Multi-model averaging improves the performance of model-guided infliximab dosing in patients with inflammatory bowel diseases.

Infliximab dosage de-escalation without prior knowledge of drug concentrations may put patients at risk for underexposure and trigger the loss of response. A single-model approach for model-informed precision dosing during infliximab maintenance therapy has proven its clinical benefit in patients with inflammatory bowel diseases. We evaluated the predictive performances of two multi-model approaches, a model selection algorithm and a model averaging algorithm, using 18 published population pharmacokinetic models of infliximab for guiding dosage de-escalation. Data of 54 patients with Crohn's disease and ulcerative colitis who underwent infliximab dosage de-escalation after an earlier escalation were used. A priori prediction (based solely on covariate data) and maximum a posteriori prediction (based on covariate data and trough concentrations) were compared using accuracy and precision metrics and the classification accuracy at the trough concentration target of 5.0 mg/L. A priori prediction was inaccurate and imprecise, with the lowest classification accuracies irrespective of the approach (median 59%, interquartile range 59%-63%). Using the maximum a posteriori prediction, the model averaging algorithm had systematically better predictive performance than the model selection algorithm or the single-model approach with any model, regardless of the number of concentration data. Only a single trough concentration (preferably at the point of care) sufficed for accurate and precise prediction. Predictive performance of both single- and multi-model approaches was robust to the lack of covariate data. Model averaging using four models demonstrated similar predictive performance with a five-fold shorter computation time. This model averaging algorithm was implemented in the TDMx software tool to guide infliximab dosage de-escalation in the forthcoming prospective MODIFI study (NCT04982172).

WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

The benefits of model‐informed precision dosing (MIPD) using a single infliximab population pharmacokinetic model showed clinical benefits over label dosing in patients with inflammatory bowel diseases. Model selection and external evaluation remain challenging.

WHAT QUESTION DID THIS STUDY ADDRESS?

The performance of multi‐model approaches for guiding infliximab dosage de‐escalation was evaluated using a comprehensive set of diagnostic tools.

WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

A model averaging algorithm performed better than a model selection algorithm and a single‐model approach with any model. A posteriori prediction with a single, preferably most recently obtained, infliximab trough concentration has clinically acceptable accuracy and precision, even when covariate information is missing.

HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

Utilizing model averaging during MIPD of infliximab may increase target attainment and thereby the probability of maintaining a therapeutic response while controlling the risk of relapse. The developed algorithm was implemented in the freely available TDMx software tool and will be used for prospective evaluation.

INTRODUCTION

For over 2 decades, infliximab, an anti‐tumor necrosis factor‐alpha monoclonal antibody, has been approved for the treatment of several chronic immune‐mediated diseases, including the inflammatory bowel diseases (IBDs) ulcerative colitis (UC) and Crohn’s disease (CD). , The package label lists 5 mg/kg intravenous infusions at weeks 0, 2, and 6 (induction therapy) and every 8 weeks thereafter (maintenance therapy). However, ~20%–40% of the adult patients do not respond to standard induction therapy and up to half of the patients with a good initial response will lose response over time. ,

Underexposure to infliximab is a common cause of loss of response in patients with IBD. To boost infliximab trough concentrations (TCs) and subsequently regain the response, empirical dosage regimen escalations (i.e., shortening the dosing interval and/or increasing the dose) are widely practiced. However, long‐term maintenance of the escalated dosage regimen has financial, practical, and potential safety implications and is therefore not warranted. , , Accordingly, many centers have attempted to de‐escalate the infliximab dosing (i.e., extending the dosing interval and/or decreasing the dose) in patients who maintained response on an escalated infliximab dosage regimen.

Empirical de‐escalation of infliximab dosing could put patients at risk for underexposure and trigger again the loss of response due to extensive interindividual pharmacokinetic (PK) variability. Model‐informed precision dosing (MIPD) has been proposed to ensure adequate exposure and maintained response compared to traditional therapeutic drug monitoring (TDM). MIPD uses drug‐specific population PK (PopPK) models, patient‐specific monitoring data, and a Bayesian forecasting software tool to predict optimal doses for individual patients. Selecting the most suitable PopPK model is challenging, especially when many models are available, as is the case for infliximab. , A single‐model approach could potentially result in inappropriate dose recommendations, leading to suboptimal treatment outcomes or jeopardizing patients’ safety. A multi‐model selection algorithm (MSA) and a multi‐model averaging algorithm (MAA) have previously been proposed by Uster et al. to guarantee fit‐for‐purpose predictive performances during vancomycin MIPD. The multi‐model algorithms automate the MIPD procedure for selecting the prediction of either the best model (MSA) or the combination of models (MAA).

