Modeling and Simulation for Estimating the Influence of Renal Dysfunction on the Hypouricemic Effect of Febuxostat in Hyperuricemic Patients Due to Overproduction or Underexcretion of Uric Acid

Abstract

Whether renal dysfunction influences the hypouricemic effect of febuxostat, a xanthine oxidase (XO) inhibitor, in patients with hyperuricemia due to overproduction or underexcretion of uric acid (UA) remains unclear. We aimed to address this question with a modeling and simulation approach. The pharmacokinetics (PK) of febuxostat were analyzed using data from the literature. A kinetic model of UA was retrieved from a previous human study. Renal UA clearance was estimated as a function of creatinine clearance (CL_cr) but non-renal UA clearance was assumed constant. A reversible inhibition model for bovine XO was adopted. Integrating these kinetic formulas, we developed a PK-pharmacodynamic (PK-PD) model for estimating the time course of the hypouricemic effect of febuxostat as a function of baseline UA level, febuxostat dose, treatment duration, body weight, and CL_cr. Using the Monte Carlo simulation method, we examined the performance of the model by comparing predicted UA levels with those reported in the literature. We also modified the models for application to hyperuricemia due to UA overproduction or underexcretion. Thirty-nine data sets comprising 735 volunteers or patients were retrieved from the literature. A good correlation was observed between the hypouricemic effects of febuxostat estimated by our PK-PD model and those reported in the articles (observed) (r=0.89, p<0.001). The hypouricemic effect was estimated to be augmented in patients with renal dysfunction irrespective of the etiology of hyperuricemia. While validation in clinical studies is needed, the modeling and simulation approach may be useful for individualizing febuxostat doses in patients with various clinical characteristics.

Hyperuricemia is an important risk factor for not only acute gout attack but also for chronic renal disease (CKD) and other cardiovascular diseases.^1–4) Therefore, CKD patients with hyperuricemia are recommended to receive dietary and pharmacological interventions to reduce serum uric acid (UA) concentration. For CKD patients with moderate or severe renal impairment, a xanthine oxidase (XO) inhibitor is considered the drug of choice irrespective of the etiology of hyperuricemia (overproducer or underexcretor of UA), because the hypouricemic effects of uricosuric drugs (such as probenecid) are attenuated in these patients.⁵⁾ Until recently, allopurinol has been the sole XO inhibitor available for hyperuricemic patients with moderate or severe CKD. However, the use of allopurinol in patients with CKD is often hampered by an increased risk of severe cutaneous adverse reactions due probably to an accumulation of its active metabolite, oxypurinol.^6–8)

A newly developed non-purine XO inhibitor, febuxostat, may be prescribed with no need for dosage reduction in patients with mild or moderate CKD. Pre-approval pharmacokinetic (PK) studies showed that the mean area under the plasma concentration–time curve [AUC_(0–24 h)] of febuxostat observed in patients with moderate or severe CKD was elevated by 48 and 76% compared to healthy subjects,⁹⁾ whereas no adverse drug reactions associated with augmented drug exposure were observed.^10,11) Therefore, febuxostat may be preferred to allopurinol for the treatment of hyperuricemia in patients with CKD. However, it remains unclear whether the hypouricemic effects of febuxostat would be augmented in patients with CKD. As a result, no dosage guideline has been provided for these patients to date. It would be a complicated task to estimate the optimal dose of febuxostat for each CKD patient. Because patients have different baseline UA concentrations, the magnitude of UA reduction to reach a common therapeutic target (such as 6.0 mg/dL) would differ in individual patients, and the PK of the drug and disposition of UA are also altered. A comprehensive approach is needed to untangle the complex dose–response relationship of XO inhibitors in CKD patients.

Recently, an integrated PK-pharmacodynamic (PD) modeling and simulation approach using the Monte Carlo simulation method has been considered useful for understanding complex dose-response relationship of drugs. If used appropriately, this approach may help to estimate the optimal dose of febuxostat for patients with CKD taking into account relevant patient variables. Here, we report the first attempt of constructing an integrated PK-PD modeling and simulation of the hypouricemic effect of febuxostat in CKD patients with different hyperuricemia etiologies (overproducers or underexcretors of UA).

