Pharmacokinetic-pharmacodynamic modelling and simulation of ustekinumab for inflammatory bowel disease

doi:10.21203/rs.3.rs-1460533/v1

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Research Article

Pharmacokinetic-pharmacodynamic modelling and simulation of ustekinumab for inflammatory bowel disease

https://doi.org/10.21203/rs.3.rs-1460533/v1

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posted 21 Mar, 2022

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Ustekinumab (UST) therapy is effective for induction and maintenance therapy for inflammatory bowel disease (IBD). Although there are differences in dosage regimen among countries and indications, and the differences have implications for efficacy, the implications have yet to be analysed by a model-informed approach. The aim of this study is to evaluate the implications for efficacy of the different dosage regimens of UST for IBD using our pharmacokinetic-pharmacodynamic (PK/PD) model.

We constructed a PK/PD model based on an indirect response model with an effect compartment and simulated the sequential changes of therapeutic effect following various dosage regimens.

Sequential changes in the therapeutic effect obtained with our model were in good agreement with the observed values following repeated administration of UST for IBD patients. The simulation indicated the importance of an initial intravenous administration of UST for IBD patients. Furthermore, the dose interval of maintenance therapy at every 8 weeks was marginally more effective than at every 12 weeks, though there was almost no difference in the fluctuation range, and a stable therapeutic effect was obtained by both dosage regimens.

The results showed that the presented PK/PD model is capable of predicting sequential changes in the therapeutic effect of UST for IBD, and the implications for efficacy of the different dosage regimens could be evaluated by simulation with various dosage regimens.

ustekinumab

Crohn’s disease

ulcerative colitis

pharmacokinetics

pharmacodynamics

model-informed precision dosing

Inflammatory bowel disease (IBD) refers to diseases related to chronic or remitting/relapsing intestinal inflammation, primarily ulcerative colitis (UC) and Crohn’s disease (CD) [1]. IL-12 and IL-23 are involved in the development of IBD [2], and the secretion of IL-12 and IL-23 by intestinal antigen-presenting cells is increased in IBD patients [3, 4]. Ustekinumab (UST) is a humanized IgG monoclonal antibody to the p40 subunit of IL-12 and IL-23 [5]. UST therapy is effective for the induction and maintenance therapy for IBD [6, 7]. The standard dosage regimen of UST for IBD is approximately 6mg/kg according to the weight of patients (55kg or less: 260mg; between 55kg and 85kg: 390mg; more than 85kg: 520mg) as a single intravenous administration, followed by 90mg 8 weeks later as a subcutaneous administration. Then, 12 weeks after that, a maintenance dose of 90mg every 12 weeks administered subcutaneously is recommended by the Pharmaceuticals and Medical Devices Agency (PMDA) of Japan and the European Medicines Agency (EMA) [8, 9], while the Food and Drug Administration (FDA) of the USA recommends dose intervals for maintenance therapy of 8 weeks [10]. Furthermore, the dosage regimen of UST for psoriasis (PS) is an initial dose of 45mg administered subcutaneously, followed by a 45mg dose 4 weeks later, and then every 12 weeks thereafter. [8–10]. It is considered that such differences in dosage regimen will have implications on the efficacy of UST, though that has yet to be analysed by a model-informed approach.

The aim of this study is to evaluate the implications for efficacy of the different dosage regimens of UST for IBD using pharmacokinetic-pharmacodynamic (PK/PD) model.