The aim of this study was to compare the predictive performance of published PopPK models and multi‐model selection and averaging approaches for guiding infliximab dosage regimen de‐escalation to ensure the attainment of a prespecified TC target.

METHODS

Clinical data

Adult patients with IBD who underwent infliximab dosage regimen de‐escalation at the University Hospitals Leuven (Leuven, Belgium) between February 2017 and June 2020 were included. Dosage regimen de‐escalation was defined as extending the dosing interval (with or without changing the dose) and/or decreasing the dose (with or without changing the dosing interval). The study was approved by the Ethics Committee (EC) Research UZ/KU Leuven (S63206). Serum samples were available from the CCare Biobank. All included patients have given written informed consent (B322201213950/S53684).

Patients with four consecutive trough samples, three before dosage regimen de‐escalation (times T−2, T−1, and T0) and one after de‐escalation (T+1) were eligible for inclusion (Figure 1a). TCs were measured using the apDia Infliximab ELISA (apDia), with a lower limit of quantification of 0.3 mg/L. Patients with unclassified IBD, with an ileal anal pouch anastomosis, with an ostomy, and who received infliximab prophylactically were excluded.

FIGURE 1

Study diagram and workflows of multi‐model approaches. (a) Study diagram of the prediction of the infliximab trough concentration (TC) at relative time + 1 (TC+1). In addition to covariate data, Bayesian forecasting was performed using one to three consecutive previously measured infliximab trough concentrations: TC−2, TC−1, and TC0. T, time; TCs, trough concentrations. *Rapid assay needed to obtain TC0 for prospective implementation in model‐informed precision dosing. (b) Flowcharts illustrate workflows of multi‐model selection and multi‐model averaging algorithms.

Sex, age, IBD type (UC or CD), disease duration, previous IBD surgery, previous biological use, and duration of infliximab treatment were recorded right before dosage regimen de‐escalation (at T0) and were handled as time‐invariant throughout the study follow‐up.

Body weight, fat‐free mass, serum albumin, C‐reactive protein, fecal calprotectin, infliximab dose, concomitant medications use (i.e., systemic corticosteroids or the immunomodulator azathioprine), Partial Mayo score for patients with UC, and Crohn’s Disease Activity Index (CDAI) and Harvey‐Bradshaw Index (HBI) for patients with CD were handled as time‐varying throughout the study follow‐up. Single imputation with the last observation carried forward was used for handling missing covariate data.

Candidate models

A systematic literature search of PubMed from January 1996 until June 2021 was performed to identify published PopPK models of infliximab in adult patients with IBD. The query was (infliximab) AND (model) AND (population) AND (pharmacokinetics). Articles were screened in full text for eligibility.

Single‐model evaluations

The fit of the data to the candidate models was visually inspected with goodness‐of‐fit plots (measured vs. individual predicted concentrations). In addition, simulation‐based evaluations were performed, including prediction‐corrected visual predictive checks (VPCs) and normalized prediction distribution errors (NPDEs). A normal distribution of NPDEs (0, 1) was tested using a Wilcoxon signed‐rank test (to compare the median of the NPDE to zero), a Fisher variance test (to compare the variance of the NPDE to one), and a Shapiro–Wilk test (to compare the distribution of the NPDE to a normal distribution). An adjusted p value of all the three tests (a global test) was calculated to identify the best predictive model.

Multi‐model approaches

Two multi‐model approaches were evaluated using all candidate models jointly; an MSA and an MAA. The multi‐model approaches used all of the candidate models simultaneously for predicting the infliximab concentration at T+1. The prediction of the MSA was the prediction of the candidate model with the highest weight, whereas the prediction of the MAA was an ensemble of weighted predictions of all candidate models (Figure 1b). For each individual, predictions of the multi‐model approaches were based on the weight (W) calculated from the maximum likelihood estimate (MLE) of each candidate model i in relation to the sum of MLEs of all n candidate models, Equation 1.

