Differential Oral Absorption Pharmacokinetics of Tacrolimus in Simultaneous Kidney-Pancreas Transplant Compared to Kidney Transplant Recipients

Abstract

Background and Objectives

Simultaneous pancreas kidney transplantation (SPK) is a preferred option for type 1 diabetes (T1DM) patients with end-stage renal disease (ESRD). Most transplant centers use kidney transplant (KT) protocols target trough concentrations (C₀) to dose tacrolimus in SPK recipients, due to a lack of evidence for optimal tacrolimus C₀ in SPK recipients. However, tacrolimus pharmacokinetics (PK) might be altered in SPK recipients due to diabetic gastroparesis or complications from intraperitoneal surgery and/or enteric drainage. We therefore aimed to compare oral tacrolimus PK in SPK versus KT recipients as a first step to define the optimal target tacrolimus concentrations in SPK recipients.

Methods

A retrospective observational study was performed to describe and compare tacrolimus population PK in SPK and KT recipients. Relevant demographic and PK data were extracted from our local transplantation database for patients transplanted between 2005 and 2020 at our hospital. Pharmacokinetic data were analyzed using nonlinear mixed effect modeling in NONMEM. Furthermore, simulations were performed to assess potential differences in AUC_0-12h to C₀ ratios between SPK and KT recipients.

Results

Tacrolimus population PK in SPK and KT recipients were best described by two-compartmental models. The combined SPK and KT model showed a significantly reduced oral absorption rate for SPK recipients, compared to KT recipients (0.231 h⁻¹ vs 0.336 h⁻¹ respectively). Simulations indicated a 10% (95% CI 8.8%–11.1%) lower AUC_0–12h to C₀ ratio in SPK recipients compared to KT recipients.

Conclusions

We successfully developed two separate population PK models for tacrolimus in SPK and KT recipients together with a combined SPK and KT model, showing a significantly reduced tacrolimus oral absorption rate in SPK recipients. In addition, our data suggested that SPK recipients might need higher C₀ target concentrations to obtain a similar tacrolimus exposure as KT recipients.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s40262-026-01689-3.

Key Points

Simultaneous pancreas kidney transplant recipients showed a significantly reduced tacrolimus oral absorption rate and an approximately 10% lower area under the concentration time curve (AUC0-12h) to trough concentration (C0) ratios compared to KT recipients.

These differences suggest that SPK recipients might need higher C0 target concentrations to obtain an equivalent tacrolimus exposure as in KT recipients.

Introduction

Type 1 diabetes mellitus (T1DM) is associated with an approximately 50% and up to over 70% lifetime risk for developing kidney disease [1] due to higher glycemic exposure, dyslipidemia, and hypertension [2]. Despite considerable progress in the development of insulin delivery and monitoring systems, T1DM remains associated with a significant disease burden for patients, including end-stage renal disease (ESRD). A simultaneous pancreas-kidney transplantation (SPK), or perhaps alternatively a pancreas after pre-emptive living donor kidney transplantation (PAK), is still a preferred option for T1DM patients with ESRD [3, 4].

When it comes to immunosuppression after SPK, most centers empirically follow kidney transplant (KT) protocols, since optimal immunosuppressive (IS) regimens for SPK recipients are poorly defined owing to scarcity of evidence and difficulties in the diagnosis and monitoring of rejection [5–7]. Yet, a pancreas graft is considered to be a more immunogenic transplantation compared to a kidney, owing to among others, lack of human leukocyte antigen (HLA) matching within Eurotransplant allocation, increased danger signals from digestive pancreatic enzymes and the immunogenicity of the duodenum patch, which may warrant increased immunosuppression at least in the first period after transplantation [8].

Most transplant centers individualize tacrolimus dosing based on whole blood trough concentrations (C₀), assuming a reasonable correlation between tacrolimus C₀ and the overall exposure, defined as the area under the concentration-time curve (AUC) [9]. Despite C₀-based immunosuppression titration being universally accepted, it has several important limitations including a high inter-patient variability in the relation between C₀ and AUC_0-12h [10–12].