MATERIALS AND METHODS

PK Model of Febuxostat in Patients with Normal Renal Function and Those with CKD

We constructed a PK model to estimate the plasma concentration-time curve of febuxostat after administration of varying doses at different dosing intervals in patients with varying renal function. We searched for relevant articles in Medline (from 1946 to May 2, 2013) using combinations of keywords as follows: [(gout OR hyperuricemia) AND (chronic kidney disease OR renal insufficiency OR renal disease OR kidney insufficiency OR kidney impairment OR renal impairment OR impaired kidney OR impaired renal) AND febuxostat]. Inclusion criteria of articles were: descriptions of serum UA concentrations before and after febuxostat treatment, patients’ body weights, doses, dosing intervals, quantitative or semi-quantitative (mild, moderate or severe renal dysfunction) renal function assessed by creatinine clearance, and duration of febuxostat therapy longer than 1 week. In addition, we manually checked the reference lists of the retrieved articles. Furthermore, we searched for data documented only in the summary of common technical documents (CTDs) for drug approval submitted to the Pharmaceuticals and Medical Devices Agency (PMDA), Japan¹²⁾ and in the documents issued by Teijin Pharma Ltd. (i.e., the interview form and prescribing information of febuxostat).^10,11) Because only mean plasma concentrations of the drug were available at each sampling time in literature and other data sources, we performed PK analysis of the drug using the mean values available. The mean plasma concentration–time data of febuxostat presented in figures were converted to digital data using UnGraph^® 5 digitizer program, which gives X, Y coordinates of lines or points on scanned images (BIOSOFT, Cambridge, U.K.). Since plasma concentration-time curves of febuxostat after an oral dose apparently showed biphasic rather than monophasic decay,⁹⁾ the digitized data were analyzed using an open two-compartment model with first-order absorption according to Eq. 1, using the Phoenix® WinNonlin® program (Certara G.K., Tokyo).   

(1)

where FX₁ and FX₂ are the amounts of febuxostat in the central and peripheral compartments, respectively; F_oral is the oral bioavailability of the drug; Dose is the oral dose; k_a is the first-order absorption rate constant; k₁₂ and k₂₁ are the rate constants of transfer from the central to peripheral and from the peripheral to central compartment, respectively; and k₁₀ is the rate constant of elimination from the central compartment. Plasma and apparent tissue concentrations of febuxostat were calculated by dividing FX₁ and FX₂ by the volumes of distribution of the corresponding compartments (Vd₁ and Vd₂, respectively). Because no k_a values were available from the literature, plasma drug concentration–time data in the literature were considered unsuitable for a precise data-fitting analysis of the absorption kinetics. Thus, we assumed the value for k_a to be 2.18 h^－1, because the gastrointestinal absorption of febuxostat is rather rapid (t_max=1 h).^9–11) In addition, we assumed the mean F_oral of febuxostat to be 65% based on the data of a mass-balance study performed in healthy human subjects showing 49 and 35% recovery of radioactivity in urine and feces, respectively, as metabolites and only 10% in feces as an unchanged form after a single oral dose of 80 mg of radio-labelled febuxostat.^10,12) F_oral of the drug in canines and rats determined using intravenous and oral administration of the drug were reported to be 48 and 78%, respectively.^10,12) Because the plasma concentration–time data available for PK analysis for patients with CKD were obtained after repeated once daily dosing for 7 d,⁹⁾ we offset plasma concentrations measured at each sampling point on the 7th day by subtracting contribution of the previous dosing estimated by the pre-dose plasma drug concentrations, assuming exponential decay at subsequent sampling points in each group of patients according to the elimination phase rate constant.

Kinetic Model of XO Inhibition for Febuxostat

The kinetic model of XO inhibition was constructed using published data obtained from in vitro experiments using bovine XO.¹³⁾ We assumed that the enzyme kinetic parameters (V_max and K_m) and the enzyme inhibition constants obtained from these experiments were largely comparable to those of humans. Consequently, we adopted Eqs. 2 and 3 for expressing XO activity in the presence (v′) and absence (v) of febuxostat, respectively. According to previous study,¹³⁾ we assumed that febuxostat inhibits human XO in a reversible, mixed type inhibition. We also assumed that febuxostat (as an inhibitor), UA and xanthine concentrations in the vicinity of XO (I) at any time are rapidly equilibrated with unbound plasma concentrations of each substance.   

(2)

  

(3)

  

(4)

where K_m is the Michaelis–Menten constant for bovine XO; K_i and K_i′ are the inhibition constants of the mixed type inhibition model for febuxostat; these values were assumed to be 2.7 µM, 0.6 nM and 3.1 nM, respectively, according to the previous bovine XO study.¹³⁾ [S] is the serum concentration of xanthine (ranging from 1.57–1.91 µM⁹⁾) in the absence of an XO inhibitor. Because plasma xanthine concentrations are approximately only one-half of K_m, 2.7 µM, and they increase several folds after the administration of XO inhibitors, the XO inhibition ratio was calculated taking into account the increase in [S] after febuxostat dosing. Detailed descriptions for estimating changes in [S] after febuxostat dosing are given below. UA_syn represents the rate of synthesis of UA from xanthine by XO. We assumed that UA is synthetized exclusively from xanthine and xanthine is metabolized only to UA.