Predictive performance evaluations

The predictive performance was evaluated from the differences between the predicted and the measured TC at T+1 (TC+1) in two prediction modalities: a priori prediction (using only the patients’ covariates) and maximum a posteriori prediction (MAP; including at least one previous TC in addition to covariates). Three a posteriori prediction settings were compared: prediction with one (TC0, TC−1, or TC−2), two (TC0 and TC−1, TC0 and TC−2, or TC−1 and TC−2), and three (TC0, TC−1, and TC−2) previous TCs. The retrospective predictive performance of the models/algorithms was also evaluated by including the measured TC+1 in the a posteriori prediction in addition to the three previous TCs.

The model‐predicted versus measured TC+1 in the different single‐/multi‐model approaches, prediction modalities, and evaluation settings were compared by calculating the relative bias (rBias, Equation 2) and the relative root mean square error (rRMSE, Equation 3) to determine accuracy and precision, respectively. with n representing the total number of patients, and i each individual patient. An rBias between ±20% with a 95% confidence interval (CI) including zero was deemed clinically acceptable. No rRMSE threshold for clinical acceptability was prespecified. Lower rRMSE values indicated more precise predictions.

Robustness analysis and software implementation

A robustness analysis was performed to reduce the number of PopPK models without losing the predictive performance of the multi‐model approach algorithms. The average computation time was compared between the multi‐model approaches using all versus only the subset of models.

The subset of models was implemented in the TDMx software tool. The performance of TDMx was cross‐validated against nonlinear mixed‐effect modeling (NONMEM).

Bland–Altman analysis, classification accuracy, and sensitivity analysis

The MSA and MAA with the subset of models were evaluated using predictive performance metrics, Bland–Altman analysis, classification accuracy, and a sensitivity analysis. The Bland–Altman plot was used to assess the agreement between the predicted and measured TC+1 across the range of measured TC+1. The predicted and measured TC+1 were classified at the prespecified target TC of 5.0 mg/L. The classification accuracy was calculated as with TN and TP representing the numbers of true negative (predicted and measured TC+1 ≥ 5.0 mg/L) and true positive (predicted and measured TC+1 < 5.0 mg/L) predictions, respectively, and n representing the total number of predictions. To note, outside the TDM context, a positive test result indicates the least desirable scenario which demands a clinical/pharmaceutical intervention. In the same way, we defined a positive TDM test result as a subtherapeutic concentration measurement (TC+1 < 5.0 mg/L), warranting a dose optimization. A TC+1 ≥ 5.0 mg/L was thus defined as a negative test result, not needing any dose optimization. Consequently, a true or a false result was designated based on the correctness of the prediction with respect to the cutoff. The sensitivity of the predicted TC+1 to missing covariate data was evaluated using single imputation with the median value around which the covariate is centered in the model. McNemar’s tests were performed to evaluate differences in classification performance between the MAA and the subset of models, or the MSA.

Software

All models were coded in NONMEM (version 7.5; Icon plc) and provided in Supplementary Material. Predictions were performed using NONMEM with a GNU Fortran 95 compiler. Data were analyzed in R (version 4.0.3; R Foundation for Statistical Computing, R Core Team) with the RStudio integrated development environment (version 1.2.5001; RStudio, Inc.).

RESULTS

Data were available from 54 patients with IBD (38 [70%] patients with CD and 16 [30%] patients with UC; Table S1). The majority of these patients (61%, 33/54) received 5 mg/kg infliximab every 6 weeks before changing the dosage regimen to 7.5 mg/kg infliximab every 8 weeks. The median interquartile range (IQR) of the measured TC0 and TC+1 were 7.0, IQR 5.3–9.4 mg/L and 5.0, IQR 3.8–6.7 mg/L, respectively. Only 52% (28/54) of the patients had TC+1 above or equal to 5.0 mg/L.

Eighteen PopPK models were identified. They differed in structure, covariates, and parameter estimates, as well as population, dosing schedules, and sampling schemes that they were based on Table 1, and Tables S2 and S3. Half of the models (50%, 9/18) were developed on data from mixed UC and CD populations. The majority of the models (67%, 12/18) were two‐compartment models. Antibodies to infliximab, serum albumin, and body weight were the most frequently identified covariates on clearance. Body weight was the most commonly identified covariate on volumes of distribution.

