J Pharmacokinet Pharmacodyn (2015) 42:391–399 DOI 10.1007/s10928-015-9420-6

ORIGINAL PAPER

Quantitative characterization of circadian rhythm of pulmonary function in asthmatic patients treated with inhaled corticosteroids Di Zhou1 • Hongshan Li2 • Yaning Wang2 • Guenther Hochhaus1 • Vikram Sinha2 Liang Zhao2

•

Received: 8 January 2015 / Accepted: 31 May 2015 / Published online: 23 June 2015 Ó Springer Science+Business Media New York (outside the USA) 2015

Abstract The aim of this study was to characterize the circadian rhythm observed for forced expiratory volume in 1 s (FEV1) in patients with persistent asthma being treated with inhaled corticosteroids. The database included 3379 FEV1 measurements from 189 patients with mild to moderate asthma. A model using the sum of two Sine functions with periods of 12 and 24 h and a constant component of mean circadian rhythm adequately described the circadian rhythm in FEV1 measurements over time. The model adequateness was evaluated by various approaches including visual predictive check (VPC), prediction-corrected VPC, standardized VPC and normalized prediction distribution error. Covariates tested included age, body weight, height, body mass index, baseline FEV1, and sex. Age and height were found to have significant effects on the mean FEV1 level and no covariate was found to have an effect on the magnitude and timing of circadian rhythm. The model predicted that a minimum FEV1 occurred in the early morning and maximum FEV1 occurred in the early afternoon, with a population mean fluctuation of 170 mL, which is consistent with the finding that asthma symptoms usually exacerbate in the early morning for patients with

Electronic supplementary material The online version of this article (doi:10.1007/s10928-015-9420-6) contains supplementary material, which is available to authorized users. & Liang Zhao [email protected] 1

Department of Pharmaceutics, College of Pharmacy, University of Florida, 1600 SW Archer Road, Gainesville, FL, USA

2

Office of Clinical Pharmacology, Office of Translational Science, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, MD, USA

persistent asthma. This developed model provides the first quantitative approach to describing FEV1 circadian rhythm with ICS background treatment and provided insight in designing future registration trials for asthma drug development. Keywords Circadian rhythm  Asthma  FEV1  Pharmacodynamic model  Drug development

Introduction Circadian rhythm is defined as any biological process that displays an endogenous oscillation of about 24 h cycles, such as biological processes related to the light–dark cycle [1]. A pronounced circadian rhythm has been observed for endogenous cortisol plasma concentrations such as fluctuation in endogenous cortisol concentrations [2]. Many studies have described a circadian rhythm in an individual’s pulmonary function in both healthy and asthmatic subjects [3–6]. For patients with persistent asthma, their symptoms usually exacerbate in the early morning, which often resulting in death during this period [7]. In addition, the nocturnal asthmatic symptoms of cough and dyspnea are accompanied by circadian variations, and the lung function has been shown to fluctuate over 24 h periods in healthy subjects due to circadian variations. This fluctuation is found to be more pronounced in asthmatic patients [7–10]. In clinical studies of anti-asthmatic drugs, circadian rhythm in FEV1 is usually confounded with placebo and drug effect. The development of a pharmacometric model for describing the circadian rhythm in asthmatic patients’ FEV1 would lead to a better understanding of the relationship between patients’ lung function and asthma, differentiating circadian rhythm from placebo and drug effect,

