Adele H. Marshall

Conditional phase-type distributions for modelling patient length of stay in hospital

The proportion of elderly in the population is continuing to increase, placing additional demands on highly competitive medical budgets. The management of the care of the elderly within hospitals can be assisted by the accurate modelling of the length of stay of patients in hospital. This paper uses conditional phase-type distributions for modelling the length of stay of a group of elderly patients in hospital. The model incorporates the use of Bayesian belief networks with Coxian phase-type distributions, a special type of Markov model that describes the duration of stay in hospital as a process consisting of a sequence of latent phases. The incorporation of the Bayesian belief network in the model permits the inclusion of additional patient information which may provide a better understanding of the system, in particular the incorporation of any potential causal information that may exist in the data.

Modelling Patient Duration of Stay to Facilitate Resource Management of Geriatric Hospitals

A fundamental aspect of health care management is the effective allocation of resources. This is of particular importance in geriatric hospitals where elderly patients tend to have more complex needs. Hospital managers would benefit immensely if they had advance knowledge of patient duration of stay in hospital. Managers could assess the costs of patient care and make allowances for these in their budget. In this paper, we tackle this important problem via a model which predicts the duration of stay distribution of patients in hospital. The approach uses phase-type distributions conditioned on a Bayesian belief network.

The Northern Ireland Public Access Defibrillation (NIPAD) study: effectiveness in urban and rural populations

Objective: To assess the impact of mobile automated external defibrillators (AEDs) on out-of-hospital cardiac arrests (OHCAs) in urban and rural populations. Design: Prospective before and after intervention, population study. Setting: Urban and rural areas of 160 000 each. Patients, interventions and main outcome measures: In 2004–6 the demographics of OHCAs were assessed. In 2005–6 AEDs were deployed (29 urban, 53 rural): 335 urban first responders (FRs) and 493 rural FRs were trained in AED use and dispatched to OHCAs. Call-to-response interval (CRI), resuscitation and survival-to-discharge rates for OHCA were compared. Results: In 2004 there were 163 urban OHCAs and the emergency medical services (EMS) attended 158 (ventricular fibrillation (VF) 27/158 (17.1%)). In 2005–6 there were 226 OHCAs, EMS attended 216 (VF 30/216 (13.9%)). In 2005–6 FRs were paged to 128 OHCAs (56.6%), FRs attended 88/128 (68.8%): 18/128 (14.1%) reached before the EMS. The best combined FR/EMS mean (SD) CRI in 2005–6 (5 min 56 s (4)) was better than the EMS alone in 2004 (7 min (3); p = 0.002). Survival rate was 5.1% in 2004, 1.4% in 2005–6 (p = NS). In 2004 there were 131 rural OHCAs, EMS attended 121 (VF 19/121 (15.7%)). In 2005–6 there were 122 OHCAs, EMS attended 114 (VF 19/114 (16.7%)). In 2005–6 FRs were paged to 49 OHCAs, FRs attended 42/49 (85.7%): 23/49 (46.9%) reached before the EMS. The best combined FR/EMS mean (SD) CRI in 2005–6 (9 min 22 s (6)) was better than the EMS alone in 2004 (11 min 2 s (6); p = 0.018). Survival rate was 2.5% in 2004, 3.5% in 2005–6 (p = NS). Conclusions: Despite improvement in CRI there was no impact on survival (witnessed arrest 32.8%, VF 15.6%). Trial registration number: ISRCTN07286796.

The obstacles to maximising the impact of public access defibrillation: an assessment of the dispatch mechanism for out-of-hospital cardiac arrest