Data for pharmacokinetic and pharmacodynamic analysis

Data used for analyses in this study were extracted from previous reports. PK parameters (2-compartment model) for UST obtained from UC and CD patients in a population PK (PPK) analysis report are shown in Table 1 [11, 12]. Therapeutic effect of CD patients was evaluated using the Crohn’s disease activity index (CDAI) [13]. In addition, from an international phase III trial of maintenance therapy for CD patients (trial number: CRD3003) [11], the mean data representing continuous changes in CDAI after UST administration of 397 CD patients were collected as follows: Single intravenous administration of 130mg or 6mg/kg, followed by subcutaneous administration of 90mg every 12 weeks (Group 1) and every 8 weeks (Group 2), and placebo administration (Group 3) until Week 54. In addition, therapeutic effect in UC patients was evaluated using partial Mayo score (Mayo score without endoscopy findings) [14, 15]. From an international phase III trial of maintenance therapy for UC patients (trial number: UCO3001) [7, 16], the mean data representing continuous changes in partial Mayo score after UST administration of 523 UC patients were collected at the above-mentioned dosage regimens for CD. The maintenance trials extracting the data of therapeutic effect were conducted by re-randomizing the patients who participated in induction treatment trials, in which patients were given a single intravenous administration (130mg or 6mg/kg) and obtained an effect at day 56 after the induction treatment trials. Therefore, since the initial dose (D_i) of each group was not equal, we calculated the D_i from the following Eq. (1) using the baseline serum UST concentration of the maintenance treatment trials (C_b) and the PK parameters shown in Table 1. In this study, the weight of patients was assumed to be 65kg so that it would be 6mg/kg when 390mg was administered in the weight-based dosage regimen.

Table 1

PK parameters employed in PK/PD model
Parameter	Definition	Value	Unit	Reference
CL^CD	Clearance in CD patients	0.191	L/day	[11]
V₁^CD	Volume of distribution of the central compartment in CD patients	2.74	L	[11]
V₂^CD	Volume of distribution of the peripheral compartment in CD patients	1.88	L	[11]
Q^CD	Inter-compartmental clearance in CD patients	0.287	day^− 1	[11]
k_a^CD	Absorption rate constant in CD patients	0.181	day^− 1	[11]
F^CD	Bioavailability in CD patients	0.783		[11]
C_b1^CD	Baseline of serum UST concentration in Group 1 of CD patients	4.62	µg/mL	[11]
C_b2^CD	Baseline of serum UST concentration in Group 2 of CD patients	5.60	µg/mL	[11]
C_b3^CD	Baseline of serum UST concentration in Group 3 of CD patients	5.49	µg/mL	[11]
D_i1^CD	Estimated initial dosage in Group 1 of CD patients	218	mg	-
D_i2^CD	Estimated initial dosage in Group 2 of CD patients	264	mg	-
D_i3^CD	Estimated initial dosage in Group 3 of CD patients	259	mg	-
CL^UC	Clearance in UC patients	0.186	L/day	[12]
V₁^UC	Volume of distribution of the central compartment in UC patients	3.01	L	[12]
V₂^UC	Volume of distribution of the peripheral compartment in UC patients	1.43	L	[12]
Q^UC	Inter-compartmental clearance in UC patients	0.157	day^− 1	[12]
k_a^UC	Absorption rate constant in UC patients	0.142	day^− 1	[12]
F^UC	Bioavailability in UC patients	0.872		[12]
C_b1^UC	Baseline of serum UST concentration in Group 1 of UC patients	8.06	µg/mL	[16]
C_b2^UC	Baseline of serum UST concentration in Group 2 of UC patients	8.75	µg/mL	[16]
C_b3^UC	Baseline of serum UST concentration in Group 3 of UC patients	7.67	µg/mL	[16]
D_i1^UC	Estimated initial dosage in Group 1 of UC patients	378	mg	-
D_i2^UC	Estimated initial dosage in Group 2 of UC patients	410	mg	-
D_i3^UC	Estimated initial dosage in Group 3 of UC patients	360	mg	-

$${D}_{i}={C}_{b}\bullet \left\{\frac{{V}_{1}\bullet \left({k}_{21}-{k}_{12}\right)}{\left({k}_{10}-{k}_{12}\right)\bullet {e}^{-56\bullet {k}_{12}}}+\frac{{V}_{1}\bullet \left({k}_{12}-{k}_{21}\right)}{\left({k}_{10}-{k}_{21}\right)\bullet {e}^{-56\bullet {k}_{21}}}\right\}$$

where V₁ (L) represents the volume of distribution of the central compartment, k₁₂ (day^− 1) and k₂₁ (day^− 1) are the intercompartmental rate constants, and k₁₀ (day^− 1) is the central compartment elimination rate constant.

