Multinomial logistic estimation of Markov-chain models for modeling sleep architecture in primary insomnia patients

Practical Applications of a Nausea and Vomiting Model in the Clinical Development of Additional Doses of Dulaglutide

Dulaglutide 3.0 and 4.5 mg weekly doses were approved for additional glycemic control in adult patients with type 2 diabetes inadequately controlled with metformin and 0.75 or 1.5 mg weekly doses of dulaglutide. Effects such as nausea and vomiting are commonly reported with dulaglutide and other glucagon-like peptide-1 receptor agonist therapies. Based on a pharmacokinetic/pharmacodynamic model-informed approach, a stepwise dose-escalation scheme with 4-week intervals between dose increments was suggested to mitigate gastrointestinal events for dulaglutide. These gastrointestinal events are dose dependent and attenuate over time with repeated dosing. A Markov chain Monte Carlo pharmacokinetic/pharmacodynamic joint model was developed using AWARD-11 data (N = 1842) to optimize dulaglutide dose escalation to 3.0 and 4.5 mg to mitigate gastrointestinal events. Model simulations evaluated probabilities of nausea and vomiting events for various dosing scenarios in patients needing higher doses for additional glycemic control. The model indicated that patients may dose escalate from 1.5 to 3.0 mg, then 4.5 mg weekly after at least 4 weeks on each dose. No clinically meaningful differences in nausea or vomiting events were expected when patients escalated to 3.0 or 4.5 mg following initiation at 0.75 or 1.5 mg dulaglutide. Based on the findings of this model, a minimum 4-week duration at each dose before escalation was appropriate to reduce gastrointestinal events of dulaglutide, consistent with observed gastrointestinal events data from the AWARD-11 study and supporting the currently recommended dose-escalation regimen of dulaglutide doses of 3.0 and 4.5 mg for additional glycemic control.

Recommending encounters according to the sociodemographic characteristics of patient strata can reduce risks from type 2 diabetes

Objectives

Physician encounters with patients with type 2 diabetes act as motivation for self-management and lifestyle adjustments that are indispensable for diabetes treatment. We elucidate the sociodemographic sources of variation in encounter usage and the impact of encounter usage on glucose control, which can be used to recommend encounter usage for different sociodemographic strata of patients to reduce risks from Type 2 diabetes.

Data and methods

We analyzed data from a multi-facility clinic in the Midwestern United States on 2124 patients with type 2 diabetes, from 95 ZIP codes. A zero-inflated Poisson model was used to estimate the effects of various ZIP-code level sociodemographic variables on the encounter usage. A multinomial logistic regression model was built to estimate the effects of physical and telephonic encounters on patients’ glucose level transitions. Results from the two models were combined in marginal effect analyses.

Results and conclusions

Conditional on patients’ clinical status, demographics, and insurance status, significant inequality in patient encounters exists across ZIP codes with varying sociodemographic characteristics. One additional physical encounter in a six-month period marginally increases the probability of transition from a diabetic state to a pre-diabetic state by 4.3% and from pre-diabetic to the non-diabetic state by 3.2%. Combined marginal effect analyses illustrate that a ZIP code in the lower quartile of high school graduate percentage among all ZIP codes has 1 fewer physical encounter per six months marginally compared to a ZIP code at the upper quartile, which gives 5.4% average increase in the probability of transitioning from pre-diabetic to diabetic. Our results suggest that policymakers can target particular patient groups who may have inadequate encounters to engage in diabetes care, based on their immediate environmental sociodemographic characteristics, and design programs to increase their encounters to achieve better care outcomes.