Another limitation of C₀-based dose individualization is that potential alterations in oral tacrolimus absorption kinetics are difficult to recognize. Up to 50% of T1DM patients with poorly regulated glucose show diabetic gastroparesis, due to autonomic neuropathy, hyperglycemia and neuromuscular inflammation or injury [13], potentially leading to delayed absorption of orally administered drugs [14]. Since tacrolimus is usually orally administered, SPK patients might show a different relation between AUC_0-12h and C₀ due to delayed tacrolimus absorption compared to KT recipients, necessitating optimization of C₀ target ranges in SPK recipients. Moreover, oral absorption pharmacokinetics (PK) may change over time after SPK transplantation, due to the slow tapering of opiate analgesics after surgery, recovery of the bowel after intra-peritoneal surgery and transplantation-induced amelioration of gastric emptying [15].

Here, we report a head-to-head comparison of tacrolimus absorption PK between SPK and KT recipients by using a population PK modeling approach. We hypothesized that SPK is associated with slower tacrolimus absorption PK and therefore shows a differential relation between AUC_0–12h and C₀ compared to KT recipients. The primary aim of this study was therefore to develop and internally validate two separate population PK models for tacrolimus in SPK and KT recipients. The secondary aim included evaluation of the effects of potential differences in PK on the relationship between 12-hour tacrolimus exposure and trough concentrations.

Methods

Study Design

A retrospective observational study was performed at the Leiden University Medical Center (LUMC), Leiden, The Netherlands, to evaluate potential differences in PKs between SPK and KT recipients and was performed in accordance with the Declaration of Helsinki. The protocol for retrospective analysis was approved by our Institutional Review Board (IRB) (approval date: June 6 2020, approval number: W2020.031).

All data originated from our local online transplantation database. All patients who underwent KT or SPK between 2005 and 2020 were considered eligible for inclusion. Patients were excluded in case of an absence of tacrolimus AUC_0–12h measurements during the first year after transplantation and when they did not receive tacrolimus/mycophenolate/prednisolone triple therapy at transplantation. Because the age limit for undergoing SPK is 55 years at our center, patients older than 55 years were generally excluded from the dataset.

At our center, new SPK and KT recipients start per protocol with a twice-daily 5-mg tacrolimus dosing regimen, which is then individualized by the treating physician based on tacrolimus whole blood concentrations and the clinical situation of the patient. However, some patients may switch to once-daily tacrolimus formulations if needed. Since once-daily tacrolimus formulations are known to have prolonged absorption PKs [16, 17], patients with once-daily tacrolimus formulations were excluded from the dataset.

Manual validation of tacrolimus dosing and exposure data was required for each included patient. It was therefore not practically feasible to include the entire eligible cohort in our dataset. To obtain a representative study population while maintaining feasibility of detailed manual data verification, patients were randomly selected, meaning that the selection process was performed independent of patient or clinical characteristics.

Data on patient characteristics such as type of transplantation (i.e., SPK or KT), age, sex, body weight, height, serum creatinine and time after transplantation were extracted from the transplantation database. In addition, standard of care PK data including tacrolimus dose, time of dose administration, tacrolimus concentrations and corresponding sampling times were extracted from the local laboratory information system. Inclusion was based on the availability and completeness of the PK data.

Sampling and Bioanalysis

The exact timing of the first tacrolimus C₀ sample was left to the discretion of the treating physician but was generally sampled around Day 4 after transplantation, after steady state PKs were assumed to be reached. In addition, a whole-blood intensive sampling tacrolimus AUC (T = 0, 1, 2, 3, 4, 5 and 6 hours) was sampled one week after transplantation. Abbreviated whole blood AUCs (T = 0, 1, 2 and 3 hours) were obtained at 6 weeks, 6 months and 1 year after transplantation. Whereas the abbreviated sampling scheme was based on a published limited sampling strategy, the intensive sampling scheme included pragmatically chosen sampling times, based on information from the same study [18]. Tacrolimus whole-blood concentrations were measured with a validated liquid chromatography tandem mass spectrometry (LC-MS/MS) method, with a lower limit of quantification (LLOQ) of 0.4 μg/L [19, 20]. A complete overview of the methods, reagents, and validation can be found in the original paper.

