Mean Sojourn Times Research Articles

Design of randomized controlled trials to estimate cancer-mortality reductions from multicancer detection screening.

Determining whether screening with multicancer detection (MCD) tests saves lives requires randomized controlled trials (RCTs). To inform RCT design, we estimated cancer-mortality outcomes from hypothetical MCD RCTs. We used the Hu-Zelen model, previously used to plan the NLST, to estimate mortality reductions, sample-size, and power for 9 cancers for different RCT design parameters and MCD test parameters. Our base-case RCT with 5 yearly screens and 100,000 people ages 60-74 in each arm, who also undergo standard-of-care screens, has 87-89% power to detect an 9-10% mortality reduction (NNS = 578-724) over 7-9 years. The majority of prevented deaths were from lung-cancers (base-case (64-66%) and all sensitivity analyses), 8-10% from colorectal-cancer, and 26% from the other 7-cancers, mostly from stomach/ovary/esophagus (due to excellent stage-1 survival) and less from liver/pancreas (poor stage-1 survival) or head/neck-cancer/lymphoma (excellent stage-4 survival). There was limited power for mortality reductions at most individual cancer sites. Base-case findings were sensitive to test sensitivity, stage-shifts, and mean sojourn times in the preclinical state (especially for lung-cancer), but 90% power could be recovered by recruiting a substantially higher risk population. Large-scale MCD RCTs would have 89% power to detect a ∼10% cancer-mortality reduction over a relatively short 7-9 year timeframe from trial entry. The estimated NNS for MCD RCTs compares favorably to mammographic screening. Most prevented cancer-deaths in a well-powered MCD RCT would likely be from lung-cancer. Non-lung/CRC cancer sites could be a meaningful proportion of prevented cancer-deaths but power is insufficient to isolate non-lung-cancer mortality reductions.

Prognostic Factors for Recurrence And Survival of Patients with Breast Cancer Using A Multi-state Model

Background: In many medical studies, patients may experience various events. The analysis in such studies is often administrated using multi-state models. The current study aimed to investigate the effect of risk factors and transition probability on recurrence and death in patients with breast cancer. Materials and Methods: This study was a retrospective cohort study on 814 women with breast cancer admitted to Shahid Ramezanzadeh Radiotherapy Center in Yazd province in Iran between the years 2004 -2012 and were followed until 2016. A multi-state model is applied for data analysis in the R 3.4.1 programming language. Results: Of the 814 patients, 40(5%) experienced recovery after initial treatment and 177(20.7%) experienced the death after initial treatment. For the first year, the transition probabilities from the initial treatment to recovery were estimated at 1.4%, to death was 17% and for recovery to death, it was 29%. The mean sojourn times were estimated as 2.93 and 9.8 years for the treatment and recovery, respectively. Conclusion: Multi-state models predict the transition probabilities in different states of disease, in addition, transition probabilities, mean sojourn time, and hazard ratio in each state can help physicians find suitable care for patients with breast cancer.

Prioritization in the Presence of Self-ordering Opportunities in Omnichannel Services

Motivated by the popularity of mobile-order-and-pay applications, especially in fast-casual food restaurants and coffee shops, we study omnichannel service systems—where customers can employ mobile applications for self-ordering—with respect to sojourn times, throughput, and social welfare. Our models are two-stage queues with two customer classes: Walk-ins and mobiles. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class’s mean sojourn times. We allow customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe partial queue length information. We draw from a wide array of techniques, including steady-state, transient, busy period, hitting-time analyses, and matrix analytic methods. We showcase the significance of prioritization on the system throughput and social welfare. We demonstrate settings where a traditional service system’s (typically beneficial) transformation to an omnichannel reduces throughput. Our analysis highlights the importance of prioritization policy choice for an efficient transition to an omnichannel service system. The throughput-optimal policy choice highly depends on the operational parameters and customer patience levels; implementing a wrong policy can yield a significant loss in throughput and profitability.

Factors Associated With Treatment Pathways in Early Axial Spondyloarthritis: A Multistate Analysis of the 10-Year Follow-Up of the DESIR Cohort.

