Study Highlights.

• What is the current knowledge on the topic?

  • ○
    Infliximab is used to treat immune‐mediated diseases, but its pharmacokinetics vary significantly between individuals. Weight‐based dosing alone does not fully capture this variability.
• What question did the study address?

  • ○
    Population pharmacokinetic (PopPK) models help personalize dosing, but different models may yield inconsistent recommendations for the same patient. Which PopPK models are compatible with individual patients' data, and how does model selection influence infliximab dosing?
• What does this study add to our knowledge?

  • ○
    No PopPK model fits all patients. The study proposes a three‐tier patient classification based on model compatibility to guide dosing decisions.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    The findings support model‐informed precision dosing in clinical care and highlight the importance of selecting appropriate modeling tools. Integrating therapeutic drug monitoring can enhance model selection and optimize treatment in real time.

1. Introduction

Infliximab is a monoclonal antibody targeting tumor necrosis factor‐alpha (TNF‐α), a key inflammation mediator. By inhibiting TNF‐α, it reduces inflammation and immune overactivity. It is used to treat autoimmune diseases like rheumatoid arthritis, Crohn's disease, ulcerative colitis, and psoriasis. Administered intravenously, it is often combined with immunosuppressants to enhance efficacy and reduce antibody formation.

Infliximab's pharmacokinetics (PK) are complex, influenced by factors including concentration‐dependent elimination and immunogenicity. The latter, marked by anti‐drug antibodies formation, is specific to this class of biologics. The immune response is closely linked to circulating levels of both infliximab and TNF [1, 2, 3, 4, 5]. Thus, maintaining appropriate infliximab exposure in patients is essential to minimize potential toxicity, such as the risk of opportunistic infections, tuberculosis, reactivation of HBV infection and cancer [6], while maximizing its therapeutic efficacy, including symptom improvement and clinical remission. Additionally, infliximab's price varies widely across healthcare settings, with cost‐effectiveness depending on dose and local pricing [7]. This highlights the importance of dose optimization for economic sustainability. Given its high and variable cost, infliximab may be said to carry an unofficial additional toxicity—economic—which, though absent from pharmacology textbooks, is well recognized by healthcare systems.

Despite weight‐based dosing, significant interindividual PK variability persists, highlighting the need for further personalization using additional covariates [8]. One promising approach to achieving this balance is through the use of population pharmacokinetic (PopPK) models, enabling personalized dosing strategies based on individual patient characteristics.

Numerous PopPK models have been published, incorporating covariates influencing PK parameters. Accounting for these covariates significantly enhances the estimation of the individual PK. Depending on covariate values, drug exposure can vary significantly. If exposure is sufficient, PK variations may not affect efficacy, allowing dose reduction without compromising effectiveness, thereby minimizing toxicity and reducing treatment cost per patient. Conversely, if exposure is insufficient, it is crucial to assess the benefit of increased drug levels and the risk of anti‐infliximab antibodies development.

This modeling approach is particularly relevant since blood samples are routinely collected to measure infliximab and anti‐infliximab antibody concentrations. However, these data are underused: the numerical values are rarely interpreted with reference to PopPK covariates, nor used to estimate full PK profile, which is closely linked to pharmacodynamic outcomes.

PopPK models do not always predict the same drug exposure for a given patient, raising the question of model selection [9]. This study aims to identify, for each patient, all models compatible with available patient‐specific data and compare their predicted exposures. If all selected models predict similar exposure, model choice is inconsequential. Regardless of the model chosen, it provides useful guidance for clinical decision‐making, particularly in the absence of any previously determined Infliximab blood concentrations in the patient. However, if predicted exposures differ, it suggests that model selection remains unresolved, and additional patient‐specific data are necessary to refine dosing decisions.

2. Material and Methods

Our study is a retrospective analysis using patient data collected during hospital care, compared with simulated data derived from population pharmacokinetic models previously published in the literature.

2.1. Patient Database and Covariate Handling

Data were obtained from patients treated at the University Hospital Centre of Toulouse (France). Thirty‐four patients received at least two infliximab administrations, with at least one concentration measurement taken after each. Concentrations above the upper limit of quantification (ULOQ) were set at 20 mg/L; those below the lower limit of quantification (LLOQ) were set at 0.3 mg/L. Exceptionally, concentrations reported as > 16 mg/L were set at 16 mg/L. Values outside the calibration range were treated as left‐ or right‐censored data, as detailed in section 2.3. Missing covariate values were standardized by selecting values that minimized their impact on the typical population estimate. When a covariate appeared in multiple models, a single value was chosen for consistency, except for the FCGR3A gene. This polymorphism, analyzed separately for the wild‐type gene (noncarrier of the F allele) and F‐carriers (those carrying at least one F allele), is of clinical interest because it may alter the effectiveness of antibody‐based therapies by modulating how strong immune cells interact with therapeutic antibodies through Fc receptor binding. Some models incorporated fecal calprotectin (FC) as a covariate, a validated biomarker of intestinal inflammation [10]. In mucosal barrier dysfunction, monoclonal antibodies like infliximab can leak from the vascular compartment into the intestinal lumen, accelerating drug clearance [11]. However, FC data were unavailable for the majority of patients, and for those with available measurements, FC values did not correspond to each infliximab administration. Given that the available FC values ranged from < 10 to 1975 μg/g, selected values (50, 274, 500, 1000 μg/g) were tested in the PK models to explore their impact on PK parameters. Similarly, baseline TNF‐α concentrations were varied from 0 to 38 pM in target‐mediated drug disposition (TMDD) models. These two covariates were varied specifically because they are mechanistically linked to pharmacokinetic behavior in the models tested.