Pharmacokinetic and pharmacodynamic analysis

The presented PK/PD model for the anti- inflammatory effect of UST is based on an indirect response model with an effect compartment (Fig. 1).

The equation for the effect compartment is as follows:

$$\frac{d{A}_{e}}{dt}={k}_{1e}\cdot {{A}_{1}-k}_{eo}\cdot {A}_{e}$$

where, A₁ (µmol) is the amount of UST in the central compartment and A_e (µmol) is that in the effect compartment. In addition, k_1e (day^− 1) is the rate constant for transition from the central compartment to the effect compartment and k_eo (day^− 1) is the elimination rate constant from the effect-compartment.

When it is assumed that the central compartment and the effect compartment reach the steady state just after UST administration, k_1e and k_eo become equal. Then, the concentration of UST in the effect compartment (C_e, µM) is represented by Eq. (3):

$$\frac{d{C}_{e}}{dt}={k}_{eo}\cdot ({C}_{1}-{C}_{e})$$

where, C₁ (µM) is the serum concentration of UST.

K ^UST (day^− 1) is the rate constant of inflammation suppressed by the action of UST, and K^else (day^− 1) is the rate constant of inflammation caused by factors not affected by the actions of UST. The rate constant that reduces inflammation caused by K^UST and K^else is k_r (day^− 1). Therefore, the value of the therapeutic effect at time t (days) (E_t) after the administration of UST is represented by Eq. (4) using the indirect response model:

$$\frac{d{E}_{t}}{dt}={K}^{else}+{K}^{UST}\bullet \left(1-\frac{{I}_{max}\bullet {C}_{e}}{{IC}_{50}+{C}_{e}}\right)-{k}_{r}\cdot {E}_{t}$$

where, I_max is the maximum fractional inhibition of inflammation suppressed by the actions of UST, and IC₅₀ is the concentration of UST that produces inhibition equal to 50% of I_max. At this point, since we used K^UST and K^else in Eq. (4), we considered the value of I_max as 1.

To estimate the values of k_eo, IC₅₀, K^UST, K^else, and k_r, simultaneous fitting was performed on all E_t data (mean data of CDAI or partial Mayo score) using equations (3) and (4). The nonlinear least squares program MLAB (Civilized Software, Inc.) was used for this analysis. In addition, to avoid over-fitting, we conducted 12-fold cross validation with collection of the E_t data split into 12 groups for each time point. In each data point, the model was trained using 11 groups as training data, and the resulting model is validated on the remaining one group.

Simulation of therapeutic effect

The sequential changes of E_t following repeated administrations of UST at the tested dosage regimens (Tables 2, 3) were simulated using the estimated PK/PD parameters. UST is generally administered to patients with moderate to severe active disease, thus we considered those to have a CDAI value of 300 [13] as well as a partial Mayo score of 6 [14, 15]. In CD patients, therapeutic effect (CR-70) was defined as a decrease in CDAI of 70 points, while clinical remission was indicated by a CDAI of ≤ 150 points [13, 17]. On the other hand, in UC patients, clinical remission was defined as a partial Mayo score of ≤ 2 points [14, 15, 17].

Table 2

Dosage regimens for UST examining the necessity of intravenous administration
	Administrations (mg)
	0 weeks	4 weeks	8 weeks	16 weeks
Regimen 1*	390 mg (i.v.)	-	90 mg (s.c., then every 12 weeks)
Regimen 2	90 mg (s.c.)	-	90 mg (s.c., then every 12 weeks)
Regimen 3**	45 mg (s.c.)	45 mg (s.c.)	-	45 mg (s.c., then every 12 weeks)
usual dosage regimen for CD and UC, * usual dosage regimen for PS

Table 3

Dosage regimens for UST examining the dose interval and the administration route in the maintenance therapy
	Administrations
	0 weeks	8 weeks
Regimen 1*	390 mg (i.v.)	90 mg (s.c., then every 12 weeks)
Regimen 4**	390 mg (i.v.)	90 mg (s.c., then every 8 weeks)
Regimen 5	390 mg (i.v.)	90 mg (s.c., then every 4 weeks)
Regimen 6	390 mg (i.v.)	390 mg (i.v., then every 12 weeks)
Regimen 7	390 mg (i.v.)	390 mg (i.v., then every 8 weeks)
Regimen 8	390 mg (i.v.)	390 mg (i.v., then every 4 weeks)
usual dosage regimen in PMDA and EMA, * usual dosage regimen in FDA