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and would also help physicians determine the optimal doses and administrations of medications as well as allow the design of improved clinical studies during drug development. FEV1 has been a commonly used metric to assess lung function in patients and is accepted as a suitable clinical endpoint to quantify the degree of the pulmonary disease [11]. An established FEV1 circadian rhythm model could critically contribute to an objective measurement of clinical drug or placebo effect by recognizing the part of clinically observed FEV1 effects that were related to circadian rhythm. Objectively established benchmark values by filtering out the circadian rhythm will greatly help identification of optimized dosing regimen for new drug development in the disease areas of asthma and chronic obstructive pulmonary disease (COPD). There were several attempts to characterize the circadian FEV1–time profiles by developing population pharmacokinetic-pharmacodynamic (PK/PD) models in COPD patients. The approach proposed by Nielsen et al. used a single cosine function with a period of 24 h to model the circadian rhythm [12]. Although this model gave reasonable results, the circadian FEV1-time profile was not symmetrical as expected by a cosine function. Another approach proposed by Wu et al. used a multi-oscillator function derived from superposition of two cosine functions, which allows the characterization of the asymmetric pattern of the circadian FEV1 profiles [13]. It was also reported that the circadian FEV1-time profiles could be described by the difference of two functions with exponential declines, but the model fitting was found to be inferior to the cosine model [14]. Pharmacometric models describing the circadian FEV1 rhythm in asthmatic patients are unavailable. Long-acting beta-adrenoceptor agonists (LABAs, b2agonists) are usually prescribed for patients with persistent asthma or COPD. It relaxes the airway smooth muscle and improves the symptoms [15]. Also, LABA, when used as monotherapy in asthma, has been reported to increase hospitalization, life threatening events, and even deaths [16–18]. Therefore, asthma management guidelines recommend that LABAs only be used in combination with inhaled corticosteroids (ICS) [19]. Using ICS as background treatment has proven to reduce the asthma related adverse events, and recent clinical studies on LABA drugs were conducted with ICS as background treatment based on the requirement from U.S. Food and Drug Administration (FDA) [20]. The modeling efforts in FEV1 circadian rhythm characterization in previous publications was limited to ICS free scenarios in COPD patients [12–14]. In contrast, our model is the first attempt of characterizing FEV1 circadian rhythm under ICS background therapy in patients with persistent asthma.

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Materials and methods Study design The search for full profile FEV1 data observed during run in periods of registration studies identified only one dataset available in electronic format from the FDA database. The study was a LABA trial consisted of a 21 day screening period (pre-screening if needed), a 14 day run-in period, a baseline assessment day, a treatment period lasting up to 16 days, and a study completion evaluation 3 days after the last drug administration. Data from the baseline assessment day was extracted for circadian rhythm analysis. Spirometry assessments conducted at baseline matched the timepoints for treatment day 15, and day 16, which included 50 and 15 min pre-dose, 10, 30 min, 1, 2, 3, 4, 8 h, 11 h 10 min, 11 h 45 min, 12 h 10 min, 12 h 30 min, 13, 14, 16, 20 and 22 h post dose. A flow diagram of the study is shown in Fig. 1. A total of 190 patients with persistent asthma were enrolled and randomized to placebo and active treatment arms and 189 of them with 3379 observations were included in the analysis. The patients’ demographic characteristics are summarized in Table 1. Model development The model development was performed by nonlinear mixed effect modeling (NONMEM) via first-order conditional estimation with interaction (FOCE-I) using NONMEM 7.2 [21]. In the first step, a base model of the circadian rhythm was developed by superimposing two Sine functions with periods of 24 and 12 h, plus a constant component of mean circadian rhythm as shown in Eq. (1). This model characterized the fluctuation in FEV1 throughout the day under the influence of ICS: fcirc ðtÞ ¼ C0 þ C1  sinð2p  ðt  TS1 Þ=24Þ þ C2  sinð2p ðt  TS2 Þ=12Þ ð1Þ Here, t represents the 24-h clock time and time 0 corresponds to midnight; C0 the mean circadian rhythm; C1 and C2 the amplitudes of the two Sine function components; TS1 and TS2 time shifts for two Sine functions with TS1 likely to be related to wake up time for first FEV1 measurement. The between subject variabilities (BSVs) of C0, TS1 and TS2 were described using exponential error model; BSVs of C1 and C2 were described using additive error model; Intra-individual residual variability was evaluated using additive error model. Other structural models tested included a simplified single Sine function model, the superposition of three Sine