AM-251, A Cannabinoid Antagonist, Modifies the Dynamics of Sleep-Wake Cycles in Rats

Study Objectives: (a) To describe the microarchitecture of wakefulness and sleep following administrations of 5- and 10-mg/kg AM-251 in rats. (b) To develop a new statistical method to follow bout-to-bout dynamics. Method: Wistar rats (n = 6) had been equipped with electroencephalography (EEG) and electromyography (EMG) electrodes. Following their recovery and habituation after the surgery, the animals were injected with vehicle and 5- and 10-mg/kg AM-251 intraperitoneally and EEG, EMG, and motor activity were analyzed for the subsequent 3 h. Results: AM-251 induced a dose- and time-dependent increase in the number of bouts in active wake (AW), and it decreased this number in all other vigilance states except in passive wake (PW). In contrast, the bout duration in PW compensatory decreased. The effect of AM-251 on the sleep transition dynamics was monitored with a new tool we call "transition heatmap." The analysis of bout trajectories with transition heatmaps reveals a highly organized pattern. Conclusion: AM-251 selectively influences the frequency of vigilance state transitions, but it has no direct impact on the state lengths. AM-251 markedly changed the state transition dynamics, which was visualized with the help of state transition heatmaps.

The Color of Noise and Weak Stationarity at the NREM to REM Sleep Transition in Mild Cognitive Impaired Subjects

In Older Adults (OAs), Electroencephalogram (EEG) slowing in frontal lobes and a diminished muscle atonia during Rapid Eye Movement sleep (REM) have each been effective tracers of Mild Cognitive Impairment (MCI), but this relationship remains to be explored by non-linear analysis. Likewise, data provided by EEG, EMG (Electromyogram) and EOG (Electrooculogram)—the three required sleep indicators—during the transition from REM to Non-REM (NREM) sleep have not been related jointly to MCI. Therefore, the main aim of the study was to explore, with results for Detrended Fluctuation Analysis (DFA) and multichannel DFA (mDFA), the Color of Noise (CN) at the NREM to REM transition in OAs with MCI vs. subjects with good performances. The comparisons for the transition from NREM to REM were made for each group at each cerebral area, taking bilateral derivations to evaluate interhemispheric coupling and anteroposterior and posterior networks. In addition, stationarity analysis was carried out to explore if the three markers distinguished between the groups. Neuropsi and the Mini-Mental State Examination (MMSE) were administered, as well as other geriatric tests. One night polysomnography was applied to 6 OAs with MCI (68.1 ± 3) and to 7 subjects without it (CTRL) (64.5 ± 9), and pre-REM and REM epochs were analyzed for each subject. Lower scores for attention, memory and executive funcions and a greater index of arousals during sleep were found for the MCI group. Results confirmed that EOGs constituted significant markers of MCI, increasing the CN for the MCI group in REM sleep. The CN of the EEG from the pre-REM to REM was higher for the MCI group vs. the opposite for the CTRL group at frontotemporal areas. Frontopolar interhemispheric scaling values also followed this trend as well as right anteroposterior networks. EMG Hurst values for both groups were lower than those for EEG and EOG. Stationarity analyses showed differences between stages in frontal areas and right and left EOGs for both groups. These results may demonstrate the breakdown of fractality of areas especially involved in executive functioning and the way weak stationarity analyses may help to distinguish between sleep stages in OAs.

Mathematical modeling of sleep state dynamics in a rodent model of shift work

Millions of people worldwide are required to work when their physiology is tuned for sleep. By forcing wakefulness out of the body’s normal schedule, shift workers face numerous adverse health consequences, including gastrointestinal problems, sleep problems, and higher rates of some diseases, including cancers. Recent studies have developed protocols to simulate shift work in rodents with the intention of assessing the effects of night-shift work on subsequent sleep (Grønli et al., 2017). These studies have already provided important contributions to the understanding of the metabolic consequences of shift work (Arble et al., 2015; Marti et al., 2016; Opperhuizen et al., 2015) and sleep-wake-specific impacts of night-shift work (Grønli et al., 2017). However, our understanding of the causal mechanisms underlying night-shift-related sleep disturbances is limited. In order to advance toward a mechanistic understanding of sleep disruption in shift work, we model these data with two different approaches. First we apply a simple homeostatic model to quantify differences in the rates at which sleep need, as measured by slow wave activity during slow wave sleep (SWS) rises and falls. Second, we develop a simple and novel mathematical model of rodent sleep and use it to investigate the timing of sleep in a simulated shift work protocol (Grønli et al., 2017). This mathematical framework includes the circadian and homeostatic processes of the two-process model, but additionally incorporates a stochastic process to model the polyphasic nature of rodent sleep. By changing only the time at which the rodents are forced to be awake, the model reproduces some key experimental results from the previous study, including correct proportions of time spent in each stage of sleep as a function of circadian time and the differences in total wake time and SWS bout durations in the rodents representing night-shift workers and those representing day-shift workers. Importantly, the model allows for deeper insight into circadian and homeostatic influences on sleep timing, as it demonstrates that the differences in SWS bout duration between rodents in the two shifts is largely a circadian effect. Our study shows the importance of mathematical modeling in uncovering mechanisms behind shift work sleep disturbances and it begins to lay a foundation for future mathematical modeling of sleep in rodents.