Population Pharmacokinetic Modeling

Tacrolimus whole-blood concentration data were described with a non-linear mixed effect modeling approach. Initially, two separate population PK models were developed: i) For the SPK population (model 1) and ii) for the KT population (model 2). This approach was pragmatically chosen, since a separate tacrolimus population PK model for SPK recipients would be more easily implementable in our local clinical dosing tool.

One- and two-compartmental models with a first-order oral absorption process were initially tested to describe the concentration-time data within each cohort. In addition, an oral absorption lag time was tested to account for a potential delay in the start of the oral absorption process. Since tacrolimus oral bioavailability was unidentifiable, owing to the lack of intravenous tacrolimus data in our dataset, oral bioavailability was fixed at 23%, based on literature [18, 20].

To account for parameter variability, inter-individual variability (IIV) was tested on all structural model parameters. The IIV was modelled as θ_i = θ_pop * exp(η_IIV), where θ_i is the empirical Bayesian estimate (EBE) for individual i, θ_pop is the population value of parameter θ and η_IIV the log normally distributed inter individual variability of parameter θ_pop. Inter occasion variability (IOV) was accounted for by pragmatically including multiple sampling occasions as separate IDs in the analysis.

Since oral absorption kinetics might change over time after SPK transplantation [15], time after transplantation was tested as covariate on the oral absorption rate. The potential effect of time after transplantation was tested as a categorical covariate on the oral absorption rate parameter (i.e., 0–6 weeks, 6–26 weeks and > 26 weeks after transplantation) by using the following equation:

$$KA=\left\{\begin{array}{cc}\mathit{TVKA}& if0-6weeks\\ TVKA·\left(1+{\theta }_{\left(6-26weeks\right)}\right)& if6-26weeks\\ TVKA·\left(1+{\theta }_{\left(>26weeks\right)}\right)& if>26weeks\end{array}\right)$$

where KA is the oral absorption rate, TVKA is the estimated absorption rate in the reference group (e.g., KA at 0–6 weeks after transplantation), θ _{COV(6–26 weeks)} is the estimated effect size on KA of time after transplantation between 6–26 weeks and θ_{COV(> 26 weeks)} is the estimated effect size on KA of time after transplantation being more than 26 weeks.

Because the separate models indicated potential differences in lag time and the oral absorption rate, the full dataset, including both the SPK and KT cohort data, was fitted with a single model (model 3) to be able to test the statistical significance of the observed differences. Since no variability on the lag time parameter could be estimated in model 3, we refrained testing the effect of transplantation type on this parameter. The effect of transplantation type on the absorption rate was defined as:

$$KA=TVKA\bullet (1+{\theta }_{\mathit{SPK}})$$

where KA is the absorption rate, TVKA is the estimated KA for the reference population (i.e., KT recipients) and θ _SPK is the estimated effect of SPK transplantation on KA.

Model selection was based on a significant reduction of the Objective Function Value (∆OFV) defined as a ∆OFV of −6.63 or greater (p < 0.01, assuming a χ²-distribution with 1 degree of freedom). In addition, graphical methods were used to evaluate model performance, including population predicted versus observed concentrations, individual predicted versus observed concentrations, conditional weighted residual errors versus population predictions, conditional weighted residual error versus time, prediction-corrected visual predictive checks (pcVPCs) and by normalized prediction distribution error (NPDE) plots. Finally, a bootstrap analysis (n = 2000) was performed to assess the parameter estimate robustness.