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Fig. 1 Diagrammatic representation of the study design

Screening Period (21 days) (Pre-screening Period as Needed)

Main inclusion criteria: Patients who had been diagnosed of persistent asthma (FEV1 at screening of 50-90% predicted normal), had been on a stable dose of ICS one month prior to first study visit, and had demonstrated reversibility to albuterol/salbutamol with an increase of ≥12 % and ≥200 mL in FEV1 Main exclusion criteria: Patients who were hospitalized due to severe asthma attack in the past 6 months, visited emergency room for asthma attack or had lower respiratory tract infection 6 weeks prior to the first study visit, had seasonal allergy that was likely to deteriorate asthma during study, or required the use of ≥8 inhalations per day of the short-acting β2-agonist on any two consecutive days from screening to randomization

Run-in Period (14 days)

Monitor patient stability

Baseline Assessment (1 day)

Spirometric profiles performed included FEV1, forced vital capacity (FVC) and forced expiratory flow 25%-75% (FEF25-75). FEV1 assessments were used for circadian rhythm modeling

Treatment Period (up to 16 days)

Patients were randomized to receive different regimens of the tested product; Spirometric profiles were performed

Study Completion (3 days after last dose)

functions, and a single Sine function with a Bateman component. The single Sine function model did not fit the data due to the asymmetric nature of individual FEV1 profiles. More complex models of the latter two were either unstable or over-parameterized, suggesting that the data we have do not support the model complexities with sufficient degrees of freedom. In the second step, covariate effect on the base model parameters was investigated. The seven potential covariates assessed included both continuous covariates (i.e., age, body

weight, height, body mass index, and baseline FEV1) and categorical covariates (i.e., sex). Race and smoking status were not assessed because the majority of the patients were Caucasians, and nonsmokers. Both linear and power relations were explored in the continuous covariate modeling, and sex was tested as a binary covariate. The covariate model was established based on a stepwise selection procedure including forward inclusion and backward elimination. In the forward inclusion step, any covariate that contributed to a drop of [3.84 (v2, a = 0.05, df = 1) in the objective function value

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Table 1 Summary of patient demographic characteristics No. of patients

189

Age (years) Mean ± SD (range)

40.4 ± 12.7 (18–80)

Sex Male, female [n (%)]

110 (58.2 %), 79 (41.8 %)

Race Caucasian, Black, Asian, Pacific Islander, other [n (%)]

151 (79.9 %), 26 (13.8 %), 3 (1.6 %), 1 (0.5 %), 8 (4.2 %)

Height (cm) Mean ± SD (range)

171.2 ± 9.4 (148–196)

Weight (kg) Mean ± SD (range)

83.6 ± 16.1 (47.9–145)

Body mass index (kg/m2) Mean ± SD (range)

28.6 ± 5.0 (19.4–39.9)

Baseline FEV1 (L) Mean ± SD (range) Smoking status Never smoked, ex-smoker, current smoker [n(%)]

2.7 ± 0.7 (1.2–4.6) 151 (79.9 %), 28 (14.8 %), 10 (5.3 %)

(OFV) after inclusion was kept in the model. In the backward elimination step, a covariate was removed from the model if elimination of the covariate resulted in an OFV increase of \10.83 (v2, a = 0.001, df = 1). The proposed model was assessed by the change in the objective function value (OFV), goodness of fit plots, and simulation based evaluations. Goodness of fit plots were obtained from Xpose package (2.15.3) in R (2.15.1) [22, 23]. Visual predictive check (VPC) and prediction-corrected visual predictive check (pcVPC) were performed based on 1000 simulations using Perl-speaks NONMEM (PsN) [24]. A standardized VPC (sVPC) was also conducted using self-supplied R codes [25]. One thousand datasets were simulated using the final model based on the original dataset. The percentile (Pi,j) of the jth observation for the ith participant was calculated by: Pi;j ¼

1000 1 X dij;n 1000 n¼1

Here dij,n = 1 or 0 if yij [ y0ij;n or otherwise, where yij is the actual jth observation for the ith individual and y0ij;n is the nth simulated observation corresponding to yij. The entire modeling process was conducted with Pirana (2.9.0) [26].