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Millions of people worldwide are required to work when their physiology is tuned for sleep.

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Enforcing wakefulness during this time leads to numerous adverse health consequences including sleep problems and higher rates of some diseases.

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Rodent models of shift work have illuminated some of the effects of night shift work on subsequent sleep.

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This study uses mathematical modeling to accurately simulate rodent sleep during baseline and shift work conditions.

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A simple mathematical framework can help us understand possible mechanisms underlying the sleep disturbances seen in shift work.

Quantifying sleep architecture dynamics and individual differences using big data and Bayesian networks

The pattern of sleep stages across a night (sleep architecture) is influenced by biological, behavioral, and clinical variables. However, traditional measures of sleep architecture such as stage proportions, fail to capture sleep dynamics. Here we quantify the impact of individual differences on the dynamics of sleep architecture and determine which factors or set of factors best predict the next sleep stage from current stage information. We investigated the influence of age, sex, body mass index, time of day, and sleep time on static (e.g. minutes in stage, sleep efficiency) and dynamic measures of sleep architecture (e.g. transition probabilities and stage duration distributions) using a large dataset of 3202 nights from a non-clinical population. Multi-level regressions show that sex effects duration of all Non-Rapid Eye Movement (NREM) stages, and age has a curvilinear relationship for Wake After Sleep Onset (WASO) and slow wave sleep (SWS) minutes. Bayesian network modeling reveals sleep architecture depends on time of day, total sleep time, age and sex, but not BMI. Older adults, and particularly males, have shorter bouts (more fragmentation) of Stage 2, SWS, and they transition less frequently to these stages. Additionally, we showed that the next sleep stage and its duration can be optimally predicted by the prior 2 stages and age. Our results demonstrate the potential benefit of big data and Bayesian network approaches in quantifying static and dynamic architecture of normal sleep.

Analysis of variability in length of sleep state bouts reveals memory-free sleep subcomponents consistent among primary insomnia patients

The statistical distributions of bout lengths for the different (macro) sleep states (wake, N1, N2, N3, and REM sleep) are essential to understanding whether any memory-free subcomponent ("micro state") is involved in the organization of sleep. Micro state detection can be prevented by the fusion of data including various sources of variability, in particular by the differences in sleep architecture between individuals, along sleep time (or nighttime), or between different nights. In this analysis, a mathematical model of sleep was adopted to disentangle these features and advance the understanding of the dynamics and mechanisms of sleep and its states. The analysis involved 116 primary insomnia patients taking placebo before going to bed and undergoing polysomnography for one night. The individual sequences of macro sleep states had been previously modeled with a mixed-effect nonhomogeneous modified Markov chain model, from which individual conditional probability distributions for the bout durations were derived in this analysis as functions of sleep time. The probability distributions, affected by neither subject, night-time, nor multiple-night pooling, substantially changed at ¼ and ¾ sleep time, had modified exponential shape, and were best described as the sum of one to four exponentials, depending on the sleep state. The time constants and proportions of bouts contributing to each exponential were similar in the different subjects, changing over sleep time. Variability in bout durations thus indicated the presence of multiple memory-free sleep subcomponents whose mean residence times and access probabilities could be identified and shown to be consistent among the studied subjects. NEW & NOTEWORTHY We present a new methodology for deriving, from polysomnography data, the individual conditional probability for the duration of the bouts of wake, N1, N2, N3, and REM sleep. We evaluated the variability of this probability within and between primary insomnia patients and along sleep time. The multiexponential shapes of the probability distributions within the individuals revealed memory-free mechanisms and sleep subcomponents with consistent features in the studied population.