2.2. Selection of Population Pharmacokinetic Models

To identify PopPK models relevant to adult patients, we conducted a systematic literature search using PubMed and Google Scholar. Before applying any filters, the initial search yielded 42,600 Google Scholar and 309 PubMed results. To manage volume, the Google Scholar search was limited to titles, whereas PubMed was searched across all fields. Inclusion and exclusion criteria were predefined to ensure relevance. The literature search was performed using the following keywords: “infliximab population pharmacokinetic(s)” or “infliximab pharmacokinetic(s) model(l)ing.” Studies were excluded if they contained the terms “p(a)ediatry,” “p(a)ediatric,” “neonate,” or “neonatal,” ensuring that only adult populations were considered. Additionally, PopPK models were excluded if they lacked essential information on interindividual variability, residual variability, mean value of covariates, or units of measurement. Furthermore, if during the screening process we identified models developed for populations outside our scope—such as pregnant women—these were also excluded.

While our focus was on PopPK models, we also retained mechanistic models, such as TMDD and pharmacokinetic‐pharmacodynamic (PKPD) models when relevant. Indeed, TMDD models account for drug binding to a pharmacological target as a key determinant of drug kinetics, while PKPD models describe the relationship between drug exposure and pharmacological response. The search covered articles published between January 2000 and March 2025, as no PopPK model of infliximab was found prior to this period.

In the Buurman model [12], the individual volume ($V_i$) was originally defined as:

$$V_i=V_{\mathrm{pop}}\times 0.964\times \left(\mathrm{HBI}-6\right),$$

which presents a problem: if HBI = 6 then ${\mathit{V}}_{\mathit{i}}$ = 0, and if HBI < 6 then $V_i$ < 0, which in both cases is not meaningful. Reviewer 1 suggested an alternative linear form:

$$V_i=4.94\times \left(1-0.036\times \left(\mathrm{HBI}-6\right)\right)$$

In this study, we adopted the formulation:

$$V_i=V_{\mathrm{pop}}\times {0.964}^{\left(\mathrm{HBI}-6\right)}$$

which is consistent with ${\theta }_{\mathrm{HBI}}$ = −0.036 reported in table 3 of Buurman et al. [12]. This expression can be derived from the general equation:

$$V_i=V_{\mathrm{pop}}\times {\exp }^{{\theta }_{\mathrm{HBI}}*\left(\mathrm{HBI}-6\right)}$$

Linearization of this exponential form around HBI = 6 reproduces Reviewer 1's linear approximation. This approach ensures consistency with the original data and provides a transparent, reproducible methodology for the model.

2.3. Multivariate Exact Discrepancy (MED)

To account for concentration dependencies, models were evaluated using the MED approach [13], which estimates the probability that an individual's concentration profile originates from the tested model. This probability is interpreted similarly to a p‐value, with significance set at alpha < 5% (description of the MED approach in Supporting Information). To address patient‐data rounding at the ULOQ and LLOQ, respective simulated concentrations below the LLOQ and above the ULOQ were treated as left‐ and right‐censored data. A total of 100,000 simulations were performed for each patient with each model, using RStudio (v2024.12.1 Build 563) and the ks package [14]. To simulate the potential effect of the FCGR3A polymorphism—a genetic variation previously described to affect Fc receptor binding—the clearance parameter in all models was divided by 1.16, based on data indicating that individuals carrying the mutated gene exhibit an approximately 16% lower elimination rate (ke) compared to those with the wild‐type gene [15]. This adjustment, assuming proportionality between the ke and clearance (CL), was applied only to individuals whose data did not fit with any of the PK models, to explore whether the mutation could explain the model‐data mismatch. When covariates were manually altered, such as baseline TNF‐α or FCGR3A status, MED scores were recalculated. If modifying a covariate increased the MED score from < 5% to > 5%, the new score was retained. Accordingly, for each patient and each model, the retained MED score was the first score exceeding 5% obtained after varying these covariates, reflecting the variability between patients and how these variations affect model fit.