Kinetic Model of Endogenous UA

The kinetic model describing the synthesis and disposition of endogenous UA was adopted from the report of Scott et al..¹⁴⁾ They constructed an open two-compartment model for UA disposition as follows:   

(5)

where UA_syn is the baseline synthesis rate of UA in mg/h; k_el,R(UA) and k_el,NR(UA) are the rate constants of renal and non-renal elimination of UA, respectively; k_21(UA) and k_12(UA) are the transfer rate constants of UA from the peripheral to central and the central to peripheral compartment, respectively; and UA_Pool1 and UA_Pool2 (in mg) represent the amounts of UA existing in the central and peripheral compartments, respectively. They were calculated by multiplying the baseline (before febuxostat dosing) serum UA concentration (UA_baseline) measured in mg/dL by the corresponding apparent volumes of distributions of Pool₁ and Pool₂ (Vd_1(UA) and Vd_2(UA), respectively) according to the Eqs. 6 and 7.   

(6)

  

(7)

  

(8)

where BW is body weight in kg. Because the UA kinetic data retrieved from the report of Scott et al.¹⁴⁾ were obtained from healthy subjects or patients with average body weight of approximately 80 kg, we used body weight-normalized volume of distribution of UA to calculate the data for non-Caucasian patients. In Eqs. 6 and 7, UA_baseline is multiplied by 10 to convert the unit from mg/dL to mg/L. UA_syn was estimated by the amount of UA in UA_Pool1 at baseline times the sum of the rate constants of renal and non-renal elimination of UA[k_el,R(UA) and k_el,NR(UA), respectively], according to Eq. 8.

While UA is eliminated by both renal and non-renal routes, renal clearance has been reported to be two-fold greater than non-renal clearance.^15,16) Tykarski¹⁷⁾ reported that renal clearance of UA is related to CL_cr according to Eq. 9.   

(9)

where CL_R(UA) is renal clearance of UA in mL/min, and CL_cr is creatinine clearance in mL/min.

Because CL_R(UA) is defined as the product of k_el,R(UA) and BW × Vd_1(UA), k_el,R(UA) was calculated by substituting CL_R(UA) of Eq. 9 into Eq. 10.   

(10)

We assumed that k_el,NR(UA) is constant irrespective of altered XO activity before and after febuxostat dosing in patients with CKD.

We created a virtual normouricemic (i.e., 6.0 mg/dL) subject weighing 60 kg and with normal renal function (CL_cr 100 mL/min) as follows: the subject was assumed to have UA_syn of 41.5 mg/h according to the Eqs. 6 to 8. As a result, he/she was assumed to have CL_total(UA) of 11.5 mL/min as UA_syn is equal to serum UA times CL_total(UA). In addition, the subject was assumed to have CL_R(UA) of 9.0 mL/min according to the Eq. 9.¹⁷⁾ Consequently his/her CL_NR(UA) was considered to be 2.5 mL/min, because CL_NR(UA) is calculated as CL_total(UA)−CL_R(UA).

Serum xanthine concentrations after febuxostat dosing was estimated using a kinetic model described below. There is a paucity of knowledge about the kinetic parameters of xanthine in humans. Thus, we hypothesized that a simple open one-compartment model will describe the disposition of xanthine and that the apparent volume of distribution of xanthine (Vd_xanthine) is equal to that of UA. Plasma xanthine concentrations increased by several folds after administration of febuxostat at 80 mg once daily,⁹⁾ indicating that xanthine would be metabolized to UA almost exclusively by XO. We assumed that the synthesis rate of xanthine (Xanthine_syn) is equal to that of UA (UA_syn) at steady-state and is constant irrespective of renal dysfunction. The amount of xanthine existing in the body at baseline was calculated by multiplying the average serum xanthine concentration (0.29 mg/L) reported in healthy subjects by Vd_xanthine.⁹⁾ On these assumptions, the following equations were formulated.   

(11)

  

(12)

Pool_xanthine represents the amount of xanthine in the body, and k_el,xanthine is the elimination rate constant of xanthine.

Integrated Modeling and Simulation for Plasma Concentration–Time Courses of Febuxostat, UA and Xanthine

To estimate serum concentration–time curves of UA, febuxostat and xanthine during the repeated oral administration of febuxostat at a given dose per d from time 0 to 240 h post-dose, we performed Monte Carlo simulation using STELLA^® ver. 9.0.3 software (iSee systems, Inc. Lebanon, NH, U.S.A.) in which the relevant equations (Eqs. 1 to 12) were integrated as shown in Fig. 1. We assumed that the errors of all parameters used for simulation (PK parameters and XO inhibition constants) except F_oral and k_a are normally distributed with coefficient of variation of 30%, and we performed simulations for each data set 100 times and obtained the estimated mean values and 95% confidence intervals. We estimated the hypouricemic effects of febuxostat reported in literature by substituting mean baseline serum UA concentration, CL_cr (mL/min) of each group of healthy subjects or patients with hyperuricemia, febuxostat dose, and mean body weight into the integrated PK-PD model. As to CL_cr we used the values available in literature whenever possible. However, when renal function was given as a range of CL_cr (e.g., 50 to 80 mL/min), the mid-point value of the range (i.e., 65 mL/min) was used for estimation. When no CL_cr data was given for healthy subjects, we assumed CL_cr to be 100 mL/min. When no actual body weight was given for a data set, we assumed mean body weights for Caucasians and Japanese to be 70 and 60 kg, respectively. Dosing frequency of the drug was once daily in all the publications adopted in the present study.