Simulations & Statistics

Because of observed differences in the absorption lag time and absorption rate between SPK and KT recipients, we performed model simulations with model 1 and model 2 to evaluate the effect of this difference in PKs on the AUC_0–12h to C₀ ratios. For each model, 500 densely sampled (i.e., 0.1 hour) tacrolimus concentration-time datasets were simulated for a patient receiving twice-daily 5-mg tacrolimus. Since a first tacrolimus C₀ is generally obtained on the fourth day after transplantation, the AUC_0–12h was calculated for the first dosing interval on Day 4. In addition, the C₀ corresponding to the first dosing interval of Day 4 was extracted from each simulated dataset to calculate the AUC_0-12h to C₀ ratio. Subsequently, the potential difference in the AUC_0-12h to C₀ ratios between the SPK and KT population was assessed by using a generalized linear model (GLM) with a Gamma distribution and a log link function, to appropriately account for the strictly positive and right-skewed nature of the ratio data.

Software

Data preparation was performed in Microsoft Excel for Windows 365 MSO (Version 2208). In addition, R (version 4.4.0) in Rstudio was used for data manipulation and for graphical evaluation of the data and the population PK models. Pharmacokinetic data analysis was performed in NONMEM version 7.4.4 and PsN version 5.0.0. Model simulations were performed with the RxODE2 version 2.1.3 package for R statistics. The PKNCA (version 0.11.0) package for R statistics was used for AUC calculation.

Results

Demographics

After screening for the inclusion and exclusion criteria, a total 85 SPK and 94 KT recipients were included in the final dataset (Fig. 1), contributing 1275 and 1073 samples to the SPK and KT model development datasets, respectively. The number of patients with a T1DM diagnosis were 76 and 4 for the SPK and KT cohorts, respectively. A full overview of the patient characteristics is shown in Table 1. The observed tacrolimus concentrations versus time after dose are shown in Fig. 2.

Fig. 1.

Flowchart of the study population selection

Table 1.

Patient characteristics

	Kidney-pancreas recipients (n = 85)	Kidney transplant recipients (n = 94)
Demographic data
Age (years) (median [range])	45 [24–56]	44 [19–76]†
Sex (M/F)	55/30	54/40
Body weight (kg) (median [range])	73 [44–104]	68 [40–95]
Height (cm) (median [range])	175 [150–189]	175 [140–189]
Type 1 diabetes mellitus(n)	76	4
Laboratory data
Serum creatinine (µmol/L) (median [range])	111 [50–1105]	123 [43–1101]
Pharmacokinetic data
Samples (n)	1275	1073
Tacrolimus dose (mg) (median [range])	4.0 [1.0–12.0]	4.0 [0.5–15]
Sampling occasions per patient (n) (median [range])	5 [1–3]	2 [1–7]
Samples per patient (n) (median [range])	3 [2–10]	3 [2–9]
Sampling moment (days after transplantation) (median [range])	59 [4–502]	47 [3–535]

^†Included one patient aged > 55 years

Fig. 2.

Observed tacrolimus concentrations versus time after dose plot for combined kidney pancreas (SPK) (A) and kidney transplant only recipients (B)

Population Pharmacokinetic Modeling

The population PKs of tacrolimus in SPK and KT populations were best described by two-compartmental disposition models. Oral tacrolimus absorption was best described by incorporating a linear absorption model with an absorption lag time. The bootstrap parameter estimates and 95% confidence intervals (CIs) were in good agreement with the final models. Furthermore, the basic goodness of fit plots (Fig. 3) showed that model-predicted and individual-predicted concentrations were in acceptable agreement with the observed concentrations. The pcVPCs (Fig. S1) indicated adequate predictive performance of both models, with the observed data percentiles largely falling within the 95% CIs of the simulated data.

Fig. 3.

