On the use of multi-state multi-census techniques for modelling the survival of elderly people in institutional long-term care

^** Corresponding author. Email: chausst{at}wmin.ac.uk A good estimate of the length of stay (LOS) of elderly peoplein institutional long-term care (ILTC) is essential to bothcare providers (care home owners) and purchasers (local authoritiesin the UK) in order to forecast their resource availabilityand future requirements. Existing methods usually rely on cohortdata, which needs to be collected on a continuous basis forseveral years and are often not available electronically. Inthis paper we develop an approach based on multi-census datato fit a Markov model in continuous-time for the LOS of elderlypeople in ILTC (residential and nursing care). We use 3 yearplacement data provided by London Borough of Merton Social Servicesto compare the estimates of the model parameters obtained usingmulti-census data with those derived from cohort data, henceto validate the multi-census approach in this context. The implicationsof the proposed multi-census approach and its advantages inthe context of long-term care planning are discussed.     

Benchmarking physician practice patterns with DEA: A multi-stage approach for cost containment

Physician practice patterns in a Health Maintenance Organization (HMO) are analyzed using single and multi-stage applications of Data Envelopment Analysis (DEA). Best practice (BP) patterns are identified, which can serve as benchmark targets for inefficient physicians. Results suggest three health policy — resource utilization control strategies:

1. If managed care organizations could motivate primary care physicians to adopt the practice styles of the best practice primary care physicians, substantial clinical resource savings could be achieved, ranging from 12% to over 30% in the HMO that is the focus of this study;
2. some specialists who practice as primary care physicians (PCPs) provide more efficient care than some general practitioner PCPs, modifying the current perception that reducing specialists is the most effective way to achieve low cost practice patterns; and
3. groups of physicians in the HMO exhibit different resource use patterns, which may present opportunities to manage high cost groups as another path to contain costs.

The results suggest specific new paths which may prove effective at reducing health care costs within managed care organizations, the health care providers most likely to dominate the U.S. health system in the future. A multi-stage DEA technique is used to locate specific types of inefficient physicians. Methods to test the clinical viability of using DEA to realize the potential cost savings and extensions of this research are discussed.     

Laps Care—an operational system for staff planning of home care

The health care system in Sweden and many other countries is facing increasing costs. The major reason is the changing age distribution of the population with more elderly people in need of support. At the same time, health care systems are often very labor and staff intensive. In this paper, we focus on a staff planning problem arising in Sweden where people receive home care from the local authorities. The objective is to develop visiting schedules for care providers that incorporate some restrictions and soft objectives. Each visit has a particular task to be performed, for example: cleaning, washing, personal hygiene and/or nursing activities. Each staff member has skills and each client should, if possible, be visited by the same contact person. The operational situation is continuously changing and planning is done each day. We describe the development of a decision support system Laps Care to aid the planners. The system consists of a number of components including information data bases, maps, optimization routines, and report possibilities. We formulate the problem using a set partitioning model and, for a solution method, we make use of a repeated matching algorithm. The system is currently in operation at a number of home care organizations. We report on the practical impact of the system in the health care organization which was involved in the development. The savings are considerably in terms of saved planning time and in the quality of the routes, as well as the measured quality for the clients. Numerical experiments of the system are presented.     

A matheuristic algorithm for stochastic home health care planning

Efficient human resource planning is the cornerstone of designing an effective home health care system. Human resource planning in home health care system consists of decisions on districting/zoning, staff dimensioning, resource assignment, scheduling, and routing. In this study, a two-stage stochastic mixed integer model is proposed that considers these decisions simultaneously. In the planning phase of a home health care system, the main uncertain parameters are travel and service times. Hence, the proposed model takes into account the uncertainty in travel and service times. Districting and staff dimensioning are defined as the first stage decisions, and assignment, scheduling, and routing are considered as the second stage decisions. A novel algorithm is developed for solving the proposed model. The algorithm consists of four phases and relies on a matheuristic-based method that calls on various mixed integer models. In addition, an algorithm based on the progressive hedging and Frank and Wolf algorithms is developed to reduce the computational time of the second phase of the proposed matheuristic algorithm. The efficiency and accuracy of the proposed algorithm are tested through several numerical experiments. The results prove the ability of the algorithm to solve large instances.     