Fig. 1. A PK-PD Model of Uric Acid (UA) Disposition during Administration of Febuxostat

FX₁ and FX₂: amounts of febuxostat in the central and peripheral compartments, respectively; F_oral: oral bioavailability of the drug; Dose: oral dose; k_a: first-order absorption rate constant; k₁₂ and k₂₁: rate constants of transfer from central to peripheral and from peripheral to central compartment, respectively; k₁₀: rate constant of elimination from the central compartment.

There are two distinctly different pathophysiological etiologies for hyperuricemia: overproducers or underexcretors of UA. The hypouricemic effects of febuxostat, an XO inhibitor, may vary in patients with different etiologies of hyperuricemia. Therefore, we performed additional modeling and simulation studies to investigate this issue. We created virtual hyperuricemic (9.0 mg/dL) patients due to either UA overproduction or underexcretion. Those with or without CKD were created separately. As for a patient with normal renal function whose hyperuricemic (9.0 mg/dL) was considered due to UA overproduction, he/she was assumed to have a 50% augmented UA_syn (62.3 mg/h) as compared the normouricemic subject (41.5 mg/h, see the description given above). On the other hand, a patient with normal renal function whose hyperuricemia was considered due to UA underexcretion, he/she was assumed to have a comparable UA_syn (41.5 mg/h) but had a reduced CL_total(UA) by 2/3 (7.7 mL/min) as compared the normouricemic subject (11.5 mL/min). Because we assumed CL_NR(UA) is constant (2.5 mL/min) irrespective of hyperuricemic etiology, he/she was also assumed to have reduced CL_R(UA) of 5.2 mL/min as compared the normouricemic subject (9.0 mL/min). Next, we created virtual CKD patients with hyperuricemia. As for a normouricemic (6.0 mg/dL) CKD patient (CL_cr 30 mL/min), he/she was assumed to have CL_total(UA) of 7.9 mL/min because he/she was assumed to have a reduced CL_R(UA) of 5.4 mL/min according to Eq. 9 and the constant CL_NR(UA) of 2.5 mL/min. Consequently, the patient was assumed to have UA_syn of 28.3 mg/h, because UA_syn is equal to serum UA times CL_total(UA). It is of note that this UA_syn is less than that for normouricemic subject with normal renal function (41.5 mg/h). A hyperuricemic (9.0 mg/dL) CKD patient due to UA overproduction was assumed to have an augmented UA_syn of 42.5 mg/h as compared the normouricemic CKD patient. A hyperuricemic CKD patient due to UA underexcretion was assumed to have a reduced CL_total(UA) of 5.2 mL/min as compared the normouricemic CKD patient (7.9 mL/min). For each case of hyperuricemia, we performed Monte Carlo simulation 100 times to estimate the hypouricemic effects during the administration of febuxostat at a low dose (10 mg once daily) for 10 d, assuming the body weight to be 60 kg. We then computed the probability of attaining serum UA concentration of 6.0 mg/dL or less in the representative hyperuricemic patients due to either overproduction or underexcretion of UA. Serum UA of 6.0 mg/mL is the therapeutic target for patients with hyperuricemia according to the Japanese Society of Gout and Nucleic Acid Metabolism.

Furthermore, we conducted a sensitivity analysis of our modeling and simulation by altering K_i, K_i′, K_m and unbound fraction (f_u) of plasma febuxostat at 0.5, 1.0 and 2.0 times greater than the respective control values to study which parameters’ variability would be most sensitively associated with the inter-patient variability of the hypouricemic effects of febuxostat. We also performed a sensitivity analysis for Vd of xanthine in terms of elevations in serum xanthine concentrations and hypouricemic effects of febuxostat. We performed Monte Carlo simulations in a representative patient with UA overproduction having baseline UA level of 9.0 mg/dL and CL_cr of 100 mL/min. In addition, we performed sensitivity analysis by altering F_oral from 40 to 100%. We also performed sensitivity analysis by altering body weight from 45 to 90 kg. All sensitivity analyses were conducted by performing Monte Carlo simulation 100 times.

Statistical Analysis

The correlation between serum UA concentration at steady-state during oral administration of febuxostat at various doses estimated by the present modeling and simulation method and those reported in literature was examined by a weighted orthogonal (bivariate) regression method assuming a variance ratio of 1.0, using JMP® Pro (ver.12.0.1, SAS Institute Inc.). A p<0.05 was considered statistically significant.