Objectives: To determine the diagnostic accuracy of advanced medical priority dispatch system (AMPDS) software used to dispatch public access defibrillation first responders to out-of-hospital cardiac arrests (OHCA). Design: All true OHCA events in North and West Belfast in 2004 were prospectively collated. This was achieved by a comprehensive search of all manually completed Patient Report Forms compiled by paramedics, together with autopsy reports, death certificates and medical records. The dispatch coding of all emergency calls by AMPDS software was also obtained for the same time period and region, and a comparison was made between these two datasets. Setting: A single urban ambulance control centre in Northern Ireland. Population: All 238 individuals with a presumed or actual OHCA in the North and West Belfast Health and Social Services Trust population of 138 591 (2001 Census), as defined by the Utstein Criteria. Main outcome measures: The accurate dispatch of an emergency ambulance to a true OHCA. Results: The sensitivity of the dispatch mechanism for detecting OHCA was 68.9% (115/167, 95% confidence interval (CI) 61.3% to 75.8%). However, the sensitivity for arrests with ventricular fibrillation (VF) was 44.4% (12/27) with sensitivity for witnessed VF of 47.1% (8/17). The positive predictive value was 63.5% (115/181, 95% CI 56.1% to 70.6%). Conclusions: The sensitivity of this dispatch process for cardiac arrest is moderate and will constrain the effectiveness of Public Access Defibrillation (PAD) schemes which utilise it. Trial registration: controlled-trials.com ISRCTN 07286796.

Modelling the flow of congestive heart failure patients through a hospital system

The number of hospital admissions in England due to heart failure is projected to increase by over 50% during the next 25 years. This will incur greater pressures on hospital managers to allocate resources in an effective manner. A reliable indicator for measuring the quantity of resources consumed by hospital patients is their length of stay (LOS) in care. This paper proposes modelling the length of time heart failure patients spend in hospital using a special type of Markov model, where the flow of patients through hospital can be thought of as consisting of three stages of care—short-, medium- and longer-term care. If it is assumed that new admissions into the ward are replacements for discharges, such a model may be used to investigate the case-mix of patients in hospital and the expected patient turnover during some specified period of time. An example is illustrated by considering hospital admissions to a Belfast hospital in Northern Ireland, between 2000 and 2004.

Simulating Coxian phase‐type distributions for patient survival

Coxian phase-type distributions are a special type of Markov model that can be used to represent survival times in terms of phases through which an individual may progress until they eventually leave the system completely. Previous research has considered the Coxian phase-type distribution to be ideal in representing patient survival in hospital. However, problems exist in fitting the distributions. This paper investigates the problems that arise with the fitting process by simulating various Coxian phase-type models for the representation of patient survival and examining the estimated parameter values and eigenvalues obtained. The results indicate that numerical methods previously used for fitting the model parameters do not always converge. An alternative technique is therefore considered. All methods are influenced by the choice of initial parameter values. The investigation uses a data set of 1439 elderly patients and models their survival time, the length of time they spend in a UK hospital.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type models (DC-Ph) consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

Detection of Voigt Spectral Line Profiles of Hydrogen Radio Recombination Lines toward Sagittarius B2(N)

We report the detection of Voigt spectral line profiles of radio recombination lines (RRLs) toward Sagittarius B2(N) with the 100 m Green Bank Telescope (GBT). At radio wavelengths, astronomical spectra are highly populated with RRLs, which serve as ideal probes of the physical conditions in molecular cloud complexes. An analysis of the Hnα lines presented herein shows that RRLs of higher principal quantum number ( n> 90) are generally divergent from their expected Gaussian profiles and, moreover, arewell described by their respective Voigt profiles. This is in agreement with the theory that spectral lines experience pressure broadening as a result of electron collisions at lower radio frequencies. Given the inherent technical difficulties regarding the detection and profiling of true RRL wing spans and shapes, it is crucial that the observing instrumentation produce flat baselines as well as high-sensitivity, high-resolution data. The GBT has demonstrated its capabilities regarding all of these aspects, and we believe that future observations of RRL emissionvia the GBTwill be crucial toward advancing our knowledge of the larger-scale extended structures of ionized gas in the interstellar medium (ISM).

Computational learning of the conditional phase-type (C-Ph) distribution

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a data set as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output. The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

A Monte Carlo Simulation Model to Assess Volunteer Response Times in a Public Access Defibrillation Scheme in Northern Ireland

This paper describes the development of a model to assess the distribution of response times for mobile volunteers of a public access defibrillation (PAD) scheme in Northern Ireland. Using parameters based on a trial period, the model predicts that a PAD volunteer would arrive before the emergency medical services (EMS) to 18.8% of events to which they are paged in a given year period. This is in agreement with what has actually been observed during the trial period (where volunteers have actually reached 15% of events before the EMS), and thus assisting validation of the model. Results from this model illustrate how ongoing volunteer commitment is key to the success of the scheme