TABLE 1

Overview of the 18 candidate infliximab PopPK models

Model	N	IBD type	Treatment phase	Sampling times	Number of compartments
Aubourg 39	133	CD	Induction, maintenance	Peak, trough	2
Brandse_2016 40	20	UC	Induction	Peak, intermediate, trough	2
Brandse_2017 41	332	UC, CD	Induction, maintenance	Peak, intermediate, trough	2
Buurman 42	42	UC, CD	Induction, maintenance	Trough	2
Dotan 43	54	UC, CD, UI	Induction, maintenance	Peak, intermediate, trough	2
Dreesen_2019 44	204	UC	Induction	Trough	1
Dreesen_2021 45	116	CD	Induction, maintenance	Intermediate, trough	2
Edlund 46	68	CD	Maintenance	Intermediate, trough	2
Fasanmade_2009 33	482	UC	Induction, maintenance	Peak, intermediate, trough	2
Fasanmade_2011 34	692	CD	Induction, maintenance	Peak, intermediate, trough	2
Grisic 47	121	UC, CD, UI	Maintenance	Intermediate, trough	2
Matsuoka 48	121	CD	Maintenance	Trough	1
Passot 49	79	UC, CD	Induction, maintenance	Trough	1
Petitcollin 36	91	UC, CD	Maintenance	Trough	1
Ternant_2008 50	33	UC, CD	Induction, maintenance	Peak, intermediate, trough	2
Ternant_2015 51	111	CD	Maintenance	Intermediate, trough	1
Ternant_2018 52	50	UC, CD	Induction, maintenance	Trough	1
Xu 53	788	UC, CD	NS	NS	2

Abbreviations: CD, Crohn’s disease; IBD, inflammatory bowel diseases; N, number of patients; NS, not specified; PopPK, population pharmacokinetic; UC, ulcerative colitis; UI, undetermined inflammatory bowel disease type.

Each patient contributed the same number of consecutive TC samples (i.e., four). The individual predicted concentrations of each model were in good agreement with their measured concentrations, except for the Edlund model predictions that showed a spread deviating from the identity line (Figure S1). The VPCs of the models differed markedly (Figure S2). The Buurman model displayed the best alignment of predicted and measured concentrations. In line with the VPC results, the Buurman model was identified as the best predictive model regarding the distribution of the NPDEs (Figure S3, Table S4).

Using the MSA in the a posteriori prediction modality, the Buurman model was selected for 36% (32%–40%) of the patients, followed by the Ternant_2008 model (25% [16%–34%] of patients) and the Dotan model (22% [22%–24%] of patients; Figure 2). Using the MAA in the a posteriori prediction modality with one previous TC, all models had nearly equal weights (Figure S4). By adding more previous TCs, some models started dominating the a posteriori predictions of the MAA.

FIGURE 2

The weight distribution of population pharmacokinetic models in the study population in seven a posteriori prediction settings and the general model fit setting. Four candidate models that were not selected by any patient in any of the evaluated settings are not shown in the legend (Brandse_2017, Fasanmade_2009, Fasanmade_2011, and Xu model). TC, trough concentration.

Predictive performances evaluations

A priori prediction of the TC+1 was clinically unacceptable with both single‐ and the multi‐model approaches (rBias −75% to +483%, rRMSE 58% to 629%; Figure 3a), except for the prediction with the Edlund model (rBias +16%; 95% CI ‐5% to +36%, rRMSE 77%).

FIGURE 3

The predictive performance of 18 single candidate population pharmacokinetic models versus the multi‐model approaches using all 18 models versus the four models for predicting the infliximab trough concentration (TC) at time + 1 (TC+1). (a) a priori prediction (with only covariate data); (b) a posteriori prediction settings using covariate data and one previous TC (TC0, TC−1, or TC−2). Whiskers indicate the 95% confidence interval (CI) of the relative bias calculated via the standard error (black whiskers indicate 95% CIs including 0). Horizontal red lines indicate ±20% range of the relative that is deemed clinically acceptable. Note: Model weights during a priori prediction are equal (1/number of models), precluding a model selection procedure in this setting. MAA, multi‐model averaging algorithm; MSA, multi‐model selection algorithm; rBias, relative bias; rRMSE, relative root mean square error.