RESULTS

Modeling and Simulation of the Hypouricemic Effect of Febuxostat in Healthy Subjects and Patients with Various Serum UA Levels and Renal Function

We retrieved the dose–response data of febuxostat in healthy subjects (n=156) or hyperuricemic patients (n=579)^{9–11,18–20)} from 4 articles via Medline and a set of data from the interview form of febuxostat. Among these subjects, 215 had normal renal function (CL_cr >80 mL/min), 383 had mild CKD (CL_cr 50 to 80 mL/min), 130 had moderate CKD (CL_cr 30 to 49 mL/min) and 7 had severe CKD (CL_cr <29 mL/min). In the present study we considered that estimated glomerular filtration rate (GFR; mL/min per 1.73 m²) and CL_cr (mL/min per body) to be exchangeable. The subjects received febuxostat orally once daily for 7 d or longer at doses ranging from 10 to 240 mg. Details of the data set retrieved from the literature are listed in Table 1.

Table 1. The Literature Data Used for Qualifying the Performance of the PK-PD Model in Estimating Serum UA during Febuxostat Dosing

Data set No.	Subject (n)	Dose (mg)	CLcr (mL/min)	BW (kg)	Initial UA (mg/dL)	Final UA (mg/dL)	References
1	11	80	112	82	5.3	2.2	9
2	6	80	64	70	5.1	1.9
3	7	80	42	75	6.8	2.9
4	7	80	19	88	7.9	3.5
5	1	10	100*	60	7.8	7.2	10
6	16	10	75	60	8.7	6.9
7	12	10	45	60	10.0	7.1
8	15	20	100*	60	8.2	6.5
9	59	20	75	60	8.6	6.1
10	33	20	45	60	9.2	6.0
11	30	40	100*	60	8.3	5.1
12	156	40	75	60	8.7	5.0
13	52	40	45	60	9.1	5.2
14	7	60	100*	60	8.1	5.2
15	28	60	75	60	8.7	4.1
16	10	60	45	60	8.6	4.4
17	9	80	100*	60	8.0	5.1
18	25	80	75	60	8.7	3.9
19	7	80	45	60	9.2	3.6
20	10	10	100*	76	5.0	3.6	18
21	9	20	100*	77	4.8	3.2
22	9	30	100*	76	4.2	2.6
23	8	40	100*	82	5.3	3.2
24	18	50	100*	80	4.8	2.6
25	10	70	100*	78	4.4	2.2
26	10	90	100*	72	4.5	1.8
27	9	120	100*	80	4.7	1.6
28	10	160	100*	76	4.8	1.4
29	7	180	100*	86	5.3	1.5
30	8	240	100*	81	5.1	1.2
31	8	40	99	70	8.9	6.3	19
32	29	40	70	70	9.3	5.7
33	9	80	112	70	9.8	5.6
34	29	80	72	70	10.0	5.4
35	7	120	108	70	10.1	4.2
36	30	120	64	70	9.5	3.9
37	10	20	115	76	5.9	3.9	20
38	5	20	65	65	6.3	4.3
39	9	20	42	59	6.8	4.3

Patients were assigned to each data set according to febuxostat dose or renal function. The data shown for each data set are mean values. *When no specific values were given for renal function in healthy subjects, we assumed creatinine clearance (CL_cr) to be 100 mL/min. UA=uric acid.

The PK analysis for the data set obtained from the article,⁹⁾ where the plasma concentrations–time data of febuxostat in healthy subjects and those with CKD were available, yielded a set of PK parameters necessary for constructing a PK model for estimating plasma concentration–time courses of febuxostat in patients with varying demographic characteristics and renal function. Scrutinizing the data obtained from literature, however, we found that AUCs of febuxostat increases by 48 to 76% in patients with renal impairment compared with those with normal renal function despite only negligible amounts of unchanged form eliminated via the kidney.^9–11) As a result, we considered that it would be a more pragmatic approach to estimate mean plasma concentrations of febuxostat in patients with mild, moderate and severe CKD using the parameters obtained from the PK analysis on patients with comparable CKD in the previous study,⁹⁾ rather than to build a PK model where the systemic clearance of the drug is directly correlated with CL_cr. Specifically, we estimated PK parameters of febuxostat for subjects with normal renal function and 3 classes of CKD by analyzing the plasma concentration–time data obtained from the patients with comparable severity of CKD⁹⁾ using WinNonlin® as described in Methods. As a result, we were able to estimate that AUCs of the drug would increase by +48 and +74% in moderate and severe CKD. These values were compatible with those reported in CKD patients with corresponding severity (48, 76%).⁹⁾ Because f_u of febuxostat in patients with normal renal function and those with mild, moderate and severe CKD were reported to be 0.9, 0.9, 0.8 and 1.2%, respectively,⁹⁾ we calculated the unbound drug concentration at each sampling point by multiplying plasma total drug concentration by f_u.