2.4. Metropolis Hastings Algorithm (MHA)

To assess whether different PK models suggest consistent dosing recommendations across administrations for the same patient, MHA [16] was implemented to estimate the posterior distribution of PK parameters, particularly clearance, which directly determines exposure (area under the concentration vs. time curve, AUC). This analysis included only patient‐model pairs with MED ≥ 0.05, indicating acceptable fit. For each patient, we performed 10,000 iterations of the PK parameters using the log‐likelihood equation, generating a distribution that represents all possible parameter alternatives for each individual. As no definitive AUC threshold is established in the literature, a target AUC_∞ of 2079 mg*D/L [17] was selected, based on values observed in treated patients. Toxicity was not factored into dose calculations, as the only toxic AUC found in the literature was a cumulative AUC over 6 months that increases the risk of infection [18]. In all cases, this “infectious risk threshold” is achieved with the standard dosing regimen. Using a 90% confidence interval (90% CI), we calculated the dosage required to reach the target AUC for the lowest (5%) and the highest (95%) clearance values. Imprecision was defined as CI width (Dose₉₅—Dose₅), representing the range of dosing due to uncertainty in the estimated clearance. The median dose (i.e., the dose corresponding to the median clearance) was also calculated for each case. The mean of the median doses and mean imprecision were calculated by averaging the values across all patient‐model pairs.

2.5. Ethical Considerations

A collection and computer processing of personal and medical date was implemented to analyze the results of the research. Toulouse University Hospital signed a commitment of compliance to the reference methodology MR‐004 of the French National Commission for Informatics and Liberties (CNIL). After evaluation and validation by the data protection officer and according to the General Data Protection Regulation, this study completing all the criteria, it is registered in the register of data study of the Toulouse University Hospital (number's register: RnIPH 2025–72) and cover by the MR‐004 (CNIL number: 2206723 v 0).

3. Results

3.1. Population Pharmacokinetic Models

Using inclusion and exclusion criteria, 227 Pubmed and 36 Google Scholar articles were retained (Figure 1). Among the 263 articles, 248 were excluded for the following reasons: literature reviews; articles not addressing PopPK models of infliximab; inaccessible articles; articles addressing a population beyond the scope of our study; articles investigating a different route of administration; articles lacking information on PK parameter or variability; duplicate records between PubMed and Google Scholar. The remaining 15 articles are described in Table 1 and include 2 bi‐compartmental TMDD models and 12 PopPK models (4 mono‐ and 9 bi‐compartmental), with one article proposing both a mono‐compartmental PopPK model and a PKPD model.

FIGURE 1.

A PRSIMA‐style flowchart of Model Selection from the Literature. It illustrates the screening process conducted in PubMed and Google Scholar to identify pharmacokinetic models.

TABLE 1.

Description of the 14 Infliximab population pharmacokinetic models retained.