Current recommendations for the management of patients with axial spondyloarthritis (axSpA) emphasize the need of an individualized strategy in therapeutic decision-making. The study objectives were to describe therapeutic strategies observed in axSpA, and to assess the factors associated with treatment intensification over time. We included patients with axSpA from the French prospective cohort DESIR (Devenir des Spondylarthropathies Indifférenciées Récentes), with a scheduled 10-year follow-up. A multistate model with 4 ordered treatment states (no treatment, nonsteroidal antiinflammatory drugs [NSAIDs], conventional synthetic disease-modifying antirheumatic drugs [csDMARDs], and tumor necrosis factor inhibitors [TNFi]) was defined, with 6 possible transitions. Restricted mean sojourn times in each state were estimated. Then, predictors of those transitions were assessed by multivariable Cox models. A total of 686/708 (96.9%) patients who had > 1 visit were analyzed. At cohort entry, 199 (29%) were untreated, 427 (62.2%) were receiving NSAIDs, 60 (8.7%) csDMARDs, and none were receiving TNFi. Over the follow-up period, patients mostly (46.4% of the time) received NSAIDs, followed by TNFi (24.4% of the time). The presence of sacroiliitis on radiographs, inflammatory bowel disease, and articular index were jointly associated with the transition to NSAIDs. Longer duration in the previous state often decreased the hazard of the transition to csDMARDs or TNFi. Worse disease activity outcomes increased the hazard of most transitions. To our knowledge, this was the first study using a multistate model to easily represent different treatment states, detailing the transitions across them and their associated factors. Different time profiles for the management of patients with axSpA were identified, including in those abstaining from treatment up to a significant proportion of patients treated with csDMARDs.

Stochastic modeling of enhancing energy efficiency for HAP in HAP-LEO systems using Markov regenerative process

The sixth-generation (6G) communication systems heavily rely on space-air-terrestrial networks (SAT), which integrate high-altitude platforms (HAPs) and low Earth orbit (LEO) satellites. LEO satellites play a crucial role in ensuring global coverage and supporting a large number of users, while HAPs are strategically deployed to cover regions with high demand, providing a more reliable communication service to ground users. The principal aim of the proposed model is to explore techniques for energy conservation and efficient energy harvesting within the multi-layered system for HAP. In this energy harvesting scenario, it is assumed that HAPs will store the energy units generated through solar power. Moreover, the presented model incorporates two energy-saving states: standby and sleep states, during which HAPs consume minimal or zero energy. To analyze the described multi-layer system, a stochastic model is formulated using Markov regenerative process (MRGP), with consideration for the mean sojourn times of energy-saving states following a non-exponential distribution. The numerical results vividly demonstrate the significant contribution of energy-saving states in enhancing the energy efficiency of the HAP system. Also, trade-offs have been presented to analyze the impact of energy harvesting and energy saving in the proposed model. These findings are visually presented in graphs, and to validate the proposed model, simulation results have been carried out.

A multistate transition model of changes in loneliness and carer stress among community-dwelling older adults in Aotearoa New Zealand.

To identify changes in loneliness and carer stress between two time points for older people of different ethnicities who had repeated interRAI home care assessments. Participants consisted of community-dwelling older adults across New Zealand who received two interRAI-HC assessments between 5 July 2012 and 31 December 2019. Two multistate models were developed: the first model was not lonely versus lonely, and the second model was no carer stress versus carer stress. The one-year transition probabilities were calculated. Mean sojourn times were calculated for each state except death. Paired t-tests assessed the differences in transition probabilities between the different ethnic groups. The mean age of the cohort was 82.5 years (SD 7.7 years). At first assessment, 14,646 (21%) older people stated they were lonely and 26,789 carers (38%) experienced stress. The most common first transition type was not lonely to not lonely: Māori 42%, Pacific 54%, Asian, 48% and Other 40%. The highest one-year transition probability in the loneliness model was living in aged residential care to death (0.79). The most common first transition type for the carer stress was no carer stress to no carer stress: Māori 35%, Pacific, 46%, Asian, 43% and Other 33%. The highest one-year transition probability in the carer stress model was living in aged residential care to death (0.80). The statuses not lonely and no carer stress had a mean sojourn time of approximately one year, and eight months to one year, respectively. Loneliness can change over time due to circumstances and an individual's perception of loneliness at the time of assessment. Carer stress is enduring and has a low probability of improvement.