OR and language planning: modelling the interaction between unilingual and bilingual populations

OR methodology is applied to the contemporary concern of modelling language group interaction, with a view to language planning. The change in size of two unilingual language groups, and of a third bilingual population mediating the interaction of these, is modelled using system dynamics. The model is one of highest possible endogeneity, with the minimum of external intervention in modelling runs. The model is applied to the instances of modern Canada excluding Quebec, Quebec, all Canada and Wales, and conclusions drawn regarding the use of the model in determining language planning initiatives.     

Primary care network development: the regulator’s perspective

Our research is motivated by the proliferation of primary care models in Ontario, Canada. Currently, primary care is mainly provided by facilities belonging to six models of care. These models are remunerated by various schemes—a mixture of fee-for-service, capitation and salary. In addition, they provide different levels of care and several are better adjusted than others to treat complex health needs. The proposed mixed integer programming model allows the regulator to test the outcomes of locating different types of primary care facilities on the overall cost, accessibility and appropriateness of provided care. The network design is fitted to the heterogeneity of the population residing in a defined geographical area, directly using an index (deprivation index) that was found to correlate with increased health needs and barriers to care. The model capabilities are illustrated on the geographical area of Kingston, Ontario.     

Geographical simulation modelling for the regional planning of oral and maxillofacial surgery across London

Oral and maxillofacial surgery (OMFS) is a recognized surgical specialty, with its foundations in dentistry. The current configuration of OMFS services across London has evolved over time and reflects historical rather than contemporary patterns of care. The creation of a London Health Region in 1998 provided the opportunity for rational planning of hospital services to serve the resident population of London (7.2 million) and beyond, with recent change focusing on London's five sectors that are represented within this planning model. A detailed geographical simulation model has been developed and has enabled planners to consider a number of OMFS service configurations and evaluate their impact on providers, variations in caseload, travelling distances and times for patients, and thus inform consultation over change. The research confirms that any in-patient service rationalization which concentrates care in one designated hub (main centre) per sector, involves a significant increase in caseload for the designated hub. Average travelling distances and times for in-patient admissions also increase significantly. However, it does suggest that current commissioned provision of day surgery patterns may not be well aligned to the geographical distribution of need for services, resulting in many patients travelling further than necessary for day surgery treatment. These may be overcome by sending patients to their local centre, which may be out with their sector of residence.     

Stochastic Programming Applied to Human Resource Planning

This paper shows how state space models for human resource planning may be extended from linear and goal-programming formulations to cover the case where manpower demands and available resources for future periods are not known with certainty. Under reasonable assumptions, the problem can be treated as a multi-period stochastic program with simple recourse. Normal and Beta probability distributions are fitted to the right hand sides, and the equivalent determinstic programme solved using convex separable programming. An application of this methodology to a military human resource planning problem is described. Solution times for the stochastic model compare favourably with those for a goal-programming model of the same human resource system.     

Robustness in Practice—The Regional Planning of Health Services

Earlier work has criticized the dominant tendencies in operational research contributions to health services planning as characterized by optimization, implausible demands for data, depoliticization, hierarchy and inflexibility. This paper describes an effort which avoids at least some of these pitfalls. The project was to construct a planning system for a regional health council in Ontario, Canada, which would take account of the possible alternative future states of the health-care system's environment and would aim to keep options for future development open. The planning system devised is described in the paper. It is based on robustness analysis, which evaluates alternative initial action sets in terms of the useful flexibility they preserve. Other features include the explicit incorporation of pressures for change generated outside the health-care system, and a satisficing approach to the identification of both initial action sets and alternative future configurations of the health-care system. It was found possible to borrow and radically 're-use' techniques or formulations from the mainstream of O.R. contributions. Thus the 'reference projection' method was used to identify inadequacies in performance which future health-care system configurations must repair. And Delphi analysis, normally a method for generating consensus, was used in conjunction with cluster analysis of responses to generate meaningfully different alternative futures.     