Providing one previous TC (TC0, TC−1, or TC−2) greatly improved the predictive performance (rBias −27% to +38%, rRMSE 28% to 69%; Figure 3b). Providing more than one previous TC improved the predictive performances only marginally (Figure S5). Compared with the single‐model approach, the predictive performances of multi‐model approaches were less sensitive to the number of provided TCs for MAP.

Multi‐model averaging algorithm performed systematically better than MSA both in terms of accuracy and precision. MAA provided more precise predictions than MSA in all a posteriori prediction settings (one previous TC: rRMSE 33% to 41% for the MAA vs. rRMSE 50% to 57% for the MSA; 3 previous TCs: rRMSE 30% for MAA vs. rRMSE 46% for MSA; Figure 3b, Figure S5).

Four candidate models were selected considering their overall predictive performance metrics in the a posteriori prediction settings (Aubourg model, Dreesen_2021 model, and Passot model; all with a negative rBias), and the best model with positive rBias (Ternant_2008 model). The predictive performances of the multi‐model approaches with only the four models were in good agreement with the multi‐model approaches including all models (Figure 3a,b; Figure S5). In addition, by providing at minimum one previous TC, the predictive performances of both multi‐model approaches were clinically acceptable even when only three or two instead of four models were used (rBias −4% to +2%; Figure S6).

The average computation time of the multi‐model approaches using only the four models decreased five‐fold from the multi‐model approaches using all 18 models (average 0.115 s vs. 0.576 s per patient).

An infliximab module was added to TDMx (https://tdmx.shinyapps.io/infliximab/). Results of the objective function values and model averaging predictions using TDMx were in good agreement with NONMEM (a posteriori prediction settings with TC−1; Figures S7 and S8).

The tendency of prediction bias across the measured concentration range from 3.0 to 10.0 mg/L was the least by providing only TC0 in Bayesian forecasting (Figure 4).

FIGURE 4

Bland–Altman plots showing the agreement between the measured infliximab concentrations and the predicted infliximab concentrations across the range of measured infliximab concentrations in various prediction settings using the model averaging algorithm (MAA; orange) and the model selection algorithm (MSA; purple). The vertical red line indicates the 5.0 mg/L trough concentration (TC) target. The solid line with shaded area represents a locally weighted smoother with its 95% confidence interval based on the data (MAA in orange and MSA in purple).

A priori predictions of both single and multi‐model approaches had the lowest classification accuracy (median 59%, IQR 59%–63%) and the highest percentage of falsely predicting the TC+1 ≥ 5.0 mg/L (false negative rate median 35%, IQR 30%–37%; Figure 5). In comparison with the a priori prediction, providing at least one previous TC significantly improved not only the classification accuracy (median 72%, IQR 71%–76%; p < 0.05) but also significantly decreased the false negative prediction rate (median 8%, IQR 6%–15%; p < 0.05). A posteriori prediction with the TC0 resulted in a significantly higher classification accuracy than with the TC−1 or the TC−2 (p < 0.01). In addition, the availability of the TC0 significantly lowered the chance of falsely predicting the TC+1 < 5.0 mg/L in comparison with only providing the TC−1 (p = 0.004). Providing more than one previous TC did not improve the classification accuracy metrics (Figure 5). However, the classification performances of the MAA were not significantly different from the MSA and the other single models (p > 0.10), except for the a posteriori predictions using the Ternant_2008 model with the TC−1 (p = 0.023; Figure 5).

FIGURE 5

The percentage of patients (N = 54) in four classes based on the predicted and measured TC +1 according to the prespecified trough concentration (TC) target of 5.0 mg/L in various prediction settings: (i) true positive (TP): both measured and predicted <5.0 mg/L; (ii) true negative (TN): both measured and predicted ≥5.0 mg/L; (iii) false positive (FP): measured ≥5.0 mg/L, but predicted <5.0 mg/L; (iv) false negative (FN): measured <5.0 mg/L, but predicted ≥5.0 mg/L. (v) Classification accuracy (CA): the number of correct predictions (TP and TN) divided by the total number of predictions (n = 54).

