Recognizing duration effects in multistate population models

The risk of many demographic events varies by both current state and duration in that state. However, the use of such semi-Markov models has been substantially constrained by data limitations. Here, a new specification of the semi-Markov transition probability matrix in terms of the underlying rates is provided, and a general procedure is developed to estimate semi-Markov probabilities and rates from adjacent population data.Multistate models recognizing marriage and divorce by duration in state are constructed for United States Females, 1995. The results show that recognizing duration in the married and divorced states adds significantly to the model’s analytical value. Extending the constant-α method to semi-Markov models, 2000–2005 U.S. population data and 1995 cross-product ratios are employed to estimate 2000–2005 duration-dependent transfer probabilities and rates.The present analyses provide new relationships between probabilities and rates in semi-Markov models. Extending the constant cross-product ratio estimation approach opens new sources of data and expands the range of data susceptible to state-duration analyses.

P020 Reduced duration and continuity of N3 sleep is associated with excessive daytime sleepiness in suspected obstructive sleep apnea patients

Introduction Excessive daytime sleepiness (EDS) is a common but not universal-accompanying symptom of obstructive sleep apnea (OSA). The mechanisms explaining the presence of EDS in OSA subjects are not fully understood. We hypothesised that characteristic differences in sleep architecture can be quantified with more comprehensive descriptors of sleep continuity in those with and without severe-EDS according to the Multiple Sleep Latency Test (MSLT). Methods 2111 participants with suspected OSA and complaints of daytime sleepiness underwent in-lab diagnostic polysomnography (PSG) and next-day MSLT. Sleep continuity was quantified by calculating the cumulative-frequency relationship of continuous sleep-state duration against proportion of sleep time; and continuous sleep-state duration against absolute sleep time. Results Study contained 368 severe-EDS participants (MSLT≤5min) and 385 non-EDS participants (MSLT>15min). Severe-EDS participants had less Wake After Sleep Onset (48.1±37.7 vs. 68.1±44.2-minutes, p<0.05 [mean±SD]), and greater Total Sleep Time (366.5±50.3 vs. 336.2±58.2-minutes, p<0.05). While total NREM sleep time was similar between groups, severe-EDS participants had less N3 sleep (67.7±38.0 vs. 78.6±32.0-minutes, p<0.05) and more N2 sleep (230.7±59.3 vs. 178.4±45.9-minutes, p<0.05). Moreover, severe-EDS participants had both less cumulative N3 sleep (36.9±2.9 vs. 60.0±3.3-minutes, p<0.05) and a lower proportion of N3 sleep (66.8±5.3% vs. 77.2±4.2%, p<0.05) occurring in periods ≥10mins duration. Discussion Whilst OSA participants with severe EDS have similar NREM sleep time to non-EDS participants; they have less N3 sleep, and N3 sleep periods are less consolidated. These preliminary results suggest that individuals with OSA which disturbs both the quantity and consolidation of N3 sleep are at greater risk of severe EDS.

A Stochastic Binary Model for Regulation of Gene Expression to Investigate Treatment Effects Targeting RKIP

In this manuscript we use an exactly solvable stochastic binary model for regulation of gene expression to analyse the dynamics of response to a treatment aiming to modulate the number of transcripts of RKIP gene. We demonstrate the usefulness of our method simulating three treatment scenarios aiming to reestablish RKIP gene expression dynamics towards pre-cancerous state: i. to increase the promoter’s ON state duration; ii. to increase the mRNAs’ synthesis rate; iii. to increase both rates. We show that the pre-treatment kinetic rates of ON and OFF promoter switching speeds and mRNA synthesis and degradation will affect the heterogeneity and time for treatment response. Hence, we present a strategy for reducing drug dosage by simultaneously targeting multiple kinetic rates. That enables a reduction of treatment response time and heterogeneity which in principle diminishes the chances of emergence of resistance to treatment. This approach may be useful for inferring kinetic constants related to expression of antimetastatic genes or oncogenes and on the design of multi-drug therapeutic strategies targeting master regulatory genes.

On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

A Regularized Vector Autoregressive Hidden Semi-Markov model, with Application to Multivariate Financial Data

Hidden Markov model (HMM) has been a popular choice for financial time series modeling due to its advantage in capturing dynamic regimes. However, HMM's implicit assumption that the state duration follows a geometric distribution is too strong to hold in practice. In this work, we propose a regularized vector autoregressive hidden semi-Markov model to analyze multivariate financial time series. One challenge in such a model setting is that the number of parameters is too large to be reliably estimated unless the time series is extremely long. To address this issue, an augmented EM algorithm is developed for parameter estimation by using regularized estimators for the state-dependent covariance matrices and autoregression matrices in the M-step. The performance of the proposed model is evaluated in a simulation experiment, and demonstrated with the New York Stock Exchange financial portfolio data.

Monitoring of bearing fatigue life based on hidden Markov model

With the increase in the intelligence of the production process and the increase in reliability requirements, the monitoring of the bearing life status after the event has been unable to meet the needs of industrial production. Performance degradation assessment and life monitoring have attracted more attention as intelligent methods based on condition maintenance. Hidden Markov model is a statistical probability model based on time series, which is very suitable for modeling the performance degradation process of equipment. Therefore, this paper proposes a life monitoring algorithm based on hidden Markov model. First, the continuous wavelet transform is introduced to obtain the optimal value of the shape factor or the stretch factor. Secondly, a hidden Markov model of multi-channel information fusion is proposed. The algorithm significantly improves the effectiveness and robustness of life monitoring. The hidden Markov model explicitly expresses the state duration distribution, making the model more suitable for life monitoring.