Model goodness of fit plots for the simultaneous pancreas kidney transplantation (SPK) model (panels A–D) and the kidney transplantation (KT) tacrolimus model (panels E–H): observed versus population predicted concentrations plots (A, E); observed versus individual predicted concentration plots (B, F); conditional weighted residuals versus predicted concentration plots (C, G) and conditional weighted residuals versus time after dose (D, H)

In addition, the NPDE plots showed that the simulated data were adequately normally distributed (Fig. S4). The final model population parameters and bootstrap parameter estimates are shown in Table 2. A complete overview of the model selection process is shown in Supplemental Tables S1 and S2.

Table 2.

Model parameters

	Kidney-pancreas model				Kidney model
	Population parameter (RSE%)	Shrinkage (%)	Bootstrap median	95% Bootstrap CI	Population parameter (RSE%)	Shrinkage (%)	Bootstrap median	95% Bootstrap CI
Structural parameters
Oral bioavailability (%)	23 (Fixed)	–	23 (Fixed)	–	23 (Fixed)	–	23 (Fixed)	–
Absorption lag time (h)	0.77 (5)	–	0.76	0.64–0.87	0.53 (7)	–	0.53	0.45–0.76
KA (h−1)	0.231 (15)	–	0.240	0.170–0.363	0.336 (17)	–	0.349	0.282–0.709
CL (L/h)	6.28 (3)	–	6.27	5.92–6.62	5.35 (5)	–	5.32	4.60–5.79
Vc (L)	10.9 (26)	–	11.2	5.4–24.2	11.8 (50)	–	11.8	6.1–35.3
Q (L/h)	20.1 (15)	–	20.6	14.6–28.8	14.9 (13)	–	15.2	12.8–18.1
Vp (L)	125 (14)	–	122	93–178	177 (33)	–	178	102–287
Interindividual variability
Oral bioavailability (CV %)	48.2 (7)	5	46.3	37.5–52.7	53.5 (7)	6	51.2	43.7–59.4
KA (CV %)	86.2 (9)	24	90.5	69.4–123.9	67.8 (17)	27	65.5	22.9–153.9
CL (CV %)	16.6 (52)	47	20.2	8.1–32.4	23.7 (29)	35	25.9	13.7–37.6
Vc (CV %)	122.1 (13)	48	126.5	69.2–211.0	143.7 (14)	48	155.0	76.0–247.7
Error model
Proportional error (%)	16.2 (14)	–	16.2	12.7–16.8	16.2 (11)	–	16.2	14.1–17.9

CL clearance, CV coefficient of variation, KA oral absorption rate,  Q intercompartmental clearance, RSE relative standard error, Vc central volume of distribution, Vp peripheral volume of distribution

Parameter estimates from model 1 and model 2 suggested an increased absorption lag time and a lower oral absorption rate (0.77h vs 0.53h and 0.231 h⁻¹ versus 0.336 h⁻¹ for lag time and absorption rate in SPK and KT, respectively) in SPK recipients compared to KT patients. Inclusion of transplantation type on KA in model 3 indicated a significant difference in KA between the two populations (∆OFV = −52 points, 1 degree of freedom). Since no IIV could be estimated for absorption lag time, we refrained from testing the effect of transplantation type on this parameter. Parameter estimates and basic goodness of fit plots for model 3 are shown in supplemental Table S3 and Figure S3.

Simulations

Based on the simulations, the median (min-max) AUC_0–12h at a twice-daily 5-mg dosing regimen, was 172.62 μg*h/L (49.23–788.79 μg*h/L) and 191.37μg*h/L (33.64–783.09 μg*h/L) for the SPK and KT populations, respectively. The median (min–max) AUC_0–12h to C₀ ratios were 15.55 (13.15–19.31) and 17.50 (13.43–22.49) in SPK and KT recipients, respectively. Comparison of the AUC_0–12h to C₀ ratios between SPK and KT recipients by GLM analysis (Supplemental Table S4), showed a 10% (95% CI: 8.8%–11.1%, p <0.001) lower AUC_0-12h to C₀ ratio in the SPK population, suggesting that SPK is associated with lower tacrolimus drug exposures compared KT recipients for the same C₀. Visual representations of simulated concentration time curves with a twice-daily 5-mg tacrolimus dosing regimen are shown in Figure S4 for the SPK and KT populations. In addition, AUC_0–12h values at a tacrolimus target concentration of 8 μg/L are shown in supplemental Figure S5.