The PK-PD model adopted for estimating serum UA concentration–time courses after the administration of febuxostat is shown in Fig. 1. In this model, mean (±S.D.) of F_oral and k_a were assumed to be 65±5% and 2.18±0.22/h, respectively, and f_u ranged from 0.9 to 1.2% depending on renal function as described above. Vd₁, k₁₀, k₁₂ and k₂₁ were estimated to be 0.23–0.30 L/kg, 0.25–0.46, 0.13–0.32 and 0.16–0.20/h, respectively, depending on patients’ renal function, according to the results of PK analysis described above. The kinetic parameters of UA were retrieved from the report of Scott et al.¹³⁾: the non-renal elimination constant [k_el,NR(UA)] was assumed to be 0.010/h irrespective of renal function, and the inter-compartmental transfer constants [k_12(UA) and k_21(UA)] were assumed to be 0.0068/h and 0.031/h, respectively. Vd of the central and peripheral compartments for UA [V_12(UA) and V_21(UA)] were assumed to be 0.25 and 0.06 L/kg, respectively. Vd for xanthine (Vd_xanthine) was assumed to be equal to that of UA (0.31 L/kg).

Figure 2 shows the estimated time courses of plasma total (bound plus unbound) febuxostat concentration, serum UA and xanthine, as well as UA synthesis rate (UA_syn) from baseline until 10 d after the commencement of once daily oral administration of febuxostat at 10 mg in a representative patient. The patient weighed 60 kg, and had baseline serum UA of 9.0 mg/dL and CL_cr of 100 mL/min. The time courses of febuxostat and UA_syn showed a mirror image of each other, whereas those of serum xanthine and febuxostat showed parallel changes (Fig. 2).

Fig. 2. Time–Courses of Plasma Febuxostat, Uric Acid (UA) and Xanthine Concentrations, and of UA Synthesis Rate (UA_syn) during Repeated Once Daily Oral Febuxostat Dosing at 10 mg from Time 0 to 240 h Post-Dose Estimated by the PK-PD Model Developed in the Present Study in a Representative Patient with Normal Renal Function

See datails in the text. Data for plasma febuxostat (A), UA (B) and xanthine concentrations (C), and of UA synthesis rate (D) are mean values obtained by performing simulations 100 times.

We then extracted serum UA concentrations measured immediately before the next dose (trough) at steady-state of febuxostat therapy in patients having different body weights, renal function and baseline UA concentrations in literature, and compared the observed values with those estimated by our modeling and simulation. There was a good linear correlation between the estimated and observed serum UA concentrations (Fig. 3): Y=0.73X+0.19 (r=0.89, p<0.001). When correlation was examined in patients with or without CKD separately, a good linear correlation was also observed in both groups: Y=0.80X+0.17, r=0.94, p<0.001 for CL_cr ≥70 mL/min, and Y=0.79X−0.42, r=0.85, p<0.001 for CL_cr <70 mL/min.

Fig. 3. Correlation between the Trough Serum Concentrations of Uric Acid (UA) Observed after Repeated Dosing of Febuxostat for at Least 7 d in Literature and Those Predicted Using the Present Modeling & Simulation Method after 10 d of Dosing

The open circles (○) represent subjects with normal renal function and patients with mild CKD, the shaded circles () represent patients with moderate CKD and the closed circle (●) represents patients with severe CKD. The size of circles represents the number of subjects for each data point. The broken line represents the linear regression line (Y=0.73X+0.19, r=0.89, p<0.001) and the solid lines represent the upper and lower limits of 95% confidence interval.

Effects of Etiology of Hyperuricemia and CKD on the Hypouricemic Effects of Febuxostat

We examined whether the hypouricemic effect of febuxostat would be influenced by the presence of CKD as compared to those with normal renal function and would differ between patients with distinct etiologies of hyperuricemia. The results of the analysis demonstrated that in the case of normal renal function, febuxostat at 10 mg once daily had comparable hypouricemic effect irrespective of the etiology of hyperuricemia. However, the hypouricemic effect of the drug was augmented in CKD compared with normal renal function (Fig. 4). Our modeling and simulation study estimated that febuxostat at 10 mg once daily would attain the target serum UA level (i.e., lower than 6.0 mg/dL) in 91% of representative CKD patients having CL_cr 30 mL/min and pretreatment serum UA 9.0 mg/dL, but only in 56% of those with normal renal function.

Fig. 4. Plasma Concentration–Time Courses of Uric Acid (UA) during Repeated once Daily Oral Dosing of Febuxostat at 10 mg from Initiation of Treatment to 240 h Estimated by the Modeling and Simulation Method Developed in the Present Study

Thin and thick solid lines represent data estimated for UA overproducers with normal renal function and renal dysfunction (CKD) (CL_cr=30 mL/min), respectively. Thin and thick broken lines represent data estimated for underexcretors with normal renal function and renal dysfunction, respectively. The data represent the mean values obtained by performing simulations 100 times.