Fig. 2 Scatter plots of between subject variability (ETA1) on C0 versus covariates (age and height) for base model (left) and final model (right). Grey curves represent LOESS curves

TVC0 ¼ h0 þ h5  ðAge  41Þ þ h6  ðHeight  171Þ

Results The final model had identified age and height effects on C0 with linear relations, which were graphically illustrated in Fig. 2 and structurally quantified according to Eq. 2:

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ð2Þ Here TVC0 represents the typical value of C0; h0 the estimated mean circadian rhythm in the model; h5 and h6 the coefficients for the covariate effect. The base and final model estimates with their respective OFV are summarized

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in Table 2. Of note, both linear and power relationships for covariates were explored during model building and a linear relationship was selected over a power relationship based on the extent of reduction in objective function value. As Table 2 shows, the reduced objective function value indicated that the model fitting was improved after incorporating age and height as covariates, with a reduction in between-subject variability for C0 from 26.8 to 17.7 %. As shown by Fig. 2, correlation of age and height with the baseline parameter C0, as identified by the base model, were accounted for in the final model. Additional graphical evaluations found no other correlation between screened covariates and the five model parameters in Eq. 1 (i.e., C0, C1, C2, TS1 and TS2). A typical population circadian curve, along with two curves representing the contributions from the two circadian components as described in Sine functions of Eq. 1, was shown in Fig. 3 to aid an appreciation of the overall circadian rhythm pattern throughout a day. Model evaluations The diagnostic plots demonstrated that the final model described the observed data reasonably well. As shown by Fig. 4, compared to the base model, the final model explained a significant portion of variance associated with the observed FEV1s as reflected by a much wider spread of FEV1 population predictions along the identity line. Both the individual weighted residuals (IWRESs) and the conditional weighted residuals (CWRESs) evenly distributed about 0 against time, indicating no major systemic prediction bias. Representative individual plots, shown in Fig. 5, demonstrated that the final model was sufficiently flexible to capture the observed data manifesting diversified patterns. The final model was also evaluated by visual predictive check (VPC) and prediction-corrected visual predictive check (pcVPC) [27]. As shown in supplementary file

Fig. 3 Model predicted FEV1 vs time (solid line) throughout the day and time 0 corresponds to midnight. The dashed line represents the first Sine function and the dotted line represents the second Sine function as described in Eq. 1

Fig. 1a–b, the 5th, 50th, and 95th model predicted percentiles overlapped with their corresponding observed percentiles, with slight over prediction for the 95th predicted percentile. VPC and pcVPC plots demonstrated that the model captured the central tendency with reasonable prediction performance. For sVPC, the 5th, 50th, and 95th percentiles of model simulated data were calculated and supplementary file Fig. 1c showed that the model-predicted 5th and 95th percentiles overlapped with the corresponding observed percentiles, although there is a slight separation between the observed and model-predicted 50th percentiles in a random manner, Pi,js were well distributed between 0 and 1 across the whole time course, indicating a good model performance to characterize both fixed and random effects. This finding is consistent with the evaluation by normalized prediction distribution error (NPDE) as shown in supplementary file Fig. 1d [28]. NPDE versus time plot did

Table 2 Parameter estimates of base model and final model Parameter

Definition

Population estimates (RSE %)

Between subject variability (%) (RSE %)

Base model OFV -6737.98

Base model OFV -6737.98

Final model OFV -6897.40

Final model OFV -6897.40

C0 (L)

Mean circadian rhythm

2.59 (2)