Quasi-supervised scoring of human sleep in polysomnograms using augmented input variables

The limitations of manual sleep scoring make computerized methods highly desirable. Scoring errors can arise from human rater uncertainty or inter-rater variability. Sleep scoring algorithms either come as supervised classifiers that need scored samples of each state to be trained, or as unsupervised classifiers that use heuristics or structural clues in unscored data to define states. We propose a quasi-supervised classifier that models observations in an unsupervised manner but mimics a human rater wherever training scores are available. EEG, EMG, and EOG features were extracted in 30s epochs from human-scored polysomnograms recorded from 42 healthy human subjects (18-79 years) and archived in an anonymized, publicly accessible database. Hypnograms were modified so that: 1. Some states are scored but not others; 2. Samples of all states are scored but not for transitional epochs; and 3. Two raters with 67% agreement are simulated. A framework for quasi-supervised classification was devised in which unsupervised statistical models-specifically Gaussian mixtures and hidden Markov models--are estimated from unlabeled training data, but the training samples are augmented with variables whose values depend on available scores. Classifiers were fitted to signal features incorporating partial scores, and used to predict scores for complete recordings. Performance was assessed using Cohen's Κ statistic. The quasi-supervised classifier performed significantly better than an unsupervised model and sometimes as well as a completely supervised model despite receiving only partial scores. The quasi-supervised algorithm addresses the need for classifiers that mimic scoring patterns of human raters while compensating for their limitations.

Chronic escitalopram treatment attenuated the accelerated rapid eye movement sleep transitions after selective rapid eye movement sleep deprivation: a model-based analysis using Markov chains

Background

Shortened rapid eye movement (REM) sleep latency and increased REM sleep amount are presumed biological markers of depression. These sleep alterations are also observable in several animal models of depression as well as during the rebound sleep after selective REM sleep deprivation (RD). Furthermore, REM sleep fragmentation is typically associated with stress procedures and anxiety. The selective serotonin reuptake inhibitor (SSRI) antidepressants reduce REM sleep time and increase REM latency after acute dosing in normal condition and even during REM rebound following RD. However, their therapeutic outcome evolves only after weeks of treatment, and the effects of chronic treatment in REM-deprived animals have not been studied yet.

Results

Chronic escitalopram- (10 mg/kg/day, osmotic minipump for 24 days) or vehicle-treated rats were subjected to a 3-day-long RD on day 21 using the flower pot procedure or kept in home cage. On day 24, fronto-parietal electroencephalogram, electromyogram and motility were recorded in the first 2 h of the passive phase. The observed sleep patterns were characterized applying standard sleep metrics, by modelling the transitions between sleep phases using Markov chains and by spectral analysis.

Based on Markov chain analysis, chronic escitalopram treatment attenuated the REM sleep fragmentation [accelerated transition rates between REM and non-REM (NREM) stages, decreased REM sleep residence time between two transitions] during the rebound sleep. Additionally, the antidepressant avoided the frequent awakenings during the first 30 min of recovery period. The spectral analysis showed that the SSRI prevented the RD-caused elevation in theta (5–9 Hz) power during slow-wave sleep. Conversely, based on the aggregate sleep metrics, escitalopram had only moderate effects and it did not significantly attenuate the REM rebound after RD.