Discussion

To our knowledge, this is the first study reporting a head-to-head comparison of tacrolimus oral absorption PKs in SPK versus KT recipients. We successfully developed two population PK models for tacrolimus for both populations. In addition, we showed a significantly slower oral absorption rate in SPK recipients. Subsequently, model simulations suggested lower AUC_0–12h to C₀ ratios in SPK recipients compared to KT recipients.

Type 1 diabetes mellitus is associated with multiple physiological changes that might affect oral drug absorption, including decreased gastric mucosal blood flow and changes in gastric emptying and intestinal transit times [21]. Moreover, gastrointestinal motility has shown to be directly affected by blood glucose concentrations [22, 23]. The primary aim of the current study was therefore to evaluate potential differences in tacrolimus oral absorption PKs between SPK and KT recipients.

Models 1 and 2 showed differences between both groups in the absorption lag time and absorption rate. Although further testing showed a significant difference in the absorption rate between SPK and KT recipients, we were unable to test the significance of the observed difference in absorption lag time. However, visual assessment of the simulated concentration-time curves (Fig. S4) showed that the impact of the observed difference in absorption lag time on the concentration time curves was neglectable. We therefore postulate that the lower absorption rate in SPK recipients is the most important driver that causes differential oral absorption kinetics of tacrolimus in SPK recipients compared to KT recipients.

Literature about the effect of diabetes and SPK transplantation on tacrolimus PKs is extremely scarce and mostly limited to older data in relatively small study populations. Duijnhoven et al reported a study evaluating the effect of diabetes on single-dose tacrolimus PKs in 7 diabetic and 11 non-diabetic patients awaiting a kidney or combined pancreas-kidney transplantation [24]. In line with our findings, their non-compartmental analysis showed reduced AUC_0–12h values in diabetic patients, compared to the non-diabetic patient group. Although this difference was not statistically significant—possibly due to the small study population—their results suggested slightly differential absorption kinetics and a potential need for differential tacrolimus dosing in diabetic patients. In addition, they reported a small but non-significant difference in the median maximum concentrations (C_max) between the diabetic and non-diabetic group, with a nearly equal time to maximum concentration (T_max). These results are in line with our findings in SPK patients (Fig. S4), which show a slightly reduced C_max in the SPK population, but a nearly unchanged T_max.

Interestingly, a study reporting on the steady state tacrolimus PKs in a cohort of 11 diabetic and 9 non-diabetic stable kidney transplant patients, indicated a slightly higher, but non-significant, dose normalized AUC_0–12h in diabetic patients compared to non-diabetic patients [25]. Although these findings suggest that diabetes might influence tacrolimus PKs, caution is needed when projecting these findings on the SPK population, due to procedural differences in SPK recipients, such as the intraperitoneal surgery, enteric drainage, prolonged opiate use, or the occurrence of ileus.

Our data did not show a significant effect of time after transplantation on AUC_0–12h to C₀ ratios. Mechanistically, it might be expected that drug absorption PKs slowly normalize after SPK transplantation, because of the slow tapering of opiates, recovery after intraperitoneal surgery and amelioration of the diabetic gastroparesis because of improved glucose regulation after transplantation [15]. Possibly, we lacked sufficient power with our current population size to identify a potentially slow recovery process. In addition, the variability in absorption PK might be partially explained by procedural factors. However, since our data did not include information on opiate use after SPK and all transplantations had enteric drainage, we were not able to perform a sub-analysis to evaluate the extent to which these factors might contribute to the altered tacrolimus absorption kinetics. Therefore, for future studies, it would be interesting to analyze larger patient cohorts and to evaluate the extent to which clinical characteristics, such as opiate use, influence tacrolimus PKs.