Publication	Model	N	Age (years)	Weight (kg)	Alb (g/dL)	Disease	CMT	IIV (%)	RE	LLOQ
Passot et al. 2016 [8]	M1	218	95% > 15	67 [28.2–125]	—	41.7% AS//8.3% RA//13.8% PsA//28.9% CD//7.3% UC	1	ωCL = 30.4 ωV1 = 22.4	σprop = 22.3 σadd = 0.72	0.04 mg/L CV 9.8%
Seo et al. 2023 [19]	M2	100	27 [17–77]	65.6 [33–102.3]	—	CD	1	ωCL = 19.24 ωV1 = 4.47 COV = −0.004	σpro = 21.3 σadd = 0.209	—
Zhu et al. 2024 [20]	M3	140	34 [15–58]	59.9 [39–80]	3.83 [27.5–53.1]	CD	1	ωCL = 25.1 ωV1 = 0	σpro = 26.6 σadd = 0.15	0.5 mg/L
Ternant et al. 2015 [15]	M4	111	31 [25–39]	67 [57–75]	—	CD	1	ωKe = 37 ωV1 = 0	σpro = 41 σadd = −	0.04 mg/L CV 9.8%
Xu et al. 2008 [21]	B1	274	40 [18–74]	77 [43–133.4]	4.3 [3.2–5.1]	AS	2	ωCL = 34.1 ωV1 = 17.5 ωQ = 0 ωV2 = 0	σpro = 22.9 σadd = 2.89	0.1 mg/L at 1:25 dilution CV 12.39%–15.94%
Ternant et al. 2008 [22]	B2	33	33 [19–53]	67 [44–110]	—	91% CD//9% UC	2	ωCL = 22.5 // 27.4 ωV1 = 14.1 // 11.3 // 19.2 ωQ = 10 ωV2 = 15	σpro = − σadd = 1.02	0.04 mg/L CV 12%
Fasanmade et al. 2009 [23]	B3	482	40 [18–81]	77 [40–177.3]	4.1 [2.4–5.2]	UC	2	ωCL = 37.68 ωV1 = 22.11 ωQ = 0 ωV2 = 0	σpro = 40.3 σadd = 0.0413	0.1 mg/L at 1:25 dilution CV 12.39%–15.94%
Ternant et al. 2012 [24]	B4	14 + 12	45.5 [29–55] or 42.5 [27–59]	77 [60–123] or 70.5 [52–104]	—	AS	2	ωCL = 24 ωV1 = 14 ωQ = 0 ωV2 = 22	σpro = 18 σadd = 2.6	0.04 mg/L CV 9.8%
Buurman et al. 2015 [12]	B5	42	44 [19–80]	75 [51–145]	4.1 [3.3–5]	81% CD//19% UC	2	ωCL = 18 ωV1 = 17.1 ωQ = 0 ωV2 = 0	σpro = 21.7 σadd = 0.98	0.002 mg/L—
Dreesen et al. 2021 [25]	B6 PKPD	116	30 [22–45]	65 [57–75]	3.9 [3.4–4.2]	CD	2	ωCL = 28.5 ωV1 = 0 ωQ = 0 ωV2 = 0	σpro = − σadd = 0.364	0.3 mg/L—
Kantasiripitak et al. 2021 [26]	B7	104	62 [38–68]	66 [60–78]	4 [3.5–4.2]	38% CD//62% UC	2	ωCL = 29.6 ωV1 = 0 ωQ = 0 ωV2 = 81.5	σpro = 26.9 σadd = 1.24	0.3 mg/L CV ≤ 25%
Su et al. 2023 [27]	B8	44 + 133	33 [18–70]	58 [36–77.3]	4.65 [4.11–5.19] 4.38 [3.32–5.56]	Healthy//RA	2	ωCL = 25.5 ωV1 = 11 ωQ = 0 ωV2 = 45.8	σpro = 31.4 σadd = −	0.0391 mg/L CV ≤ 25%
Magro et al. 2024 [28]	B9	369	40.12 ± 13.59	69 [59–78]	4.16 [3.96–4.37]	78% CD//22% UC	2	ωCL = 18.17 ωV1 = 40 ωQ = 0 ωV2 = 50	σpro = 25.8 σadd = 2.32	—
Berends et al. 2019 [29]	TMDD1	20	36 [19–69]	70 [47–90]	3.8 [2.3–4.5]	UC	2	ωCL = 29.2 ωV1 = 22.7 COV = 12.3 ωQ = 0 ωV2 = 74.2	σpro = 21 σadd = −	0.06 mg/L CV 12%
Ternant et al. 2021 [30]	TMDD2	133	34 [25–41]	64 [56–72]	—	81.2% CD//18.8% UC	2	ωCL = 35 ωV1 = 27 ωQ = 0 ωV2 = 39	σpro = 20 σadd = 1.8	0.103 mg/L CV 10.3%

Note: The symbol “‐” indicates that data for the respective parameter are not available in the study.

Abbreviations: AS, ankylosing spondylitis; B, bicompartmental model; CD, Crohn's Disease; CMT, number of compartments describing the model; COV, covariance CL_V1; CV, coefficient of variation; IIV, inter‐individual variability (ω); M, mono‐compartmental model; N, number of patients; PsA, Psoriatic Arthritis; RA, Rheumatoid Arthritis; RE, residual error (σ) proportional in %, additive in mg/L; UC, Ulcerative Colitis.

In Passot 2016, Ternant 2012, Ternant 2015, and Kantasiripitak 2021, proportional errors were reported as values less than 1%, which were unrealistic given the expected variability in the analytical techniques used. We assumed this was a mistake and likely meant to indicate σ (sigma) as a fraction (not as a percentage). Consequently, we adjusted the proportional error to a more reasonable percentage. In Dreesen et al. [25], the additive error σ was written as a negative value, so we corrected it to a positive value. This correction allowed us to apply a residual error that more accurately reflected the variability inherent in the employed analytical techniques. In Buurman et al. [12], the volume equation, as presented in the article, implies that the volume is nullified when the HBI score equals 6. Therefore, we interpreted this as suggesting that it should be raised to the power, rather than multiplied, to align with the intended model formulation.

3.2. MED Results

The performance of retained models was evaluated using the MED approach and the complete set of patient data. Simulations showed that incorporating the FCGR3A genotype in clearance estimation did not impact model performance. Similarly, varying baseline FC concentrations had negligible effects across tested models. As such, these variations were excluded from the final model comparison presented in Table 2. However, baseline TNF concentrations led to meaningful differences in certain patients and were retained for cases where MED ≥ 0.05.

TABLE 2.

Table of MED for all couple patient‐model.