The predictive performance of the single‐model approach with any model was maintained when applying median covariate imputation (Figure 6). In addition, there was no change of accuracy and precision of predictive performances for multi‐model approaches in the a priori setting (MAA: rBias +68%, rRMSE 125% for true value vs. rBias +66%, rRMSE 125% for imputed value), and the a posteriori setting (MAA: rBias −5%, rRMSE 36% for both true value and imputed value; MSA: rBias −3%, rRMSE 38% for true value vs. rBias −1%, rRMSE 39% for imputed value).

FIGURE 6

Comparison of the predictive performance between scenarios with and without covariate data available. The scenario of missing covariate information used a single imputation strategy with the median covariate value around which the covariate effect was centered in the respective model. (a) A priori prediction (with only covariate data); (b) the a posteriori prediction settings using covariate data and one previous TC (TC−1). Whiskers indicate the 95% confidence interval (CI) of the relative bias calculated via the standard error (black whiskers indicate 95% CIs including 0). Horizontal red lines indicate ±20% range of the relative that is deemed clinically acceptable. MAA, multi‐model averaging algorithm; MSA, multi‐model selection algorithm; rBias, relative bias; rRMSE, relative root mean square error.

DISCUSSION

The selection of a PopPK model for guiding individualized dose optimization is a crucial step in MIPD. For infliximab, 18 PopPK models have been developed to describe the PK characteristics of adult patients with IBD. To date, the benefits of MIPD with a single infliximab model in patients with IBD have been evidenced both retrospectively and prospectively. However, alternative approaches that integrate multiple PopPK models have not been investigated for infliximab. In our study, we found that an MAA resulted in the most accurate and precise a posteriori predictions, regardless of the number of TCs provided, as compared to a single‐model approach. A priori prediction using covariate data alone resulted in biased and imprecise predictions with either single‐ or multi‐model approaches. The predictive performance of both single‐ and multi‐model approaches was robust to the lack of covariate data.

PK variability of infliximab is challenging for traditional flowchart‐guided TDM. No significant clinical benefits were shown for proactive TDM during infliximab induction therapy in patients with immune‐mediated inflammatory diseases (i.e., NOR‐DRUM A ). During infliximab maintenance therapy, the clinical benefit of proactive TDM could also not be addressed in patients with IBD (i.e., TAXIT and TAILORIX ), yet it was addressed in a mixed population of patients with immune‐mediated inflammatory diseases (i.e., NOR‐DRUM B ). Recently, the PRECISION trial using a single‐model approach implemented in a Bayesian dashboard for infliximab dosing showed significant clinical benefit over label dosing during maintenance therapy. Due to the acknowledged benefits of MIPD in personalized medicine, , great efforts are being made to improve components of MIPD, such as methods for the selection of models , and methods for the estimation of parameters. , In this study, we investigated alternative approaches allowing the incorporation of multiple PopPK models simultaneously for MIPD. The MSA and MAA could provide more flexibility in PK parameter estimation and potentially increase generalizability to unseen data compared to MIPD using a single‐model approach. In agreement with findings from Uster et al. using vancomycin as a case study, the multi‐model approaches had better predictive performance than any single‐model approach. Furthermore, we found that the MAA outperformed the MSA and single‐model approaches because the MAA systematically resulted in more precise predictions.

The predictive performance of infliximab PopPK models was previously externally evaluated in patients with inflammatory diseases, including patients with IBD. , In the studies of Santacana et al. and Schräpel et al., the two models developed by Fasanmade et al. , (using data from the phase III trials) demonstrated the best predictive performance in patients with IBD. In our study, both Fasanmade models gave inaccurate a posteriori predictions in most of the evaluated settings. In addition, these two models were not selected for any of the patients in the MSA. The differences in predictive performances of candidate models between studies could potentially be caused by differences in the approaches used to assess the model’s predictive performance (e.g., provided measured concentration for MAP, the estimation of empirical Bayes PK parameter approach, and predictive performance metrics). The observed differences emphasize the importance of site‐specific external validation prior to clinical implementation. In our study, we evaluated predictive performance of candidate models for predicting TCs. Infliximab clearance is the PK parameter that mainly drives the TC. Our case is different from, for example, vancomycin, where the exposure target is an area under the curve, which is driven by all PopPK parameters. Therefore, as expected, we did not observe any difference in the predictive performance of one‐ and two‐compartment models (data not shown). Although we reduced the number of models participating in the multi‐model approach to gain computation time without losing predictive performance, this action may not be as innocent as it appears and may show to be a sacrifice in a more extensive external validation/application. Therefore, external validation with all identified 18 models may be suggested prior to using our developed software in other settings.