Conclusion

In conclusion, chronic SSRI treatment is capable of reducing several effects on sleep which might be the consequence of the sub-chronic stress caused by the flower pot method. These data might support the antidepressant activity of SSRIs, and may allude that investigating the rebound period following the flower pot protocol could be useful to detect antidepressant drug response. Markov analysis is a suitable method to study the sleep pattern.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Cost-effectiveness of long-acting injectable risperidone versus flupentixol decanoate in the treatment of schizophrenia: a Markov model parameterized using administrative data

We use longitudinal patient-level data from a German sickness fund with 7.26 million insured in a Markov-simulation model to assess the cost-effectiveness of long-acting injectable risperidone (LAI-RIS) compared with long-acting injectable flupentixol (LAI-FLX) in the long-term management of schizophrenia. We simulate treatment costs from the payer's perspective, hospitalization, the probability to be prescribed co-medication, and treatment discontinuation over a 2-year time horizon. Model inputs were derived from 935 patients hospitalized with schizophrenia between 2005 and 2008 who received either LAI-RIS or LAI-FLX for at least 1 month. After 2 years, 89.4% (95.8%) of patients who were initiated on LAI-RIS (LAI-FLX) discontinued the initial regimen. The number of days spent in hospital per month and patient was slightly lower with LAI-RIS (1.08 vs. 1.28 days, p<0.001). The proportion of patients receiving side-effect co-medication was lower with LAI-RIS (8.3 vs. 15.0% per month, p<0.001). Mean total costs of treatment per patient and month were 1,015 € under LAI-RIS and 395 € under LAI-FLX, resulting in an ICER of 3,088 € (95% CI [-913 €; 3,551 €]) for an avoided hospital day per patient and month in the base case scenario with a 15.1% probability of LAI-FLX being the dominant treatment strategy. Cost differences were mainly attributable to the higher drug costs of LAI-RIS. The effectiveness of LAI-RIS in preventing hospital days appears to be similar to LAI-FLX, with a slight superiority in side-effect and switching rates. This comes at the cost of substantially higher treatment expenses. From a decision-maker's point of view, the use of health insurance data as a source of input for decision models appears to be a reasonable alternative to models driven by clinical data only.

Comparisons of Analysis Methods for Proof-of-Concept Trials

Drug development struggles with high costs and time consuming processes. Hence, a need for new strategies has been accentuated by many stakeholders in drug development. This study proposes the use of pharmacometric models to rationalize drug development. Two simulated examples, within the therapeutic areas of acute stroke and type 2 diabetes, are utilized to compare a pharmacometric model-based analysis to a t-test with respect to study power of proof-of-concept (POC) trials. In all investigated examples and scenarios, the conventional statistical analysis resulted in several fold larger study sizes to achieve 80% power. For a scenario with a parallel design of one placebo group and one active dose arm, the difference between the conventional and pharmacometric approach was 4.3- and 8.4-fold, for the stroke and diabetes example, respectively. Although the model-based power depend on the model assumptions, in these scenarios, the pharmacometric model-based approach was demonstrated to permit drastic streamlining of POC trials.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e23; doi:10.1038/psp.2012.24; advance online publication 16 January 2013.

Pharmacokinetic-pharmacodynamic modeling of severity levels of extrapyramidal side effects with markov elements

A major problem in the treatment of schizophrenic patients with current antipsychotic drugs, mainly acting as dopamine-2 receptor antagonists, is the occurrence of side effects such as extrapyramidal symptoms (EPS). Meta-analyses of summary data of EPS occurrence, and receptor occupancies inferred from mean plasma concentrations, have shown the incidence of EPS to rise when receptor occupancy is above ~80%. In this analysis, individual longitudinal EPS data from 2,630 patients participating in one of seven different trials and treated with haloperidol, paliperidone, ziprasidone, olanzapine, JNJ-37822681, or placebo were analyzed using a continuous time probability model with Markov elements. The developed pharmacokinetic–pharmacodynamic model describes the longitudinal changes of spontaneously reported EPS-related adverse events and their severity levels rated by clinicians. Individual steady-state concentrations and occupancy levels were found to be predictors for EPS. The results confirm 80% occupancy as a level of increased EPS occurrence rates, also at the individual level.