2.61 (1.3)

26.8 (5.3)

17.7 (10.1)

C1 (L)

24 h cycle amplitude

0.0863 (11.6)

0.0855 (13.6)

12.3 (8.6)

12.4 (16.6)

C2 (L) TS1 (h)

12 h cycle amplitude Time shift for 24 h cycle

-0.0285 (33.4) 7.61 (4)

-0.0267 (84) 7.58 (5.2)

10 (10) 31 (10.2)

10 (20.7) 32.6 (51.2)

TS2 (h)

Time shift for 12 h cycle

4.54 (7.9)

4.49 (13.2)

28.9 (17.6)

29.3 (20.5)

h5

Coefficient for age effect

–

-0.0274

–

–

h6

Coefficient for height effect

–

0.035

–

–

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Fig. 4 Goodness of fit. Upper left and right predicted versus observed FEV1 for base model and final model, respectively; lower left and right individual weighted residual and conditional weighted residual versus clock time for the final model, respectively. Grey curves represent LOESS smooth lines

Discussion

Fig. 5 Individual prediction (IPRED, solid line), population prediction (PRED, dashed line) and observation (DV, circle) over clock time for a representative set of patients

not reveal apparent deviating trend, with NPDE data points in similar percentages within both the 95 % and the 90 % confident intervals, respectively.

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In this paper, we developed a circadian rhythm model to characterize the longitudinal FEV1 response in patients with persistent asthma. The data were extracted from a clinical dose-ranging study for a long acting beta-adrenoceptor agonist (LABA) drug. Based on clinical findings that LABA drug monotherapy could cause severe safety issues, it is currently recommended that LABAs be used in combination with ICS to reduce adverse events. According to study protocol, the patients in this study were previously treated with ICS and remained on stable dose of ICS throughout the study. Of note, the circadian model for patients with ICS background treatment has not been previously reported. The data analyzed was based on a 24 h intensive sampling schedule. To the best of our knowledge, this is the only FEV1 data available in the study run in period from registration studies for NDA submissions, mainly due to the logistic challenge of obtaining FEV1 data during midnight, which serves as a valuable source of information for us to evaluate circadian rhythm. Based on the data, several base models were attempted including single Sine function, single Sine function plus a Bateman component, double Sine function, and triple Sine function models. Due to the asymmetry of circadian profiles, single Sine function model was not able to adequately describe the data.

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Although adding a Bateman function to a single Sine function to describe the second FEV1 peak as observed for some patients can marginally improve individual fits, it either led to model over parameterization or resulted in the parameter estimates violating the steady state premise. Having triple Sine functions in the model led to parameter identifiability issues. Overall, the double Sine function model with periods of 24 and 12 h adequately described the data, since this model allowed the asymmetric pattern of the circadian profiles and assumes the steady state automatically. Out of the screened covariates, only age and height were found to be the significant covariates for the mean FEV1 level, C0, and no covariate effect was found for other model parameters. The correlation between C0 and age was identified to be negative while the correlation between C0 and height was identified to be positive. Plausible physiological explanation for the age effect is that the structure of chest wall and thoracic spine change with age, and the respiratory muscle strength decreases with age, which can result in impairment of pulmonary functions [29, 30]. The positive effect of height on C0 can be explained by its positive relationship to lung volumes [31, 32]. Figure 6 graphically demonstrated the relationship of mean FEV1 versus age, and mean FEV1 versus height for both male and female patients. Although there were reports of effect of smoking status on baseline FEV1, the data we have did not recognize this relationship due to the limited number of patients in ex- and current smoker groups and the potentially confounding ICS effect [29, 33–35]. For model evaluations, various simulation based methods were exploited to assess the performance of final model including VPC, pcVPC, sVPC and NPDE. VPC is the conventionally used diagnostic approach to graphically compare different percentiles of observed data to percentiles of simulated data, usually grouped together within bins of the time. However, the diagnostic power of VPC sometimes can be hampered by binning observed values of large variability from different origins. In this situation, pcVPC provides a solution by normalizing the observed

