Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits

Marshall, A.H.; Zenga, M

doi:10.1007/s11009-010-9174-y

Cited by 21 publications

(27 citation statements)

References 20 publications

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“…This will also prevent an over-fitted model as reported in earlier literature (Marshall et al 2012). In each stage we calculated the probability of leaving the hospital ward due to death, transfer or returning home.…”

Section: The Length Of Staymentioning

confidence: 90%

The coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

Zenga

Marshall

Crippa

et al. 2015

Communications in Statistics - Theory and Methods

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This paper presents multi-level models that utilise the Coxian phase-type distribution in order to be able to include a survival component in the model. The approach is demonstrated by modelling patient length of stay and in-hospital mortality in geriatric wards in Italy. The multi-level model is used to provide a means of controlling for the existence of possible intra-ward correlations, which may make patients within a hospital more alike in terms of experienced outcome than patients coming from different hospitals, everything else being equal. Within this multi-level model we introduce the use of the Coxian phasetype distribution to create a covariate that represents patient length of stay or stage (of hospital care). Results demonstrate that the use of the multi-level model for representing the in-patient mortality is successful and further enhanced by the inclusion of the Coxian phase-type distribution variable (stage covariate).

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Section: The Length Of Staymentioning

confidence: 90%

The coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

Zenga

Marshall

Crippa

et al. 2015

Communications in Statistics - Theory and Methods

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“…These methods have been used extensively within the literature for distribution fitting (Marshall & Zenga, 2010).…”

Section: Parameter Estimation Methodsmentioning

confidence: 99%

Modelling activities at a neurological rehabilitation unit

Griffiths

Williams

Wood

2013

European Journal of Operational Research

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DeclarationThis work has not previously been accepted in substance for any degree and is not concurrently being submitted in candidature for any degree. Signed:Date: Statement 1This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged by giving explicit references. A bibliography is appended. Signed:Date: Statement 2I hereby give consent for my thesis, if accepted, to be available for photocopying and interlibrary loan, and for the title and summary to be made available to outside organisations. SummaryA queuing model is developed for the neurological rehabilitation unit at Rookwood Hospital in Cardiff. Arrivals at the queuing system are represented by patient referrals and service is represented by patient length of stay (typically five months). Since there are often delays to discharge, length of stay is partitioned into two parts: admission until date ready for discharge (modelled by Coxian phase-type distribution) and date ready for discharge until ultimate discharge (modelled by exponential distribution). The attributes of patients (such as age, gender, diagnosis etc) are taken into account since they affect these distributions. A computer program has been developed to solve this multi-server (21 bed) queuing system to produce steady-state probabilities and various performance measures.However, early on in the project it became apparent that the intensity of treatment received by patients has an effect on the time, from admission, until they are ready for discharge. That is, the service rates of the Coxian distribution are dependent on the amount of therapy received over time. This directly relates to the amount of treatment allocated in the weekly timetables. For the physiotherapy department, these take about eight hours to produce each week by hand. In order to ask the valuable what-if questions that relate to treatment intensity, it is therefore necessary to produce an automated scheduling program that replicates the manual assignment of therapy. The quality of timetables produced using this program was, in fact, considerably better than its alternative and so replaced the by-hand approach. Other benefits are more clinical time (since less employee input is required) and a convenient output of data and performance measures that are required for audit purposes.Once the model is constructed a number of relevant hypothetical scenarios are considered.Such as, what if delays to discharge are reduced by 50%? Also, through the scheduling program, the effect of changes to the composition of staff or therapy sessions can be evaluated, for example, what if the number of therapists is increased by one third? The effects of such measures are analysed by studying performance measures (such as throughput and occupancy) and the associated costs.

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“…We investigate these aspects by fitting latent CTMCs to discretely and fully observed processes simulated from known distributions. Others have investigated the use of phase-type models to approximate generic distributions [17,21,22], but to our knowledge, no one has examined their performance with discretely observed data or investigated confidence interval coverage.…”

Section: Introductionmentioning

confidence: 99%

Fitting and interpreting continuous‐time latent Markov models for panel data

Lange

Minin

2013

Statistics in Medicine

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Multistate models are used to characterize disease processes within an individual. Clinical studies often observe the disease status of individuals at discrete time points, making exact times of transitions between disease states unknown. Such panel data pose considerable modeling challenges. Assuming the disease process progresses according a standard continuous-time Markov chain (CTMC) yields tractable likelihoods, but the assumption of exponential sojourn time distributions is typically unrealistic. More flexible semi-Markov models permit generic sojourn distributions yet yield intractable likelihoods for panel data in the presence of reversible transitions. One attractive alternative is to assume that the disease process is characterized by an underlying latent CTMC, with multiple latent states mapping to each disease state. These models retain analytic tractability due to the CTMC framework but allow for flexible, duration-dependent disease state sojourn distributions. We have developed a robust and efficient expectation-maximization (EM) algorithm in this context. Our complete data state space consists of the observed data and the underlying latent trajectory, yielding computationally efficient expectation and maximization steps. Our algorithm outperforms alternative methods measured in terms of time to convergence and robustness. We also examine the frequentist performance of latent CTMC point and interval estimates of disease process functionals based on simulated data. The performance of estimates depends on time, functional, and data-generating scenario. Finally, we illustrate the interpretive power of latent CTMC models for describing disease processes on a data-set of lung transplant patients. We hope our work will encourage wider use of these models in the biomedical setting.

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Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits

Cited by 21 publications

References 20 publications

The coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

The coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

Modelling activities at a neurological rehabilitation unit

Fitting and interpreting continuous‐time latent Markov models for panel data

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