Sensitivity Analysis

Results of the sensitivity analysis revealed that variability in f_u and one of the inhibition constants of XO (K_i) had greater impact on the hypouricemic effect of febuxostat compared with other parameters. Specifically, if the simulation was performed with a two-fold greater f_u than the reported value, hypouricemic effects of the drug was augmented by 0.9 mg/dL (from 6.1 to 5.2 mg/dL) in a typical hyperuricemic patient with a baseline serum UA of 9.0 mg/dL, normal renal function and body weight of 60 kg after the drug administration at 10 mg once daily for 7 d. It was also shown that a two-fold increase in K_i as compared with the reported value¹³⁾ was associated with an attenuated hypouricemic effect from 6.1 to 6.7 mg/dL. Variabilities in other parameters were shown to have less impact on the hypouricemic effects of the drug than the two parameters. In addition, the sensitivity analysis for Vd of xanthine showed that variability of Vd of xanthine from 0.2 to 10 times greater than that of UA showed no appreciable influence on the hypouricemic effect of febuxostat. However, the elevation of serum xanthine concentration calculated by assuming Vd of xanthine would be equal to that of UA was considered most closely to the reported value in in vivo human study⁹⁾ (data are not shown).

DISCUSSION

To the best of our knowledge, the present study is the first to attempt modeling and simulation for estimating the hypouricemic effect of a XO inhibitor, febuxostat, in humans. We were able to construct a PK-PD model (Fig. 1) that allows estimation of the time course of the hypouricemic effect of febuxostat as a function of baseline UA level, dose, duration of treatment, body weight and CL_cr using the Monte Carlo simulation method (Fig. 2). Using data from the literature, we demonstrated that our model provides good estimates for the hypouricemic effect of febuxostat in patients with a wide variety of demographic characteristics and renal function (Fig. 3). While the validity of our model should be verified in clinical studies, our novel pharmacometric approach for estimating hypouricemic effect of febuxostat may be a promising tool in predicting optimal doses of febuxostat therapy for individual patients.

Treatment of hyperuricemia in patients with moderate to severe CKD has been problematic, because of the complex effects of CKD on the PK of hypouricemic drugs and the disposition of endogenous UA. Particularly, the hypouricemic effects of uricosuric drugs (such as probenecid) are substantially attenuated in patients with CKD, because delivery of the drugs to their sites of action (renal tubules) is reduced in CKD patients.⁵⁾ While allopurinol, an XO inhibitor, is effective in these patients, studies have suggested that patients with CKD may have an increased risk of adverse drug reactions due to substantial accumulation of its active metabolite, oxypurinol.^6,7) On the other hand, febuxostat may be preferable for hyperuricemic patients with CKD, because the AUCs of febuxostat in patients with mild, moderate and severe renal impairments were shown to be elevated at most by 48 to 76%.⁹⁾ As a result, the prescribing information for febuxostat in Japan states that the drug can be prescribed without dosage modifications in patients with mild to moderate CKD, and with caution in patients with severe CKD.¹¹⁾ However, detailed dose–response relationship of the drug in CKD patients has not been studied. The present study indicates that the hypouricemic effect of febuxostat may be augmented in patients with CKD compared to those with normal renal function (Fig. 4). The results of sensitivity analysis indicated that the hypouricemic effects of febuxostat may be influenced not only by changes in AUCs of febuxostat but also by those in unbound plasma concentrations. Previous study demonstrated that total plasma concentrations of febuxostat are elevated in patients with moderate and severe CKD by 48 and 76% compared to healthy subjects, respectively.⁹⁾ In addition, plasma unbound fraction of the drug in patients with severe CKD was reported to be elevated.⁹⁾ Because our simulation showed that the XO activity assessed by UA_syn would be inhibited in association with increases in plasma drug concentrations, the augmented hypouricemic effects of febuxostat in patients with renal dysfunction may be attributable to augmented total and possibly unbound drug AUCs as compared those with normal renal function. We cannot categorically say that the CKD-associated augmentation in the hypouricemic effects of febuxostat is clinically relevant. Nevertheless, our data imply that it may be prudent to begin with a low dose of febuxostat (such as 10 mg once daily) in patients with CKD, because at this dose, approximately 90% of patients with CL_cr 30 mL/min are estimated to attain the target UA concentration (6.0 mg/dL) compared with only approximately 60% of those with normal renal function. Of course, our estimation should be verified by clinical studies.