Reliability modelling of a parallel-cold standby system with proviso of repair priority

Here, reliability modelling of a parallel cold standby system of four units has been done with the provision of priority to repair. Initially, the system has two operative units in parallel mode (called phase-I units) and the other two units are taken as spare in the cold standby (called phase-II units). The phase-I units (main units) are assumed as more efficient than that of the phase-II units (duplicate units). The units in phase-I and phase-II are non-identical but they are identical within the phases. The units in phase-II work simultaneously at the failure of units of phase-I. The priority to repair the units of phase-II has been given over the repair of the units of the phase-I. However, no priority is given for operation of the units of both phases. The repair activities are handled by a single server who attends the system immediately when required. The failure rate of the units follows negative exponential distribution while the distribution for repair time of the phase-I and phase-II units is assumed as arbitrary. Some significant reliability characteristics such as mean sojourn times (MST), transition probabilities, mean time to system failures (MTSF), availability, expected number of repairs (for both phase-I and phase-II units), busy period of the server, expected number of visits of the server and finally the profit function are obtained in steady state by making use of well-known semi-Markov process (SMP) and regenerative point technique (RPT). The graphical representation of these reliability characteristics has been made for arbitrary values of the rates associated with failure and repair times. The application of the present study can be seen in the power distribution system.

Cervical change times during induction in nulliparas using vaginal or buccal misoprostol

Aim To determine if the time to cervical change and time to active labor were different when misoprostol was administered by a vaginal or buccal route for cervical ripening in nulliparas undergoing labor induction at term. Methods This was a secondary analysis of nulliparous participants in the IMPROVE Study—A comparison of vaginal versus buccal misoprostol for cervical ripening for labor induction at term: a triple-masked randomized controlled trial (NCT 02408315). The parent study was a non-inferiority randomized controlled trial in which patients beginning induction with a modified Bishop score ≤6 received either vaginal or buccal misoprostol and simultaneous placebo via the opposite route. The primary outcome of the parent study was time to delivery. Primary outcomes for this secondary analysis were the time to active labor (at least 6 cm dilated) and time to change in cervical dilation. Kaplan–Meier analysis was used to compare routes for time to active labor and multistate Markov modeling was used to compare sojourn times at each cervical dilation. Results Of the 300 participants enrolled in the parent trial, 124 (41.3%) were nulliparous; 59 (47.6%) nulliparous participants underwent induction with vaginal misoprostol and 65 (52.4%) received buccal dosing. Nulliparas receiving vaginal dosing required fewer doses of misoprostol to reach active labor (median 2 vs 3, p = .003). However, this did not result in shorter time to active labor (median vaginal 23.1 h, 95% CI = [21.6, 27.2 h]; buccal 25.6 h [21.5, 29.3 h], p = .45) or higher rate of vaginal delivery within 24 h; (33.9% vs 35.4%, p = .86). There was also no significant difference in time to active labor after adjusting for covariates (adjusted HR for dose route (buccal vs vaginal) = 0.91 [0.61, 1.36], p = .649). Among people that delivered vaginally, the mean sojourn times, measuring cervical dilation state change, were not significantly different, with mean duration to active labor of 20.5 [17.6, 24.5] h for buccal and 21.8 [17.7, 28.2] h for vaginal dosing (p = .092). Satisfaction and preference for dosing routes were not different between groups. Conclusion Buccal and vaginal dosing of misoprostol for cervical ripening in nulliparas appear to have similar times to active labor and progression of cervical change during ripening.

Probabilistic Approach to Modelling, Identification and Prediction of Environmental Pollution

The probabilistic general model of environmental pollution process based on the semi-Markov one is developed and presented in the paper. The semi-Markov chain model approach is based on using prior information to predict the characteristic of some systems. Now, the semi-Markov process is used for the environmental pollution assessment. The methods and procedures to estimate the environmental pollution process’s basic parameters such as the vector of initial probabilities and the matrix of probabilities of transition between the process’s states as well as the methods and procedures to identify the process conditional sojourn times’ distributions at the particular environmental pollution states and their mean values are proposed and defined. Next, the formulae to predict the main characteristics of the environmental pollution process such as the limit values of transient probabilities and mean total sojourn times in the particular states in the fixed time interval are given. Finally, the application of the presented model and methods for modelling, identification and prediction of the air environmental pollution process generated by sulphur dioxide within the exemplary industrial agglomeration is proposed.

Multistate models for the natural history of cancer progression.