Patient	PKPD	B5	M3	B2	B4	M2	M1	TMDD1	B1	B8	B9	B6	B7	TMDD2	M4	B3
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.01019	0.01181
21	0	0	0.00105	0	0	0	0	0	0	0.00065	0	0	0	0.0237	0.02488	0.02565
13	0	0.00045	0.01322	0.00149	0	0.00009	0.00227	0.0021	0.00148	0.00965	0.01073	0	0.00821	0.0044	0.08358	0.11779
20	0	0	0.00847	0	0	0.00002	0.01271	0	0.00103	0.00866	0.00662	0	0.00719	0	0.10627	0.13811
8	0	0	0.00322	0	0.00002	0	0.00073	0.0073	0.00092	0.00537	0.00727	0	0.00632	0	0.05791	0.1162
3	0.01393	0	0.00068	0.00019	0	0	0	0.92814	0.00328	0.00912	0	0.1106	0.80905	0.38955	0.00814	0.69025
17	0	0.00123	0.01598	0.00484	0.00626	0.00606	0.08892	0.3023	0.04772	0.27972	0.07228	0.02131	0.05487	0.0924	0.42484	0.04067
19	0.41411	0.01393	0.00325	0.20267	0	0	0.00439	0.39658	0.18326	0.65569	0.02393	0.49249	0.63152	0.81508	0.35567	0.59134
7	0.00408	0.01308	0.01203	0.17655	0.03027	0.01495	0.02422	0.99316	0.43318	0.63939	0.1535	0.16828	0.35196	0.99595	0.69941	0.44342
30	0	0.01229	0.01516	0	0.67177	0.13242	0.37968	0.0126	0.73996	0.03833	0.4987	0.06801	0.06624	0.4378	0.33048	0.42697
14	0.03455	0.02234	0.04072	0.0041	0.82103	0.37379	0.39872	0.0493	0.74216	0.16245	0.38883	0.17633	0.1103	0.22302	0.69949	0.60886
26	0	0	0.63748	0.28488	0	0	0.73656	0	0.85248	0.67363	0.65084	0.74933	0.84998	0.7509	0.91154	0.93124
32	0	0.01322	0.04767	0.00292	0.72584	0.14391	0.5339	0.051	0.63289	0.16425	0.38875	0.20155	0.19753	0.20966	0.61976	0.6894
1	0.24389	0.02698	0.3078	0.02464	0	0.89488	0.59508	0.95285	0.0502	0.99734	0.92022	0.39509	0.86234	0.65931	0.99841	0.6744
11	0.01378	0.22262	0.33621	0.03751	0.03666	0.66999	0.89165	0.55533	0.26793	0.81633	0.85527	0.21761	0.43645	0.86386	0.96884	0.74849
10	0	0	0.15074	0.06704	0.97701	0.74096	0.27789	0.16183	0.89976	0.25723	0.54858	0.52684	0.32422	0.2331	0.63531	0.57865
15	0	0.79556	0.85512	0.54039	0.4687	0.91108	0.84859	0.8282	0.47556	0.61815	0.68954	0.91261	0.93671	0.75353	0.87839	0.92285
16	0	0.1553	0.99128	0.91116	0.47732	0.75762	0.96485	0.40748	0.69794	0.47292	0.96295	0.92277	0.65977	0.6857	0.98434	0.91726
22	0.00656	0.8188	0.87288	0.80673	0.07282	0.10287	0.42341	0.75059	0.57815	0.88392	0.56733	0.37655	0.86547	0.9441	0.79638	0.63765
24	0.01465	0.08563	0.22996	0.31178	0.63045	0.41676	0.37708	0.5425	0.73528	0.17876	0.67329	0.57582	0.84393	0.4738	0.37398	0.79419
28	0.28318	0.02119	0.41308	0.58751	0.99383	0.59787	0.46544	0.42732	0.99898	0.16839	0.75319	0.75127	0.60992	0.71012	0.44472	0.8343
31	0	0.28216	0.22467	0.2	0.71752	0.24101	0.72217	0.12982	0.85271	0.3642	0.75112	0.2763	0.52752	0.65956	0.87908	0.72363
33	0	0.85594	0.75102	0.57766	0.80679	0.80736	0.92724	0.6682	0.91994	0.71387	0.90548	0.88319	0.93193	0.8985	0.93629	0.98312
34	0	0.0664	0.66359	0.37046	0.07099	0.15433	0.16688	0.8626	0.29422	0.99041	0.24159	0.96445	0.93517	0.268	0.89416	0.92298
5	0.18181	0.83271	0.90646	0.89615	0.66367	0.55842	0.77666	0.98	0.64615	0.92469	0.68013	0.95738	0.87353	0.75445	0.92202	0.95953
2	0.75517	0.87844	0.97313	0.72711	0.53087	0.87873	0.91978	0.98521	0.94371	0.93753	0.97509	0.91724	0.96387	0.99147	0.99782	0.81186
4	0.46449	0.2662	0.527	0.3228	0.066	0.5705	0.5663	0.98615	0.2043	0.9807	0.5289	0.209	0.962	0.5962	0.8071	0.5567
9	0.74372	0.77966	0.86066	0.94201	0.85806	0.73799	0.89709	0.99316	0.8889	0.96411	0.99629	0.88321	0.85875	0.05229	0.90016	0.95355
12	0.9285	0.22069	0.8622	0.94803	0.94451	0.72649	0.83107	0.99743	0.77793	0.81189	0.86024	0.96031	0.86654	0.99761	0.90548	0.89302
18	0.47411	0.63575	0.53518	0.26022	0.96605	0.75066	0.90678	0.35632	0.89974	0.47759	0.81557	0.75514	0.50604	0.8588	0.90575	0.98464
23	0.14175	0.66263	0.88815	0.90309	0.06715	0.76476	0.49012	0.49983	0.40682	0.83919	0.68543	0.88938	0.6283	0.8221	0.83576	0.9608
25	0.98246	0.99538	0.0904	0.63421	0.31503	0.35404	0.97011	0.9855	0.80912	0.96992	0.91379	0.86764	0.88882	0.8132	0.99237	0.89656
27	0.66171	0.68436	0.91684	0.77742	0.17708	0.70401	0.74031	0.85892	0.44579	0.83563	0.72663	0.95488	0.87131	0.62561	0.99826	0.8216
29	0.20823	0.57751	0.7625	0.43206	0.47908	0.6655	0.71143	0.64127	0.77072	0.79078	0.67506	0.88817	0.69319	0.50392	0.95771	0.96079