In our study, we used a comprehensive set of model qualification tools, ranging from closeness of study population and goodness‐of‐fit plots over predictive performance and classification accuracy assessments to Bland–Altman analysis and sensitivity analysis. Nevertheless, to control the inherent risks associated with PK prediction as much as possible, a wider set of diagnostic tools for model qualification for MIPD may still be needed. Apparent contradictory findings between model qualification tools are common. A model that conforms to various model evaluation standards may not perform well in the prediction evaluations. For example, the Edlund model fitted the data worst, but it was the only model with clinically acceptable a priori predictions. Furthermore, whereas the Petitcollin model was developed using data from a clinical setting closest to the one that we are studying, the Buurman model was the best model based on VPC and NPDE. Nevertheless, both models did not perform well in a priori and a posteriori predictions. The a priori prediction is a population prediction based solely on covariate data, whereas VPC and NDPE take into account both covariate and concentration in the evaluations. Therefore, an a priori prediction performance may not be indicated via VPC and NDPE. The complementary use of a comprehensive set of model qualification tools should be considered during model selection. In addition, standard goodness‐of‐fit evaluations are not appropriate for evaluating the suitability and predictive performance of models for MIPD. Yet, because the multi‐model approaches rely on the calculation of model weights based on a goodness‐of‐fit measure, the standard model evaluation toolkit should not just yet be discarded, and the relation between the descriptive and predictive ability of models requires further investigation.

A single TC suffices to allow accurate and precise MIPD. Based on our findings, the acceptable timeframe of TC monitoring to predict the TC+1 accurately was TC from previously consecutive dosing that was not further than three dosing intervals before dosage regimen de‐escalation. Due to interoccasion variability, an “old” concentration may have lost the ability to predict future exposure. Therefore, the predictive performance of MIPD using TCs from the later timepoints may require further investigation. Moreover, providing only one TC adequately informs about PK parameters and subsequently makes the covariate data become relatively unimportant for the predictive performance. Median imputation of missing covariate data is, therefore, a safe strategy. This finding is intuitive, knowing that covariates generally only explain a small part of the interindividual variability (up to 6% for clearance , ), whereas Bayesian forecasting can identify the remaining, often high “unexplained” interindividual variability (median of 32.7%, IQR 28.0–36.0% on clearance , ).

Theoretically, utilizing point‐of‐care testing may improve the clinical and economic benefits of MIPD. In this study, we found that a single most recent TC (at T0) resulted in the highest classification accuracy with not only a low chance of falsely predicting the TC+1 ≥ 5.0 mg/L (i.e., risk of losing therapeutic response) but also a low chance of falsely predicting the TC+1 < 5.0 mg/L (i.e., risk of unnecessary dose escalation). However, a recently published prospective study using a rapid assay during traditional flowchart‐guided proactive TDM (i.e., a decision making flowchart designed to maintain infliximab concentration within the desirable therapeutic range) could not show clinical benefits in patients with IBD during infliximab maintenance therapy. Nevertheless, a rapid assay may show its full potential when used in combination with an MIPD software tool. Yet, a prospective evaluation is warranted.

An MIPD approach could potentially improve the treatment efficacy in patients undergoing dosage regimen de‐escalation. Petitcollin et al. reported that the clearance of infliximab in these patients was not only a factor in patient selection but also a predictor for disease relapse after treatment de‐escalation. In addition, the infliximab clearance gradually increased over time in association with body weight variations. Therefore, the MAA as implemented in the TDMx Bayesian forecasting software tool will be used to guide infliximab dosing in the forthcoming prospective MODIFI study (NCT04982172). In the MODIFI study, we aim to deliver proof‐of‐concept of the superiority of MIPD over empirical dosage regimen de‐escalation. The primary end point is the proportion of patients maintaining steroid‐free, combined clinical and biological remission during 1 year after the start of infliximab de‐escalation.

