Markov Chain Modelling for Geriatric Patient Care

2005 ◽  
Vol 44 (03) ◽  
pp. 369-373 ◽  
Author(s):  
M. J. Faddy ◽  
S. I. McClean
Keyword(s):  
Markov Chain ◽  
Maximum Likelihood ◽  
Patient Care ◽  
Geriatric Patient ◽  
Geriatric Patients ◽  
Community Based ◽  
Ordered Phases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markov Chain Modelling

Summary Objectives: To show that Markov chain modelling can be applied to data on geriatric patients and use these models to assess the effects of covariates. Methods: Phase-type distributions were fitted by maximum likelihood to data on times spent by the patients in hospital and in community-based care. Data on the different events that ended the patients’ periods of care were used to estimate the dependence of the probabilities of these events on the phase from which the time in care ended. The age of the patients at admission to care and the year of admission were also included as covariates. Results: Differential effects of these covariates were shown on the various parameters of the fitted model, and interpretations of these effects made. Conclusions: Models based on phase-type distributions were appropriate for describing times spent in care, as the ordered phases had an interpretable structure corresponding to increasing amounts of care being given.

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (3) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

Professional Practice and Patient Care: Multidisciplinary Teamwork in Geriatric Wards

1982 ◽  
Vol 2 (1) ◽  
pp. 57-75 ◽  
Author(s):  
Helen Evers
Keyword(s):  
Health Care ◽  
Patient Care ◽  
Professional Practice ◽  
Health Care Professionals ◽  
Geriatric Patient ◽  
Geriatric Patients ◽  
The Elderly ◽  
Policy And Practice ◽  
Professional Literature ◽  
Multidisciplinary Teamwork

ABSTRACTThis paper aims to examine aspects of the nature of multidisciplinary teamwork in geriatric care. First, some of the medical profession's current views of teamwork in geriatrics will be summarized. Second, case studies from a research project on care of geriatric patients in hospital will be used to illustrate some of the strengths and limitations of the adoption of a teamwork approach by health care professionals. Evidence from research suggests that under only a few circumstances does care of the geriatric patient match the images of teamwork as portrayed in the professional literature. This finding in part reflects piecemeal developments in interprofessional responsibilities and relationships in policy and practice of care of the elderly.

scholarly journals A Kronecker Algebra Formulation for Markov Activity Networks with Phase-Type Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1404
Author(s):  
Alessio Angius ◽  
András Horváth ◽  
Marcello Urgo
Keyword(s):  
Markov Chain ◽  
Markov Models ◽  
Risk Measures ◽  
Stochastic Scheduling ◽  
Efficient Computation ◽  
Objective Functions ◽  
Kronecker Algebra ◽  
Activity Networks ◽  
Phase Type ◽  
Phase Type Distributions

The application of theoretical scheduling approaches to the real world quite often crashes into the need to cope with uncertain events and incomplete information. Stochastic scheduling approaches exploiting Markov models have been proposed for this class of problems with the limitation to exponential durations. Phase-type approximations provide a tool to overcome this limitation. This paper proposes a general approach for using phase-type distributions to model the execution of a network of activities with generally distributed durations through a Markov chain. An analytical representation of the infinitesimal generator of the Markov chain in terms of Kronecker algebra is proposed, providing a general formulation for this class of problems and supporting more efficient computation methods. This entails the capability to address stochastic scheduling in terms of the estimation of the distribution of common objective functions (i.e., makespan, lateness), enabling the use of risk measures to address robustness.

scholarly journals Using a multi-state model to enhance understanding of geriatric patient care

2007 ◽  
Vol 31 (1) ◽  
pp. 91 ◽  
Author(s):  
Malcolm J Faddy ◽  
Sally I McClean
Keyword(s):  
Patient Care ◽  
Statistical Models ◽  
Geriatric Patient ◽  
Community Care ◽  
Routine Data ◽  
Male And Female ◽  
Differential Effects ◽  
Male Patients ◽  
Analyse Data ◽  
Markov Chain Modelling

Objectives: To use multi-state Markov chain modelling to analyse data on geriatric patient care, and to make comparisons between male and female patients. Methods: Estimation, from observed data, of covariate (age of patient and date of admission to hospital or community care) dependent parameters of statistical models for time in care and subsequent events. Results: Differential effects of these covariates shown on the parameters of the models for female and male patients, where these parameters can be interpreted as affecting different features of the distributions of time in care. Conclusions: Multi-state modelling is an appropriate means of analysing data on geriatric patient care and can reveal underlying patterns of differential effects, some of which may not be apparent from more routine data processing.

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (03) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

scholarly journals Integrating Genomic Screening into Primary Care: Provider Experiences Caring for Latino Patients at a Community-Based Health Center

2021 ◽  
Vol 12 ◽  
pp. 215013272110002
Author(s):  
Tarika Srinivasan ◽  
Erica J. Sutton ◽  
Annika T. Beck ◽  
Idali Cuellar ◽  
Valentina Hernandez ◽  
...  
Keyword(s):  
Primary Care ◽  
Health Care ◽  
Patient Care ◽  
Health Center ◽  
Care Provider ◽  
Primary Care Provider ◽  
Genomic Sequencing ◽  
Community Based ◽  
Genomic Screening

Introduction: Minority communities have had limited access to advances in genomic medicine. Mayo Clinic and Mountain Park Health Center, a Federally Qualified Health Center in Phoenix, Arizona, partnered to assess the feasibility of offering genomic screening to Latino patients receiving care at a community-based health center. We examined primary care provider (PCP) experiences reporting genomic screening results and integrating those results into patient care. Methods: We conducted open-ended, semi-structured interviews with PCPs and other members of the health care team charged with supporting patients who received positive genomic screening results. Interviews were recorded, transcribed, and analyzed thematically. Results: Of the 500 patients who pursued genomic screening, 10 received results indicating a genetic variant that warranted clinical management. PCPs felt genomic screening was valuable to patients and their families, and that genomic research should strive to include underrepresented minorities. Providers identified multiple challenges integrating genomic sequencing into patient care, including difficulties maintaining patient contact over time; arranging follow-up medical care; and managing results in an environment with limited genetics expertise. Providers also reflected on the ethics of offering genomic sequencing to patients who may not be able to pursue diagnostic testing or follow-up care due to financial constraints. Conclusions: Our results highlight the potential benefits and challenges of bringing advances in precision medicine to community-based health centers serving under-resourced populations. By proactively considering patient support needs, and identifying financial assistance programs and patient-referral mechanisms to support patients who may need specialized medical care, PCPs and other health care providers can help to ensure that precision medicine lives up to its full potential as a tool for improving patient care.

Phase Type Distributions with Finite Support

2014 ◽  
Vol 30 (4) ◽  
pp. 576-597 ◽  
Author(s):  
V. Ramaswami ◽  
N. C. Viswanath
Keyword(s):  
Finite Support ◽  
Phase Type ◽  
Phase Type Distributions

Analysis of R-out-of-N repairable systems: the case of phase-type distributions

2004 ◽  
Vol 36 (1) ◽  
pp. 116-138 ◽  
Author(s):  
Yonit Barron ◽  
Esther Frostig ◽  
Benny Levikson
Keyword(s):  
Repairable System ◽  
Repairable Systems ◽  
Regenerative Processes ◽  
Numerical Examples ◽  
Independent Components ◽  
Duality Results ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Two Systems ◽  
Repair Facility

An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R-1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

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