Oral bioavailability was fixed at 23% for both populations, based on previous studies [18, 20]. Because we hypothesized that SPK might have differential tacrolimus absorption PKs, it might be possible that besides the oral absorption rate, oral bioavailability is also altered in the SPK population. However, our data did not include tacrolimus concentrations after intravenous tacrolimus administration. It was therefore not possible to estimate the oral bioavailability parameter. However, since the other structural parameters are proportionally related to the oral bioavailability parameter, we considered it to be unlikely to affect our final conclusions.

Model simulations indicated that median AUC_0–12h to C₀ ratios were approximately 10% lower in SPK recipients compared to KT recipients, suggesting that slightly higher target C₀ concentrations are needed in SPK recipients to achieve similar overall tacrolimus exposures as in KT recipients. However, the scope of the current study was confined to the assessment of potential differences in tacrolimus absorption PKs between SPK and KT recipients. Therefore, we were unable to evaluate the relationship between tacrolimus exposure and clinical outcomes in SPK recipients. To enable clinical translation of our findings and identify the optimal tacrolimus exposure range for SPK recipients, our group is currently working on a study focusing on the relation between tacrolimus exposure metrics and clinical outcomes. This follow-up study will be published separately.

Finally, an important strength of the current study is that we had access to a unique dataset that included PK data both from SPK and KT recipients. This not only enabled the evaluation of population PKs of tacrolimus in SPK recipients but also enabled a head-to-head comparison of the tacrolimus population pharmacokinetics in SPK versus that in KT recipients.

Conclusion

In the current study, we successfully developed two separate population PK models for tacrolimus in SPK and KT recipients. In addition, we showed differential tacrolimus oral absorption PKs between SPK and KT patients, suggesting that KT-based tacrolimus C₀ targets might not be optimal for SPK recipients. Future studies on the relation between tacrolimus exposure and clinical outcomes are warranted, to determine the optimal tacrolimus exposure range in SPK recipients.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

Open access funding provided by University of Oslo (incl Oslo University Hospital). No external funding was used in the preparation of this manuscript.

Declarations

Conflict of interest

Dirk Jan Moes is Editorial Board member of Clinical Pharmacokinetics. Dirk Jan Moes was not involved in the selection of peer reviewers for the manuscript nor any of the subsequent editorial decisions. Jasper Kamp, Armin Gelinck, Maryam Lyousoufi, Soufian Meziyerh, Siebe Spijker, Volkert Huurman, Paul van der Boog and Aiko de Vries declare that they have no conflict of interests.

Availability of data and material

Data are available from the corresponding author upon reasonable request. All the model codes have been provided in supplementary materials.

Code availability

The R code required to run the simulations and analyses is available upon request from the corresponding authors.

Ethics approval

This study was conducted in accordance with Good Clinical Practice guidelines and the Declaration of Helsinki. The protocol was approved by the Institutional Review Board (IRB), Medical Ethics Review Committee Leiden/Den Haag/Delft (date of approval: June 6, 2020, approval number: W2020.031).

Consent to participate

A waiver was granted by the IRB for the requirement for informed consent, because obtaining consent was not practically feasible given the large number of patients and the likelihood that some patients were deceased. All data were handled in accordance with institutional policies to protect patient confidentiality and were analyzed in de-identified form.

Consent for publication

Not applicable.

Author contributions

Conception and design: Dirk Jan Moes , Aiko de Vries. Acquisition of data: Maryam. Lyousoufi, Soufian Meziyerh. Analysis and interpretation of data: Jasper Kamp, Armin Gelinck. Writing, review and/or revision of the document: All authors. Final approval of manuscript: All authors.