Multistate models can be effectively used to characterise the natural history of cancer. Inference from such models has previously been useful for setting screening policies. We introduce the basic elements of multistate models and the challenges of applying these models to cancer data. Through simulation studies, we examine (1) the impact of assuming time-homogeneous Markov transition intensities when the intensities depend on the time since entry to the current state (i.e., the process is time-inhomogenous semi-Markov) and (2) the effect on precancer risk estimation when observation times depend on an unmodelled intermediate disease state. In the settings we examined, we found that misspecifying a time-inhomogenous semi-Markov process as a time-homogeneous Markov process resulted in biased estimates of the mean sojourn times. When screen-detection of the intermediate disease leads to more frequent future screening assessments, there was minimal bias induced compared to when screen-detection of the intermediate disease leads to less frequent screening. Multistate models are useful for estimating parameters governing the process dynamics in cancer such as transition rates, sojourn time distributions, and absolute and relative risks. As with most statistical models, to avoid incorrect inference, care should be given to use the appropriate specifications and assumptions.

Design and analysis of AGV-based cross-docking operations using analytical models

ABSTRACT Cross-docking is important for logistics because it reduces inventory, lead-times, and shipments. However, dynamic imbalances between supply and demand usually results in some inventory being warehoused in cross-docks. Therefore, flexible automation using robots, such as automated guided vehicles (AGV), can be used to improve performance of cross-docking, a trend in industry. This paper focuses on mathematical modeling of cross-docking operations when packages are moved in AGVs. A model based on Mean Value Analysis (MVA) is developed for determining the number of AGVs and estimating the service rate. This service rate is used as a parameter in a fork/join queuing model to characterize the performance of cross-docks in which outbound trucks get their packages directly from in-bound trucks as well as warehouses by estimating the queue lengths and mean sojourn times. The efficacy of the combined MVA and fork/join analytical models is verified using a discrete-event simulation as a case study, which shows that the models are largely in agreement in a test range with difference of 28% at the lowest throughput tested. Future study could use advances in sensors and Industry 4.0 for estimating parameters in the proposed models and improve performance and sustainability.

Stochastic analysis of two unit system

The paper analyzes the sensitivity of two unit system for system parameters uses Regenerative Point Graphical Technique (RPGT). Taking failure and repair rates constant. A state diagram of the system depicting the transition rates is drawn. Expressions for path probabilities mean sojourn times, mean time to system failure, availability of the system, busy period of the server, expected number of server’s visits are derived using RPGT. Sensitive analysis of the system is done. Tables and graphs are prepared to compare and draw the conclusion.

Determining Risk Factors That Affect Progression in Patients with Nonproliferative Diabetic Retinopathy.

Purpose To determine risk factors that affect nonproliferative diabetic retinopathy (NPDR) progression and establish a predictive model to estimate the probability of and time to progression in NPDR. Patients and Methods. Charts of diabetic patients who received an initial eye exam between 2010 and 2017 at our county hospital were included. Patients with proliferative diabetic retinopathy (PDR), fewer than 2 years of follow-up, or fewer than 3 clinic visits were excluded. Demographics and baseline systemic and ocular characteristics were recorded. Follow-up mean annual HbA1c and blood pressure, best-corrected visual acuity, and the number of antivascular endothelial growth factor treatments were recorded. Stage and date of progression were recorded. A 5-state nonhomogeneous continuous-time Markov chain with a backward elimination model was used to identify risk factors and estimate their effects on progression. Results Two hundred thirty patients were included. Initially, 65 eyes (28.3%) had no retinopathy; 73 (31.7%) mild NPDR; 60 (26.1%) moderate NPDR; and 32 (13.9%) severe NPDR. Patients were followed for a mean of 5.8 years (±2.0 years; range 2.1–9.4 years). 164 (71.3%) eyes progressed during the follow-up. Time-independent risk factors affecting progression rate were age (hazard ratio (HR) = 0.99, P=0.047), duration of diabetes (HR = 1.02, P=0.018), and Hispanic ethnicity (HR = 1.31, P=0.068). Mean sojourn times at mean age, duration of diabetes, and annual HbA1c for a non-Hispanic patient were estimated to be 3.03 (±0.97), 4.63 (±1.21), 6.18 (±1.45), and 4.85 (±1.25) years for no retinopathy, mild NPDR, moderate NPDR, and severe NPDR, respectively. Each 1% increase in HbA1c annually diminished sojourn times by 15%, 10%, 7%, and 10% for no retinopathy, mild NPDR, moderate NPDR, and severe NPDR, respectively. Conclusion HbA1c level is a significant modifiable risk factor in controlling the progression of DR. The proposed model could be used to predict the time and rate of progression based on an individual's risk factors. A prospective multicenter study should be conducted to further validate our model.

Orientational memory of active particles in multistate non-Markovian processes.

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.

