Peter H. Millard

A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department.

The flow of patients through geriatric hospitals has been previously described in terms of acute (short‐stay), rehabilitation (medium‐stay), and long‐stay states where the bed occupancy at a census point is modelled by a mixed exponential model using BOMPS (Bed Occupancy Modelling and Planning System). In this a patient is initially admitted to acute care. The majority of the patients are discharged within a few days into their own homes or through death. The rest are converted into medium‐stay patients where they could stay for a few months and thereafter either leave the system or move on to a long‐stay compartment where they could stay until they die. The model forecasts the average length of stay as well as the average number of patients in each state. The average length of stay in the acute compartment is artificially high if some would‐be long‐term patients are kept waiting in the short‐stay compartment until beds become available in long‐stay (residential and nursing homes). In this paper we consider the problem as a queueing system to assess the effect of blockage on the flow of patients in geriatric departments. What‐if analysis is used to allow a greater understanding of bed requirements and effective utilisation of resources.

A queueing model for bed-occupancy management and planning of hospitals

The aim of this paper is, on the one hand, to describe the movement of patients through a hospital department by using classical queueing theory and, on the other hand, to present a way of optimising the use of hospital resources in order to improve hospital care. A queueing model is used to determine the main characteristics of the access of patients to hospital, such as mean bed occupancy and the probability that a demand for hospital care is lost because all beds are occupied. Moreover, we present a technique for optimising the number of beds in order to maintain an acceptable delay probability at a sufficiently low level and, finally, a way of optimising the average cost per day by balancing costs of empty beds against costs of delayed patients.

Using a queueing model to help plan bed allocation in a department of geriatric medicine.

By integrating queuing theory and compartmental models of flow we demonstrate how changing admission rates, length of stay and bed allocation influence bed occupancy, emptiness and rejection in departments of geriatric medicine. By extending the model to include waiting beds, we show how the provision of extra, emergency use, unstaffed, back up beds could improve performance while controlling costs. The model is applicable to all lengths of stay, admission rates and bed allocations. The results show why 10–15% bed emptiness is necessary to maintain service efficiency and demonstrate how unstaffed beds can serve to provide a more responsive and cost effective service. Further work is needed to test the validity and applicability of the model.

Patterns of length of stay after admission in geriatric medicirie: an event history approach

Previous work has indicated that a two-term mixed exponential distribution gives a good fit to data on lengths of stay of patients in departments of geriatric medicine. A database on the lengths of stay of patients entering a department, and their subsequent destinations, over a 16-year period, is used to examine the pattern of length of stay in ward of admission until death, discharge or transfer. The two-term mixed exponential distribution is fitted to these data using death/discharge and transfer as the two components of the mixture in order to assess to what extent the previous success of this distribution for census data may be explained by our current longitudinal data and choice of components. The model is then extended to the more sophisticated mixed exponential and log-normal distribution which better enables us to capture the exact shape of the distribution.

Stochastic models of geriatric patient bed occupancy behaviour

This paper considers a census approach to the modelling of the time that geriatric patients spend in hospital and subsequently in the community by using a stochastic compartmental Markov model. A selection process is developed using maximum likelihood estimation to fit the model to daily census data on the duration spent in the hospital or the community. Census data are used as they are easy to collect and therefore maximize the usability of the model. The model is fitted to an extensive 16-year data-set and shown to provide realistic estimates of movements of patients by using only a single days census result.

Balancing the NHS balanced scorecard

In the UK, the split between opposition and supporters views of the National Health Service (NHS) performance ratings system is growing. Objective argument and consensus would be facilitated if a methodology was developed which showed the cause and effect relationships between the components of the performance rating system. The NHS hospital trust performance ratings data used in 2002 and 2003 were downloaded from the Department of Health performance rating website. Structural equation modelling was used to construct a causal-loop diagram showing the cause and effect relationships between the 16 common performance indicators in the two years. Scenario testing suggests that indicators of delayed transfer of care and of data quality are compromised if emergency readmissions performance is improved.

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.

Where to treat the older patient? Can Markov models help us better understand the relationship between hospital and community care?

We have previously used Markov models to describe movements of patients between hospital states; these may be actual or virtual and described by a phase-type distribution. Here we extend this approach to a Markov reward model for a healthcare system with Poisson admissions and an absorbing state, typically death. The distribution of costs is evaluated for any time and expressions derived for the mean and variances of costs. The average cost at any time is then determined for two scenarios: the Therapeutic and Prosthetic models, respectively. This example is used to illustrate the idea that keeping acute patients longer in hospital to ensure fitness for discharge, may reduce costs by decreasing the number of patients that become long-stay. In addition we develop a Markov Reward Model for a healthcare system including states, where the patient is in hospital, and states, where the patient is in the community. In each case, the length of stay is described by a phase-type distribution, thus enabling the representation of durations and costs in each phase within a Markov framework. The model can be used to determine costs for the entire system thus facilitating a systems approach to the planning of healthcare and a holistic approach to costing. Such models help us to assess the complex relationship between hospital and community care.

A three compartment model of the patient flows in a geriatric department: a decision support approach

As users of long term geriatric services occupy the beds for prolonged periods of time it is important that decision makers understand how clinical and social decisions interact to influence long term care costs. A flow modelling approach enables us to estimate current inpatient activity and to test different care options, thereby optimising decision making.In previous work we developed a two compartment model of patient flows within a geriatric hospital, where patients are initially admitted to an acute or rehabilitative state from which they either are discharged or die or are converted to a long‐stay state. Long‐stay patients are discharged or die at a slower rate. This initial research discussed the use of a compartmental model to describe flows through the hospital system.We now discuss a three compartment model where the compartments may be described as consisting of acute care, rehabilitation and long‐stay care. A Markov model is then used to count and cost the movements of geriatric patients within a hospital system. Such an approach enables health service managers and clinicians to assess performance and evaluate the effect of possible changes to the system. By attaching costs to various parts of the system we may facilitate the evaluation and comparison of different strategies and scenarios. Using the model, we show that a geriatric medical service that improved the acute management of in‐patients became more cost‐efficient. Hospital planners may thus identify cost‐effective options.

Developing a Bayesian belief network for the management of geriatric hospital care

Resource management is an essential feature of hospital management. This is especially true for geriatric services, as older people often have complex medical and social needs. Hospital management should benefit from an explanatory model that provides predictions of duration of stay and destination on discharge. We describe how a Bayesian belief network models the behaviour of geriatric patients using predictive variables: personal details, admission reasons and dependency levels. This approach is illustrated using data on 4722 patients admitted to geriatric medicine at St. Georges Hospital, London; distributions of the patient outcome given typical values of the predictive variables are provided.