A multi-state spatio-temporal Markov model for categorized incidence of meningitis in sub-Saharan Africa

Meningococcal meningitis is a major public health problem in the African Belt. Despite the obvious seasonality of epidemics, the factors driving them are still poorly understood. Here, we provide a first attempt to predict epidemics at the spatio-temporal scale required for in-year response, using a purely empirical approach. District-level weekly incidence rates for Niger (1986-2007) were discretized into latent, alert and epidemic states according to pre-specified epidemiological thresholds. We modelled the probabilities of transition between states, accounting for seasonality and spatio-temporal dependence. One-week-ahead predictions for entering the epidemic state were generated with specificity and negative predictive value >99%, sensitivity and positive predictive value >72%. On the annual scale, we predict the first entry of a district into the epidemic state with sensitivity 65∙0%, positive predictive value 49∙0%, and an average time gained of 4∙6 weeks. These results could inform decisions on preparatory actions.

A hidden Markov model to assess drug-induced sleep fragmentation in the telemetered rat

Drug-induced sleep fragmentation can cause sleep disturbances either via their intended pharmacological action or as a side effect. Examples of disturbances include excessive daytime sleepiness, insomnia and nightmares. Developing drugs without these side effects requires insight into the mechanisms leading to sleep disturbance. The characterization of the circadian sleep pattern by EEG following drug exposure has improved our understanding of these mechanisms and their translatability across species. The EEG shows frequent transitions between specific sleep states leading to multiple correlated sojourns in these states. We have developed a Markov model to consider the high correlation in the data and quantitatively compared sleep disturbance in telemetered rats induced by methylphenidate, which is known to disturb sleep, and of a new chemical entity (NCE). It was assumed that these drugs could either accelerate or decelerate the transitions between the sleep states. The difference in sleep disturbance of methylphenidate and the NCE were quantitated and different mechanisms of action on rebound sleep were identified. The estimated effect showed that both compounds induce sleep fragmentation with methylphenidate being fivefold more potent compared to the NCE.

Multinomial logistic functions in markov chain models of sleep architecture: internal and external validation and covariate analysis

Mixed-effect Markov chain models have been recently proposed to characterize the time course of transition probabilities between sleep stages in insomniac patients. The most recent one, based on multinomial logistic functions, was used as a base to develop a final model combining the strengths of the existing ones. This final model was validated on placebo data applying also new diagnostic methods and then used for the inclusion of potential age, gender, and BMI effects. Internal validation was performed through simplified posterior predictive check (sPPC), visual predictive check (VPC) for categorical data, and new visual methods based on stochastic simulation and estimation and called visual estimation check (VEC). External validation mainly relied on the evaluation of the objective function value and sPPC. Covariate effects were identified through stepwise covariate modeling within NONMEM VI. New model features were introduced in the model, providing significant sPPC improvements. Outcomes from VPC, VEC, and external validation were generally very good. Age, gender, and BMI were found to be statistically significant covariates, but their inclusion did not improve substantially the model's predictive performance. In summary, an improved model for sleep internal architecture has been developed and suitably validated in insomniac patients treated with placebo. Thereafter, covariate effects have been included into the final model.

Modeling sleep data for a new drug in development using markov mixed-effects models

PURPOSE

To characterize the time-course of sleep in insomnia patients as well as placebo and concentration-effect relationships of two hypnotic compounds, PD 0200390 and zolpidem, using an accelerated model-building strategy based on mixed-effects Markov models.

METHODS

Data were obtained in a phase II study with the drugs. Sleep stages were recorded during eight hours of sleep for two nights per treatment for the five treatments. First-order Markov models were developed for one transition at a time in a sequential manner; first a baseline model, followed by placebo and lastly the drug models. To accelerate the process, predefined models were selected based on a priori knowledge of sleep, including inter-subject and inter-occasion variability.

RESULTS

Baseline sleep was described using piece-wise linear models, depending on time of night and duration of sleep stage. Placebo affected light sleep stages; drugs also affected slow-wave sleep. Administering PD 0200390 30 min earlier than standard dosing was shown through simulations to reduce latency to persistent sleep by 40%.

CONCLUSION

The proposed accelerated model-building strategy resulted in a model well describing sleep patterns of insomnia patients with and without treatments.