It is also interesting to investigate whether the hypouricemic effect of febuxostat is altered in patients with different etiologies of hyperuricemia. The etiology of primary hyperuricemia is categorized into UA overproduction, UA underexcretion, and the combination thereof. Previous studies suggest that underexcretion of UA may account for 60 to 85% of primary hyperuricemia.²¹⁾ One may intuitively assume that the hypouricemic effect of febuxostat may be greater in patients with overproduction of UA compared to those with underexcretion of UA. However, our data revealed that the hypouricemic effect of the drug was comparable irrespective of the etiology of hyperuricemia as far as their renal function was comparable (Fig. 4). Because febuxostat inhibits XO in a reversible manner (Eqs. 2, 3),¹³⁾ the extent of XO inhibition is considered to be associated with the ratios of plasma febuxostat concentrations to its inhibition constants for XO (i.e., [I]/K_i and [I]/K_i′). Plasma AUCs of febuxostat were shown to be elevated in patients with moderate and severe CKD⁹⁾ and there is no reason to assume that the PK of febuxostat is altered according to hyperuricemic etiology. As a result, the extent of XO inhibition elicited by the drug would be comparable irrespective of their hyperuricemic etiology as far as their renal function is comparable (Fig. 4). In addition, hyperuricemic patients with CKD need a longer time–course than those with normal renal function before reaching to the new steady-state serum UA concentration during the repeated febuxostat therapy. This is because CKD patients have reduced renal and total UA clearance as compared with those with normal renal function, because UA is eliminated mainly via the kidneys^15,16) As a result, CKD patients have longer elimination half-life of UA than those with normal renal function assuming both groups have comparable Vd for UA. Similarly, hyperuricemic patients due to UA underexcretion showed longer time-courses than those due to UA overproduction as far as both groups have comparable renal function (Fig. 4). This is because hyperuricemic patients due to UA underexcretion were assumed have reduced total UA clearance as compared those due to UA overproduction. Previous studies demonstrated that approximately 70 and 30% of UA is cleared via the renal and non-renal routes, respectively.^14,15) Assuming that the non-renal clearance of UA is unaltered irrespective of renal function or etiology of hyperuricemia, patients with UA underexcretion may have reduced renal UA clearance as compared those with UA overproduction even if both group have comparable renal function. However, further studies are definitely required for validating our hypothetical consideration.

There are several limitations in the present study. First, the PK model and its parameters for febuxostat employed were estimated using the average concentration–time data reported in the literature, and not using individual patient data. In addition, we adopted F_oral and k_a that were extrapolated from the mass-balance study in humans¹²⁾ and bioavailability measured in animal studies¹²⁾ for modeling and simulation, because no data were available for humans at present. As a result, the PK model employed in the present study may be less accurate than one constructed using the original data. Second, we assumed that human and bovine XO inhibition kinetics of febuxostat are largely comparable. Third, we made several assumptions about the kinetic parameters of endogenous UA and xanthine. The kinetics and disposition of UA was available only from the study of Scott et al.¹⁴⁾ and no data are available for that of xanthine. Because no data is available for Vd of xanthine, we premised that the Vd of xanthine would be equal to UA. However, it would have been better to measure it in animals using radiolabeled xanthine and extrapolate the data to humans in order to make our model more accurate. Collectively, these premises might have introduced systematic errors in the prediction of hypouricemic effects of febuxostat. Indeed, while there was a good correlation (r=0.89) between the predicted and observed serum UA concentration after the administration of the drug, the estimated values tended to overestimate those observed by approximately 20% (Fig. 3). The sensitivity analysis of our modeling and simulation indicated that estimation of serum UA levels during febuxostat therapy was influenced by the variability of K_i of XO inhibition, among the prediction model parameters examined. In this context, the K_i for human XO might have be lower than that for bovine. In addition, there is a possibility that we ignored the contribution of oxidative metabolites of febuxostat (i.e., M1, 2, 3, 4) that have been shown to inhibit XO as potently as the unchanged drug.^10,12) However, the sum of their plasma concentrations was reported to be barely 10% of the parent compound in healthy subjects and 15% in patients with severe CKD.^10,12) Finally, we assumed that the non-renal clearance of UA is unaltered irrespective of renal function, whereas this assumption has not been verified in clinical studies. Collectively, the reasons why our modeling and simulation overestimated the actual hypouricemic effect by 20% remain unclear at present and further studies are warranted.

It is of interest to apply our model to other hypouricemic drugs for estimating their effects. Particularly, it is interesting and plausible to apply our model to another non-purine XO inhibitor, topiroxostat, if necessary PK-PD parameters are obtained. On the other hand, extensive modifications in the PK are required for applying our model to allopurinol, because the hypouricemic effect of the drug is attributed its active metabolite, oxypurinol, rather than allopurinol. For uricosuric drugs (e.g., probenecid) extensive modifications are required in the PD model, because they have different mechanism of actions (i.e., inhibition of renal UA reabsorption) and the sites of action at the renal tubules.

In conclusion, we constructed a PK-PD model that allows prediction of the hypouricemic effect of a non-purine XO inhibitor, febuxostat, in patients with various renal function and with different hyperuricemic etiologies. We demonstrated that serum UA concentrations during oral treatment with febuxostat at doses ranging from 10 to 240 mg may be estimated by our modeling and simulation method. We also demonstrated that the hypouricemic effect of febuxostat may be augmented in patients with CKD compared to those with normal renal function. We also predicted that the magnitude of hypouricemic effect of febuxostat is similar in UA overproducers and underexcretors. We understand that our hyperuricemic model needs to be verified by further studies. While confirmatory clinical studies are required, the present study provides a novel approach for individualizing doses of febuxostat and possibly of other XO inhibitors in hyperuricemic patients with diverse clinical background.

Conflict of Interest

The authors declare no conflict of interest.

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