Note: The rows represent the 34 patients, ordered from the patient with the greatest number of MED values lesser than 5% (at the top) to the patient with the lowest number of MED values lesser than 5% (at the bottom). The columns represent the models, ordered from the model with the greatest number of MED values lesser than 5% (on the left) to the model with the lowest number of MED values lesser than 5% (on the right). The color coding allows for a quick visual assessment of model performance, with green cells indicate good fits and red cells highlight areas where the model may not be as appropriate for the patient. Furthermore, three distinct blocks of patients can be observed: a green block at the bottom, where all models perform well; an orange middle block, where approximately 5 to 15 models show good performance; and a red block at the top, where only a few models achieve acceptable fits.

In Table 2, each cell in the table shows the MED score for a given patient‐model pair. The data can be analyzed from two perspectives: by patient or by model. From the patient perspective, 32 out of 34 patients (94%) had concentration profiles compatible with at least one model. Among these, 8 patients (green block, 29.4%) matched all tested models, while 21 patients (orange block, 55.9%) were compatible with 5 to 16 models. From the model perspective, none fit all patients. Models M4 and B3 initially performed the best, fitting the data of 31 out of 34 patients. Upon further examination, we excluded these models from further analysis due to high proportional errors, meaning the models captured noise rather than meaningful trends, reducing their reliability. Among the remaining models, a distinct pattern emerged: a subset of patients, seen as a “red block” in the results matrix (14.7%), could not be fitted by any model. These represent outliers whose data did not align with any of the models tested.

3.3. Dosage Interval

To evaluate the consistency of dosing recommendations across administrations for the same patient, MHA was applied. The analysis was restricted to patient‐model pairs that demonstrated a good fit, as indicated by a MED score ≥ 0.05, except for models M4 and B3 that were rejected for the above‐mentioned reason. The following section presents the corresponding dosing recommendations for each patient, based on the target AUC of 2079 mg*D/L. The median dose and the imprecision were found for each patient‐model pair. Each facet represents an individual patient, with the models color‐coded to differentiate the predictions. There was minimal variation in the recommended dose across administrations; therefore, only the first administration is represented here. Results for subsequent administrations are available in the Supporting Information.

For the 1st administration (represented in Figure 2), the mean of median doses was 9.28 mg/kg, with the lowest dose at 3.07 mg/kg and the highest at 19.60 mg/kg. The mean imprecision was 6.48 mg/kg, with a minimum of 0.38 mg/kg and a maximum of 17.53 mg/kg. The highest imprecisions were observed in patients 3, 7 and 19, who had negligible infliximab concentrations at the time of dosing. Across all administrations, the values did not differ by a lot with a mean of median doses at 9.25 mg/kg (2.74–23.21) and a mean imprecision at 6.63 mg/kg (0.37–25.69).

FIGURE 2.

A faceted scatter plot figure displaying the relationship between the imprecision (mg/kg) (defined as Dose₉₅—Dose₅, the difference between the doses at the 95th and 5th percentiles of clearance) and the median recommended dose (mg/kg) for each patient. In practical terms, ideally, all models would yield the same x‐value, with imprecision minimized (i.e., y approaching 0). It shows dose recommendations from various models for individual patients. Each subplot corresponds to a different patient, numbered from 1 to 34. The x‐axis represents the median dose (in mg/kg) and the y‐axis represents the imprecision in dose (also in mg/kg). Each colored dot in a subplot corresponds to a dose recommendation from a specific model, with different colors representing different models.

4. Discussion

We chose to implement the MED approach, a novel method for selecting the model(s) that best fit(s) each patient. Unlike traditional empirically used metrics, MED provides valuable insight into which PK model most accurately captures the full kinetic profile of each patient, rather than focusing solely on pointwise deviations. Three patients (8.8%) had concentration profiles not aligned with any model, without clear explanation—except for Patient 3, whose PK parameters evolved over time. Interestingly, for this patient, the data remained interpretable when only the first four concentration measurements were considered. This suggests that current PK models do not adequately account for significant changes in PK parameters over time, implying that treating them as stationary may not accurately reflect inter‐occasion variability (IOV). Overall, 32 patients (94%) had concentrations compatible with at least one model; 7 (29.4%) were compatible with all models tested, and 21 (55.9%) matched 5 to 16 models.

