Hyerang Roh (1,3), Lay Ahyoung Lim (1) , Hankil Son (1,3) , Young Deuk Choi (2), Kyungsoo Park (1)
(1) Department of Pharmacology, Yonsei University College of Medicine, Seoul, Korea; (2) Department of Urology, Yonsei University College of Medicine, Seoul, Korea ; (3) Brain Korea 21 Project for Medical Science, Seoul, Korea
Background: Nocturia, defined currently by the ICS as the complaint that an individual has to wake at night one or more times to void [1], is a common disorder affecting both elderly(over 70 years) men and elderly women[1-3]. It is known that increased urination frequency, 24-hr urine volume and nocturnal urine volume are the major symptoms of nocturia, and some researchers have reported that a combined medication of alpha 1 blocker and anticholinergic drug provides a better therapy for nocturia patients with benign prostatic hyperplasia than traditional mono-therapies [2,4].
However, so far there has been no method that is able to quantitatively evaluate the drug effect on the improvement of symptoms. A nonlinear mixed effects model, by quantitatively describing the time course of drug response and incorporating random individual differences, can become a solution for this problem and help understand the characteristics of the change in drug effect or disease status over time.
Objectives: With urination frequency data observed from dysuria patients, this study was intended to develop a quantitative method that can provide a time course of predicted drug response for the period not only after a short-term treatment but also after a long-term treatment. In particular, it aimed at estimating the rate of drug effect reaching the maximum drug effect, and up to how much the symptom can be reduced at the maximum effect, in an effort to provide the supportive information in designing an optimal treatment plan.
Methods
1. Data
To quantitatively assess the improvement of combined medication of alpha 1 blocker and anticholinergic drug for male patients with severe nocturia, we selected male patients with more than 3 times of nocturia a day who was treated with tamsulosin (harnalR) as an a1 blocker and solifenacin (vesicareR) q.d. as an anticholinergic drug with the same dose amount q.d. Data were collected for three periods, before the medication, 3 months and 6 months after starting the medication. Obtained data were not from the clinical trial but from the real patients treated in outpatient clinics, which were collected using frequency volume chart (FVC) from the Department of Urology of Chung-Ang university Hospital, collaborated with the department of Urology of Severance Hospital Seoul, Korea.
2. Time varying urination frequency with count model.
To estimate the frequency of urination, a count model with Poisson distribution was used where the urination was considered as an event and the lambda(λ) was described as an expected mean urination frequency in a certain time interval [5]. Modelling was performed using NONMEM 7.2.
Several cosine functions were combined to describe the periodical changes of urination frequency over 24 hours for the data obtained before the drug treatment starts (Placebo model).
To reflect the multiple-dose drug effect on the decline of patients' urination frequency, without loss of generality, the concentration versus time curve of one-compartment pharmacokinetic model for an oral dose was used to describe the periodic nature of the drug effect whose values will be the same every 24 hrs of dosing interval at steady-state.
To consider the decreased change in baseline urination frequency due to cumulative drug effect as the treatment period goes by, concept of "drug progression (Kdp)" was applied by assuming the exponential decrease of baseline lambda over the treatment time (day) up to BB, where Kdp is the rate constant (1/day) accounting for the exponential decrease and BB the maximum decrease expected.
Then, the overall lambda was described as a multiplicative function of placebo model, drug effect model, and drug progression model, multiplied by inter-individual random effect.
Using these concepts, we described the characteristic nature of the time course of urination frequency which is fluctuating over a day but is decreasing overall with treatment time.
Results
1. Data
A total of 20 male patients over the age of 18 were included in this study.
2. Time varying urination frequency with count model.
The model that best described the mean urination frequency patterns before the medication (Placebo model) was the sum of cosine functions with circadian rhythms, composed of 8- and 24-hour periodic functions. The baseline of lambda or mean urination frequency in this model (i.e., period 1) was 1.03.
In terms of drug effect, a similarly decreasing and increasing tendency in mean urination frequency was observed in data obtained in period 2 and 3. An inverse Bateman function adjusted for steady-state well described this tendency in time course of drug effect. The hypothetical elimination rate constant (k10) relevant to drug effect, not the actual elimination rate constant of drug, was 0.000155 (1/time) and hypothetical absorption rate constant (K01), not the actual absorption rate constant, was 0.000591 (1/time).
When it comes to the drug progression effect, Kdp, the rate constant accounting for the exponential decrease in baseline lambda, was 0.0319 (1/day), and BB, the coefficient of exponential function that indicates the amount that can be maximally reduced, was 0.229. In this case, t1/2 associated with the improvement through the given medication was predicted to be 22 days (= 0.693/0.0319), meaning the baseline urination frequency can be reduced by 11.5% (= 50% of BB = 50% of 0.229) in 22 days. Thus, after about 110 days (= 5t1/2) of treatment, the reduction in urination frequency is expected be reached the maximum of 22.9%, with no more drug effect or improvement of frequent urination symptom expected beyond that time.
Conclusions: The present results showed that the developed model described the data adequately and provided the useful information that can be used for predicting the time course of treatment effect. It is hoped that the model developed can be used to assess the improvement of symptom of voiding at night and frequent urination systemically. However, this is the preliminary result and further analyses will be needed including covariates analysis that can characterize individual differences in drug effect across patients, so that the model can be used to provide tailored information for each individual patient. Since not only urination frequency but also 24-hr urine volume and nocturnal urine volume are among the three major symptoms of nocturia [6], further analyses including 24-hr urine volume and nocturnal urine volume should be conducted in the future. If an appropriate model incorporating all three symptom indices were built, it would become a more accurate and useful tool offering a reliable basis for clinicians to make a better decision and set an optimized treatment plan for clinical outcome and ultimately better quality of life for patients.
References:
[1] Van Kerrebroeck P, Abrams P, Chaikin D et al. The standardization of terminology in nocturia: report from the standardization subcommittee of the International Continence Society. BJU Int 2002; 90 (Suppl. 3): 11-5
[2] The Committee for Establishment of the Clinical Guidelines for Nocturia of the Neurogenic Bladder Society, Clinical guidance for nocturia, Int J Urol 2010; 17, 397-409
[3] Jeffrey P. Weiss et al., The evaluation and treatment of nocturia: a consensus statement, BJU Int 2011; 108, 6-21 REVIEW ARTICLE
[4] TM Johnson et al. Changes in nocturia from medical treatment of benign prostatic hyperplasia: secondary analysis of the Department of Veterans Affairs Cooperative Study Trial., J Urol 2003 Jul;170(1):145-8.
[5] Elodie L. Plan et al. Transient Lower Esophageal Sphincter Relaxation Pharmacokinetic-Pharmacodynamic Modeling: Count Model and Repeated Time-To-Event Model, JPET, December 2011 vol. 339 no. 3 878-885
[6] Yukihiro Udo et al. Analysis of nocturia with 24-h urine volume,nocturnal urine volume, nocturnal bladder capacity and length of sleep duration: concept for effective treatment modality, BJU Int 2010; 107 , 791-798
Reference: PAGE 21 (2012) Abstr 2320 [www.page-meeting.org/?abstract=2320]
Poster: Other Drug/Disease Modelling