ARTICAL ON THE SYSTEM RELIABILITY AND AVAILABILITY ANALYSIS USING RPGT-A GENERAL APPROACH

In the current paper, reliability analysis is examined for consistent state. The Processing/Manufacturing industry is isolated into numerous subsystems. Subsystems are either in parallel/equal or in arrangement. Taking failure and repair rates constant. The subsystem may flop totally through partial disappointment. At the point when any subsystem flops then the framework is in bombed state. A state diagram of system portraying the transition rates is drawn. Articulations for way probabilities mean sojourn times, MTSF, availability, busy period of the server and expected no. of server’s visits are inferred utilizing RPGT. Behaviour analysis of the framework is done. Graphs are prepared to compare and draw the conclusion.

Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.

Understanding wealth transitions among households in urban slums of Nairobi: A multi-state transition modelling approach

Disparities in wealth are socially undesirable and may result in economic inequalities that have destabilizing effects on communities. Globally, more than 700 million people who live in extreme poverty still struggle for the most basic human needs. It is important to note that poverty is not static as households and individuals may transition from one wealth state to another with the passage of time. As such, the examination of poverty levels at one point does not offer a sufficiently complete picture of the dynamics in states of wealth through the dimension of time. In this paper, we study transitions in wealth status of households in two informal settlements (slums) in Nairobi, Kenya from 2006 to 2015. We employed the multistate transition model to assess the influence of potential risk factors on wealth transitions for households in urban slums. The results of the analysis indicate that slum areas, age of the household head, ethnicity, gender, household ownership type, food security, and household size have an effect on at least one transition between wealth states. A considerable proportion of households still remain in the lowest and middle wealth states. Households were found to easily transition forward, from the lowest to the highest wealth state than the reverse transition. The estimated mean sojourn times for the lowest, middle and highest wealth tertile were approximately 10, 7, and 14 months, respectively. These highlights the need for interventions that reduce the time spent in the lowest and middle wealth tertile while ensuring retention of households in the highest tertile. Our findings underscore the need for policy options around the provision of economic opportunities with targeted attention to households in vulnerable settings.

Profit Analysis of a Manufacturing Biscuit Plant

This paper is concerned with profit analysis as far as failure/repair rates of subunits of a biscuit manufacturingplant consisting of a various subunits of varying nature. The system comprise of five different subsystem particular:- tilter system (B), batter container (C), cutter (G), transport (H) and metal detector (A). To make the framework progressively dependable and an extra litter unit of similar nature is additionally taken in parallel configuration with the concerned sub unit. Five processing units are working in arrangement all together B, C, A, G, H, so if any of the units come up short, the system fails.Units ‘A’ and ‘B’ have sub components in series, thus are exposed to major failures when anybody of their sub-part comes up short. Articulations for path probabilities mean sojourn times, mtsf, availability of the system, expected number of server’s visits are determined to utilize RPGT. A fuzzy concept is utilized to decide the disappointment of units and the entire system. Benefit analysis of the system is done. Tables and Graphs are attracted to delineate the effect of failure and repair rates on the system parameters.

Stationary Characteristics of an Unreliable Single-Server Queueing System with Losses and Preventive Maintenance

This paper considers an unreliable restorable single-server queueing system with losses in which server failures may occur during operation. The random variables describing the system have general distributions. For increasing the efficiency of this system, it is proposed to carry out preventive maintenance of the server as soon as the accumulated operating time exceeds an upper permissible threshold. A semi-Markov model of the system’s evolution over time is constructed. The explicit-form expressions for the final probabilities and mean sojourn times of the system in different physical states are derived using the stationary distribution of the embedded Markov chain. The frequency of preventive maintenance of the server is optimized via maximizing the average specific profit and minimizing the average specific costs of the system.

Designing Efficient Omni-Channel Services

Motivated by the popularity of mobile-order-and-pay applications that are especially prevalent in coffee shops, we explore how to design efficient omni-channel service systems — where customers have the option to employ mobile applications for self-ordering — with respect to sojourn times, throughput, and/or social welfare. Our models are two-stage queues with two customer classes: walk-ins require service at both stages, while mobile customers skip the first stage by self-ordering. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class's mean sojourn times. We allow for customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe the queue length of the first stage, and are left to infer that of the second. Our performance evaluations draw from a wide array of techniques, including steady-state, transient, busy period, and hitting-time analyses, together with matrix analytic methods. We showcase the significance of the choice of prioritization policy on the system throughput and social welfare, and we demonstrate the existence of settings where the (typically beneficial) transformation of a traditional service system to an omni-channel one can reduce throughput.