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and simulated values with respect to the median prediction for each bin across the time [27]. For our final model, the 5th, 50th, and 95th model predicted percentiles overlapped with their corresponding observed percentiles for both VPC and pcVPC, indicating that the final model reasonably captured the central tendency and dispersion. Similar to pcVPC, the sVPC displays simulated and observed percentiles in the context of a uniform distribution and can assess data derived from different conditions in dose, dosing frequency, PK scheduling, or covariate values [36]. NPDE is similar to sVPC with percentiles being plotted in the context of a normal distribution and a global statistical test of consistency of the entire data for an assumed error model can be tested [25]. The sVPC plot for the final model demonstrated that the model-predicted 5th and 95th percentiles overlapped with their corresponding observed percentiles, although there was a slight separation between the observed and model-predicted 50th percentiles in a random manner. For the sVPC plots, Pi,js were evenly distributed between 0 and 1 across the whole time course, which was in agreement with the NPDE assessment where the NPDE data points approximately followed a normal distribution as reflected by their distribution inside and outside of the 90 and 95 % confident intervals. Based on the final model, the predicted magnitude of FEV1 fluctuation attributed to circadian rhythm is 170 mL, corresponding to a population FEV1 range of 2.55–2.72 L. The maximum FEV1 occurred at around 1:30 PM and remained stable for an hour (DFEV1 \ 10 mL), while the minimum FEV1 occurred at around 4:10 AM and remained relatively constant for two hours (DFEV1 \ 10 mL). In a former report on the longitudinal FEV1 response to an inhaled long-acting anti-muscarinic in COPD patients, Wu et al. employed the superposition of two Cosine functions to describe the circadian rhythm [13]. Their model predicted that times for peak and trough FEV1 were at around 3 PM and 7 AM respectively, and the magnitude of fluctuation was approximately 120 mL. Therefore, the time to peak and trough FEV1 predicted from our model are consistent with results of Wu et al. and other literature [37].

Fig. 6 Relationship of mean FEV1 versus age (left) and mean FEV1 versus height (right) for male (circle) and female (filled triangle) patients

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Our model also confirms the morning exacerbation of asthmatic symptoms in patients with persistent asthma. The slightly higher predicted magnitude of FEV1 fluctuation due to circadian rhythm from our model may be explained by the larger lung capacity and better lung function for asthmatic patients than for COPD patients. It could also be attributable to the background therapy of ICS when the use of ICS improved the patients’ lung function and led to a higher circadian fluctuation. Since the model developed in this paper offered a quantitative approach to characterize the FEV1 time course profile resulted from circadian rhythm in asthmatic patients with ICS background treatment, it can offer better characterization of placebo and drug treatment effects with ICS as background therapy in future modeling efforts. Of note, this model also has its own limitations and is subject to be further fine-tuned when more data become available. First, since it is based on the FEV1 data of a single day, the model lacks the power to predict day to day FEV1 variation. Upon the availability of longitudinal FEV1 data across multiple days, inter occasion variability can potentially be added to characterize the day to day variations [38]. Second, it is also difficult in this model to evaluate potentially varying ICS effect resulted from varying dose intensity due to the lack of detailed ICS use information. Finally, the model may have left out effects of some meaningful covariates such as smoking status and race on circadian rhythm due to data scarcity and narrow range of covariate distribution.

Conclusion In summary, we developed a circadian rhythm model for patients with persistent asthma. This was the first modeling attempt when ICS was introduced as background treatment, with both inter and intra-individual variability taken into account. This model is able to quantitatively characterize the time course FEV1 of circadian rhythm in persistent asthmatic patients. The model offers a good opportunity to better characterize placebo and/or drug treatment effects in asthma clinical trials.

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