We examined the necessity of intravenous administration using three different regimens (Table 2). Patients who received Regimen 1 as the usual dosage regimen for IBD were given UST at a dose of 390mg as an intravenous administration, followed by 90mg 8 weeks later as a subcutaneous administration. Then, 12 weeks after that, a maintenance dose of 90mg every 12 weeks administered subcutaneously was begun. For Regimen 2, patients were given 90mg at 0, 8, and 20 weeks, and then every 12 weeks subcutaneously. For Regimen 3 which is the usual dosage regimen for PS, patients were given 45mg at 0, 4, and 16 weeks, and then every 12 weeks subcutaneously.

Next, we simulated the therapeutic effect when the dose interval of subcutaneous administration was set to every 12 weeks (Regimen 1), 8 weeks (Regimen 4), or 4 weeks (Regimen 5) in maintenance therapy, and then examined the dose interval of UST (Table 3). We also simulated the therapeutic effect when UST was administered intravenously with each dose interval (Regimens 6, 7, 8), and then examined the effect of the administration route in the maintenance therapy (Table 3).

Pharmacokinetic and pharmacodynamic analysis

The sequential changes of serum UST concentration (µg/ml) after repeated administration were predicted based on the PK parameters shown in Table 1 (Fig. 2). Goodness-of-fit plots for the PK model are shown in Fig. 3. The relationship between predicted values and observed values [11, 16] was well matched. Therefore, it was suggested that the sequential changes of serum UST concentration were represented by the PK parameters used in this analysis.

The sequential changes in therapeutic effect following repeated administrations of UST are shown in Fig. 4. The estimated parameters are presented in Table 4. The results showed that the estimated IC₅₀, K^UST, and K^elsefor CD were 5.21 times, 160 times, and 93.6 times higher than those for UC, respectively. The K^UST/K^else ratios were 14.7 for CD and 8.64 for UC, and the value was greater than 1 for both diseases. Goodness-of-fit plots are shown in Fig. 5. The predicted values and observed values were well matched. The results of 12-fold cross-validation are shown in Fig. 6. Since the predicted values were in good agreement with the observed values, it was considered to show the validity of generalization. These results suggest that this PK/PD model is useful for determining the therapeutic effect of UST for IBD.

Table 4

The estimated pharmacokinetic and pharmacodynamic parameters for UST
Parameters	Definition	Estimated value (± S.E.)		Unit
Parameters	Definition	CD	UC	Unit
k_eo	Effect-compartment equilibrium rate constant	0.0183 (± 0.0010)	0.00563 (± 0.00056)	day^− 1
IC₅₀	Half-maximal inhibitory concentration	0.122 (± 0.005)	0.0234 (± 0.0036)	µM
K^UST	Inflammation rate constant suppressed based on the action of ustekinumab	99.6 (± 2.6)	0.624 (± 0.030)	day^− 1
K^else	Inflammation rate constant caused by factors not affected by the action of ustekinumab	6.76 (± 0.59)	0.0722 (± 0.0107)	day^− 1
k_r	Inflammation remitting rate constant	0.494 (± 0.011)	0.139 (± 0.006)	day^− 1
K^UST/K^else	Ratio of K^USTand K^else	14.7	8.64

Simulation of therapeutic effect

The sequential changes of CDAI and partial Mayo score following repeated administrations of UST at different dosage regimens (Regimens 1, 2, 3) were predicted based on the PK/PD parameters (Fig. 7). In CD patients, the minimum values (E_min) of CDAI until Day 112 were 113 (Regimen 1), 168 (Regimen 2), and 185 (Regimen 3). In UC patients, the E_min of partial Mayo score were 1.75 (Regimen 1), 2.88 (Regimen 2), and 3.53 (Regimen 3).