This study had several strengths. First, we evaluated the predictive performance of multi‐model approaches for MIPD in a very different context (i.e., biological drug and chronic disease) from Uster et al. (i.e., vancomycin and infectious diseases). Second, additional analysis tools (i.e., Bland–Altman analysis and classification accuracy) for evaluating the fit‐for‐purpose of PopPK models for use in MIPD were introduced. Currently, there is no well‐established target of classification accuracy for MIPD approach. To the best of our knowledge, classification accuracy has only been included for model predictive performance evaluation for infliximab in Schräpel et al. Therefore, defining clinical relevance of these additional analysis tools still requires further investigation to facilitate the translation and appropriate use of the MIPD approaches in clinical care. Third, we also scrutinized the importance of utilizing point‐of‐care testing and the availability of covariate data on the predictive performances.

Still, our study had some limitations. First, incomplete reporting of information on error models, median values for centering covariate effects, and variance–covariance matrices limited the reproducibility of the published PopPK models. Therefore, assumptions had to be made for the missing information (Table S2). In recent years, the importance of an “Open” approach to science and the accessibility to mathematical models has become well‐recognized as a crucial step in maintaining reproducibility, rigor, and integrity in published pharmacometrics models. Second, a limited number of patient data from a single clinical center was used in this analysis. This study was an exploratory study and so was not powered to obtain statistical significance. Therefore, interpretation of our results should be done with care and we recognize the importance of continued validation of our MIPD algorithm in patients with IBD in other clinical centers. In addition, the need for center‐specific external validation of our algorithm will be required before broader clinical implementation. The differences between clinical centers include level of health care (e.g., primary care, secondary care, and tertiary care), bioanalysis method, clinical workflows, etc. To allow us and others to do so, we provide the weblink to the MIPD tool in this paper. Third, due to the retrospective nature of our study, a potential selection bias cannot be ruled out. We only collect data of patients who have given written informed consent for collecting their data and serum samples. Therefore, future prospective confirmation of our findings will be needed. Last, the generalizability of our work beyond the studied clinical context will require further investigation to rule out potential bias. We studied the value of MIPD specifically for guiding dose de‐escalation, but the value of our work may be of interest in other clinical scenarios as well (e.g., dose intensification, proactive TDM, and reactive TDM). In addition, concentration data used in this analysis were measured using only one commercially available assay. Therefore, external validations with larger and different cohorts in other clinical centers using other bioanalysis assays are needed to confirm the generalizability of our work.

To conclude, we developed a robust and precise MAA for guiding infliximab MIPD using a single recently measured TC. The algorithm is implemented in the freely available TDMx software tool and will be evaluated in the prospective MODIFI study (NCT04982172).

AUTHOR CONTRIBUTIONS

W.K. wrote the manuscript. W.K. and E.D. designed the research. W.K., S.G.W., A.K., Z.W., and E.D. performed the research. W.K. and E.D. analyzed the data. A.O., D.T., J.S., S.V., and M.F. contributed new reagents/analytical tools.

CONFLICT OF INTEREST

J.S. received financial support for research from Galapagos, speaker fees from Abbvie, Falk, Takeda, Janssen, and Fresenius, and consultancy fees from Janssen and Ferring. S.V. received financial support for research from AbbVie, Johnson and Johnson, Pfizer, Galapagos, and Takeda, and consultancy and/or speaker fees from AbbVie, Abivax, Agomab, Arena Pharmaceuticals, Avaxia, Bristol Myers Squibb, Boehringer Ingelheim, Celgene, Dr. Falk Pharma, Ferring, Galapagos, Genentech‐Roche, Gilead, GSK, Hospira, Janssen, Mundipharma, MSD, Pfizer, Prodigest, Progenity, Prometheus, Robarts Clinical Trials, Second Genome, Shire, Surrozen, Takeda, Theravance, and Tillots Pharma AG. M.F. received financial support for research from AbbVie, Amgen, Biogen, Janssen, Pfizer, Takeda, and Viatris, speaker fees from AbbVie, Amgen, Biogen, Boehringer Ingelheim, Falk, Ferring, Janssen, Lamepro, MSD, Mylan, Pfizer, Sandoz, Takeda, and Truvion Healthcare, and consultancy fees from AbbVie, Boehringer Ingelheim, Celltrion, Janssen, Lilly, Medtronic, MSD, Pfizer, Sandoz, Takeda, and Thermo Fisher. All other authors declare no conflicts of interest.

Appendix S1

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