Although no single model fits all patients, two models (M4 and B3) demonstrated compatibility with 91% of them. However, this apparent success was driven by high proportional errors > 40%. When residual error exceeds 20%–25%, all measured concentrations may wrongly appear compatible with the model, making model conclusions unreliable. Although we proceeded with testing these models, a preliminary examination of residual errors could have flagged these issues. Moving forward, residual error must be evaluated before applying the MED approach to avoid artificially inflated compatibility. More generally, any model with high residual error should be excluded, as it may yield imprecise PK parameter estimates and lead to incorrect dosing. Such errors can ultimately undermine clinician confidence in model‐based dosing. Selecting appropriate models begins with a nonnegotiable rejection of any model that fails to meet key performance criteria.

When excluding the two models with high residual errors, we observed a distinct group of five patients who did not fit well with any of the proposed PK models. This block of patients consistently showed poor fits across all models, indicating a need for further model refinement or the possibility of factors not captured by the current PK model assumptions.

To further explain the results, we explored the use of TMDD and PKPD models. As their name implies, the TMDD models account for the effect of the biological target (TNF) on the PK of infliximab. Monoclonal antibodies are primarily cleared through proteolytic degradation following receptor‐mediated endocytosis. For antibodies exhibiting TMDD, such as infliximab, clearance is concentration‐dependent: at low concentrations, binding to TNF leads to rapid elimination via lysosomal degradation, whereas at higher concentrations, this pathway saturates, resulting in slower clearance [29]. As disease activity intensifies, the inflammatory load increases, which results in higher TNF production and, consequently, faster clearance via TMDD. In the PKPD model, FC acts as a covariate influencing the clearance of infliximab. As previously mentioned, FC is a noninvasive biomarker for CD and it positively correlated with disease activity [10]. Severe bowel inflammation may cause endogenous as well as exogeneous proteins to leak into the stool, providing an additional clearance route for infliximab [25]. Despite testing these models, the MED scores for the “red block” did not improve significantly.

The mean of median doses across the entire cohort was 9.25 mg/kg (range: 2.74–23.21 mg/kg), which is consistent with established infliximab dosing practices, that is, standard dose typically ranges from 5 to 10 mg/kg every 8 weeks but can go up to 22.5 mg/kg for patients whom standard therapy is insufficient to manage symptoms [31]. The mean imprecision was 6.63 mg/kg (range: 0.37–25.69 mg/kg). Upon further analysis of Figure 2, we notice the median recommended dose by M3 may be responsible for shifting the mean of median doses to the higher end across all patients, at least for the 1st administration. However, when studying all administrations altogether, excluding this model has no significant impact on the median dose, going from 9.25 mg/kg (range: 2.74–23.21 mg/kg) to 8.92 mg/kg (range: 2.74–21.23 mg/kg), nor the imprecision, going from 6.63 mg/kg (range: 0.37–25.69 mg/kg) to 6.55 mg/kg (range: 0.37–17.53 mg/kg). Further examination revealed that the largest imprecisions occurred exclusively in three patients. Notably, two of these patients (patients 7 and 19) were the only ones whose concentrations fell below the LLOQ in the sample taken after the 1st administration, potentially contributing to the increased imprecision in dose estimation. The third patient, Patient 3, experienced concentrations below the LLOQ in the sample taken after the 2nd administration. This level of variability suggests that certain models may lack robustness in dose estimation for specific patient profiles, particularly those with rapid drug clearance or atypical PK. The differences in imprecision could stem from model selection, the influence of covariates, the residual error structure, or censored patient data such as when values fell below the LLOQ or above the ULOQ, as seen in the three patients mentioned above. High imprecision in dose recommendations can complicate clinical decision‐making, particularly in patients for whom precise dose adjustments are necessary. Future work will focus on refining dose selection strategies by incorporating patient‐specific data and addressing model‐based variability to enhance dose accuracy.

Despite 14.7% of the patients (Table 2) in our cohort not being compatible with any of the tested models, our study presents several strengths.

First, all accessible PopPK models for adults identified through a systematic literature review (PubMed and Google Scholar) were tested, ensuring a comprehensive evaluation of model performance, regardless of the disease type of the studied group. Therefore, our approach was exhaustive, as we did not exclude any models a priori. Additionally, the analysis utilized data from 34 hospitalized patients under controlled clinical conditions, ensuring reliable and well‐documented data collection.

Moreover, the MED approach, the most effective method currently available for assessing the compatibility between patient concentration data and PK models, was employed. This method allowed for a robust evaluation of model fit. Importantly, not all missing covariates were fixed. Genotype was treated as a binary variable due to the absence of genotype data in our cohort. In the PopPK model proposed by Dreesen et al. [25], we manually adjusted the baseline FC value to assess its impact on the MED results. Similarly, the baseline TNF value was also manually adjusted in the two TMDD models.