The sequential changes of CDAI and partial Mayo score following repeated administrations of UST at the different dosage regimens (Regimens 1, 4, 5, 6, 7, 8) were predicted (Fig. 8). First, regarding the dose interval for subcutaneous administration, in CD patients, the ranges between the minimum and maximum values (E_range) of CDAI from day 224 to day 364 were 167–184 (Regimen 1), 156–167 (Regimen 4), and 129–132 (Regimen 5). In UC patients, the E_range of partial Mayo scores were 2.01–2.18 (Regimen 1), 1.83–1.91 (Regimen 4), and 1.42–1.50 (Regimen 5). Next, regarding the administration route in the maintenance therapy, in CD patients, the E_range were 90–125 (Regimen 6), 75–94 (Regimen 7), and 54–58 (Regimen 8). In UC patients, the E_range were 1.17–1.26 (Regimen 6), 1.01–1.12 (Regimen 7), and 0.76–0.83 (Regimen 8).

In the present study, for evaluating the implications for efficacy of the different dosage regimens of UST for IBD, we constructed a PK/PD model, and simulated the sequential changes of therapeutic effect following various dosage regimens.

The predicted sequential changes of serum UST concentration, CDAI, and partial Mayo score after repeated administration of UST using the PK/PD model were in good agreement with the observed values (Figs. 2–5). Furthermore, the results of cross-validation revealed the validity of the model generalization (Fig. 6). Therefore, it is suggested that the PK/PD model is capable of predicting sequential changes in CDAI and partial Mayo score following administration of UST.

The data on the sequential changes of therapeutic effect after administration of UST was also reported in the induction treatment trials conducted prior to the maintenance treatment trials [7, 11]. However, in the induction treatment trials, there was less data that measured therapeutic effect at 0, 3, 6, and 8 weeks after a single intravenous administration than at 13 time points from 0 to 52 weeks in the maintenance treatment trials. Therefore, in the present study, the sequential changes of therapeutic effect were extracted from the maintenance treatment trials.

The estimated K^UST and K^else values for CD were approximately 160 and 93.6 times greater, respectively, than those for UC. It was considered that PD parameters are affected by the scale of therapeutic effect, as the scale of CDAI was greater than that of the partial Mayo score. To evaluate the contributions of the activities of UST to the partial Mayo score and CDAI, we calculated the K^UST/K^else ratios, which were 14.7 for CD and 8.64 for UC patients, thus the inflammation suppressed by the action of UST was greater than that caused by factors not affected by the action of UST in the patients in this analysis. However, the patients participating in the maintenance treatment trials were those who obtained the therapeutic effect of UST in the induction treatment trials, thus if the patients who did not obtain the therapeutic effect after the induction treatment trials were included in this analysis, K^UST/K^else ratios might have been smaller. Therefore, in the present study, there is a limitation that the estimated PD parameters are values for patients who obtained the therapeutic effect after the induction therapy.

The validity of the initial intravenous administration of UST for IBD was evaluated (Fig. 7). The E_min of CDAI and partial Mayo score was the smallest in Regimen 1, and clinical remission was obtained only in Regimen 1 for both diseases. Therefore, it was shown by the model-informed approach that the initial intravenous administration is important for UST instead of the initial subcutaneous administration, such as in Regimen 2 or Regimen 3, in order to induce remission. Our results are considered reasonable, as the clinical trials found that the clinical response rate and the remission rate of inflammation markers after initial intravenous administration of UST at 4.5mg/kg were superior to those after initial subcutaneous administration at 90mg [18, 19].

The different dose intervals and administration routes (Regimens 1, 4, 5, 6, 7, 8) were evaluated (Fig. 8). The results showed that Regimen 4 remained at a slightly lower value than Regimen 1, though there was almost no difference in the fluctuation range of CDAI (Regimen 1: 17, Regimen 4: 11) and partial Mayo score (Regimen 1: 0.17, Regimen 4: 0.08), and a stable therapeutic effect was obtained. The dose interval for subcutaneous administration in the maintenance therapy has been recommended at every 12 weeks (Regimen 1) in PMDA and EMA [8, 9], while the FDA recommends every 8 weeks (Regimen 4) [10]. In CD patients, previous studies showed that the remission rate at Week 44 tended to be slightly lower in Regimen 4 than in Regimen 1 (48.8% and 53.1%, respectively), though a clear difference was not found [6, 18]. In addition, in UC patients of the maintenance treatment trial, it was reported that the clinical remission rate at Week 44 was similar between Regimen 1 and Regimen 4 [7, 20]. On the other hand, the predicted value of Regimen 5 was lower than of Regimen 1 and 4. Some real-word studies have reported the experience with ustekinumab intensification from 90mg q8W to q4W and even to q3W [21–25]. Recently, the University of Chicago group reported the effectiveness of ustekinumab dose interval shortening from 90mg q8W to q4W in 51 patients with a Harvey–Bradshaw score > 4 [26]. They showed that dose escalation resulted in improvement in clinical indices of disease activity. There are important points to consider with regard to the present findings that the safety of q4W was not examined in this study, thus further study is needed.

The sequential changes of CDAI and partial Mayo score were lower in intravenous administration than in subcutaneous administration (Fig. 8). It has been reported that the re-induction with intravenous administration after secondary loss of response is considered an important rescue treatment option in patients with refractory CD [27, 28]. Therefore, it was suggested that intravenous administration will present a higher therapeutic effect than subcutaneous administration during the maintenance therapy. However, as far as we know, there is no study reporting the actual efficacy and safety of repeated intravenous administration of UST for IBD during the maintenance therapy, thus it is necessary to examine the efficacy and safety of repeated intravenous administration.

The amount of the initial intravenous administration of UST for IBD was also evaluated (Supplementary Table 1, Supplementary Fig. 1). The E_min of CDAI and partial Mayo score in each dosage regimen are shown in Supplementary Table 2. The E_min was the smallest in 6mg/kg, and clinical remission was obtained only in 6mg/kg and 3mg/kg for CD and 6mg/kg for UC. Therefore, it was shown that the dose of 6mg/kg is important for the induction of remission after the initial intravenous administration. Our results are considered reasonable because of the results of the following clinical trials. In CD patients, the clinical response rate at Week 6 was compared among the 1mg/kg group, 3mg/kg group, and 6mg/kg group of initial intravenous administration [18, 29]. The results were 23.5% (31/132 patients) in the placebo group, 36.6% (48/131 patients) in the 1mg/kg group, 34.1% (45/132 patients) in the 3mg/kg group, and 39.7% (52/131 cases) in the 6mg/kg group [18, 29]. Furthermore, in a phase III clinical trial comparing the secondary endpoint of therapeutic effect rate at Week 8 between the 6mg/kg group and the 130mg (2mg/kg at 65kg) group for UC patients, the results were 61.8% (199/322 patients) in the 6mg/kg group and 51.3% (164/320 patients) in the 130mg group [7].

In conclusion, his study showed that the presented PK/PD model is capable of predicting sequential changes of therapeutic effect of UST for IBD, and the implications for efficacy of the different dosage regimens could be evaluated by simulation with various dosage regimens. These findings are useful for model-informed precision dosing of individual IBD patients by predicting the serum UST concentration and therapeutic effect in individual patients [30].

Compliance with Ethical Standards

Disclosure of potential conflicts of interest

KK has no competing interests to declare. AY received personal fees from Mitsubishi-Tanabe Pharma and Janssen Pharmaceutical K.K..

Funding

No funding was received for conducting this study

Data availability statement

All data analysed during this study are available in the published reports [11,16].

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Competing interest reported. KK has no competing interests to declare. AY received personal fees from Mitsubishi-Tanabe Pharma, Janssen Pharmaceutical K.K., and Abbvie Inc.

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Pharmacokinetic-pharmacodynamic modelling and simulation of ustekinumab for inflammatory bowel disease

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Abstract

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Introduction

Methods

Data for pharmacokinetic and pharmacodynamic analysis

Pharmacokinetic and pharmacodynamic analysis

Simulation of therapeutic effect

Results

Pharmacokinetic and pharmacodynamic analysis

Simulation of therapeutic effect

Discussion

Declarations

References

Competing Interests

Supplementary Files

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