Lastly, right‐ and left‐censored data—including concentrations below the LLOQ and above the ULOQ—were fully incorporated. These data were considered both in the calculation of MED values and in the construction of dose intervals, ensuring a more accurate representation of the uncertainty in infliximab PK. In line with our effort to account for uncertainty, we also estimated dose ranges that reflect the uncertainty in the estimation of individual pharmacokinetic parameters—particularly clearance, which determines AUC. Instead of providing a single predicted dose based on the most likely parameter value, we proposed a dosing range that incorporates a 90% interval of plausible clearance values, thereby accounting for uncertainty in parameter estimation.

Despite its strengths, this study has several limitations.

First, for covariates with missing values, we opted for the median value to avoid a combinatorial explosion in the analysis. While this approach ensured feasibility, it may have masked inter‐individual variability. Also, the inclusion of censored data (< LLOQ and > ULOQ) introduced additional uncertainty in individual clearance estimates, which in turn affected dose predictions. As a result, the calculated doses required to achieve the target exposure (2079 mg*day/L) had a higher degree of imprecision.

Importantly, clearance varied discontinuously from one administration to the next, meaning that the amount of drug remaining from the previous dose was eliminated at a newly estimated clearance rate. This is not physiologically plausible, as clearance should not change abruptly between dosing intervals. Instead, it should evolve progressively over time. This issue is closely tied to a broader limitation: the PK of individual patients was not stationary. Specifically, PK parameters, such as clearance, changed over time—sometimes from 1 month to the next or even between consecutive administrations. This variability was influenced by covariates that either fluctuated significantly over time (e.g., antibody‐to‐infliximab), changed more gradually (e.g., body weight), or remained relatively stable (e.g., disease type, such as Crohn's disease). As a result, the values of these covariates could differ between administrations, and so did the corresponding PK parameters. More clearly, pharmacokinetic parameters estimated from previous blood samples cannot reliably inform the patient's current or future pharmacokinetics, as η continuously changes. In our analysis, we assumed that η (individual variability) changes whenever covariate values change, while Ω (inter‐individual variability) remains constant due to a lack of information suggesting otherwise. This assumption is particularly relevant in cases where pharmacodynamics (PD) influences PK and administrations are spaced far apart (e.g., several weeks), leading to changes in covariates such as kidney function, hepatic function or weight over time. By allowing η to vary, we accounted for IOV, under the assumption that prior concentration measurements provide useful information for estimating the remaining concentration at the time of the next administration. A key practical implication of this assumption is that, to reduce dose uncertainty and minimize imprecision, it would be important to collect multiple blood samples between two administrations. This approach would provide better insights into the evolution of PK parameters over time, leading to more accurate dose predictions.

In conclusion, our study highlights several key insights. First, as no model was compatible with all the patients in our cohort, it is not feasible to recommend an initial dose based solely on covariates. In such cases, clinicians have no choice but to rely on the standard dosing regimen as outlined in current guidelines.

Second, once infliximab concentrations become available, a reasoned therapeutic decision can be guided using the “red–orange–green” classification system. For patients in the red category, pharmacokinetics is highly individualized, making it impossible to recommend a dose with confidence and the selection of the dosing regimen is subsequently guided by the patient's response to treatment. For those in the orange category, multiple models may apply. When multiple models are compatible, one must decide whether to use them individually—where choosing one excludes the others—or to combine them, assigning a weight to each. This point represents our next challenge. For patients in the green category, model selection as well as model combination is less critical, as the various models yield similar dosing recommendations.

Third, the precision of dose recommendations improves with the number of post‐administration blood samples collected, as this enhances the understanding of the patient's pharmacokinetic profile over time. Consequently, therapeutic drug monitoring plays a central role in the individualized management of patients treated with infliximab.

Author Contributions

S.C., P.G., D.C., N.C. and T.J. wrote the manuscript; D.C. and P.G. designed the research; S.C., P.G. and D.C. performed the research; S.C., P.G. and D.C. analyzed the data.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Figure S1: Title: Plots displaying the relationship between the imprecision (mg/kg) (defined as Dose₉₅—Dose₅, the difference between the doses at the 95th and 5th percentiles of clearance) and the median recommended dose (mg/kg) for each patient across all administrations. In practical terms, ideally, all models would yield the same x‐value, with imprecision minimized (i.e., y approaching 0).

Data S1: Material and Method—S1: MED description.

Chaiben S., Gandia P., Jamme T., Congy N., and Concordet D., “Pharmacokinetic Model Selection for Personalized Infliximab Dosing in IBD ,” CPT: Pharmacometrics & Systems Pharmacology 15, no. 1 (2026): e70152, 10.1002/psp4.70152.

Data Availability Statement

The R code supporting this study can be found in the repository: Sahira C [32], https://doi.org/10.17632/s86hys6tdn.2.