An evaluation of the applicability of system dynamics to patient flow modelling

The objective of this research is to determine whether Systems Dynamics (SD) is a beneficial method for modelling hospital patient flow from a strategic planning perspective. While discrete event simulation has frequently been used as a tool for analysing and improving patient flow in health care settings, the desire to assess and understand patient flow and resource demand from a more strategic, and therefore aggregate, perspective led to the use of SD. To evaluate the suitability of such an approach, a model was developed in collaboration with the General Campus at The Ottawa Hospital with particular attention paid to the delays experienced by patients in the emergency department. The modelling techniques used, model validation and scenarios tested with the model are discussed, accompanied by comments regarding the appropriateness of SD for such a model.     

Matching patient and physician preferences in designing a primary care facility network

This paper introduces an integer programming model for planning primary care facility networks, which accounts for the interests of different stakeholders while maximizing access to health care. Physician allocation to health-care facilities is explicitly modelled, which allows consideration of physician incentives in the planning phase. An illustrative case study in the Turkish primary care system is presented to show the implications of focusing on patient or physician preferences in the planning phase. A discussion of trade-offs between the different stakeholder preferences and some recommendations for modelling choices to match these preferences are provided. In the context of this case, we found that using an access measure that decays with distance, and incorporating nearest allocation constraints improves performance for all stakeholders. We also show that increasing the number of physicians may have adverse affects on access measures when physician preferences are addressed.     

On Microanalytic Simulation and Its Applications in Population Projection

Population projections by various variables are often required by decision makers for a variety of planning problems in both the private and public sectors. Mathematical population models have not yet been developed which are suitable for making population projections stratified by large numbers of variables. However, stochastic simulation called microanalytic simulation provides us with a feasible approach for obtaining population projections of this nature. In this paper the structure of a microanalytic population simulation model and its advantages over the transitional matrix method are discussed. Then a general method is presented to condition the course of simulations over historical periods using available aggregate vital statistics data. In this way, deviations of the simulated from the actual population can be controlled to a certain degree allowing us to recreate otherwise unavailable historical time series and cross-sectional population samples with reasonable precision. Numerical results are presented for the population of Alberta, a province of Canada, over the period 1961-1971.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Combining simulation and goal programming for healthcare planning in a medical assessment unit

This paper describes a detailed simulation model for healthcare planning in a medical assessment unit (MAU) of a general hospital belonging to the national health service (NHS), UK. The MAU is established to improve the quality of care given to acute medical patients on admission, and to provide the organisational means of rapid assessment and investigation in order to avoid unnecessary admissions. The simulation model enables different scenarios to be tested to eliminate bottlenecks in order to achieve optimal clinical workflow. The link between goal programming (GP) and simulation for efficient resource planning is explored. A GP model is developed for trade-off analysis of the results obtained from the simulation. The implications of MAU management preferences to various objectives are presented.     

First,do no harm? A framework for evaluating new <Emphasis Type="Italic">versus</Emphasis> reprocessed medical devices

More than ever before, health care providers are under intense pressure to control costs. Medical devices represent a significant ‘hard’ cost, with worldwide spending exceeding USD 235 billion. A growing number of health care providers are engaging in the practice of reprocessing—sterilizing and reusing medical devices labelled only for a single use. The ethical and technical dimensions of this practice have received much attention, but its economic aspects remain largely unexamined. This paper presents a Markov decision process framework that a health care provider can use to decide whether to use new or reprocessed devices in a given context. Two cases are studied: completely observable device condition and partially observable device condition. After briefly discussing structural results for the two cases, several examples are presented to illustrate how the model can be applied in practice. Useful results can be computed quickly with minimal data. A key insight of the model is that perfect information regarding the device condition is often not required to make a sound decision.     

Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.     

Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research.     

Information resource planning for a health-care system using an AHP-based goal programming method

This paper presents a goal programming (GP) model which aids in allocating a health-care system's information resources pertinent to strategic planning. The model is developed based on the data obtained from a major health-care system in the United States. The overall objective is to design and evaluate a model for effective information resource planning in a health-care system. The proposed model: (1) utilizes a GP approach to reflect the multiple, conflicting goals of the health-care system; (2) employs a GP solution process to reflect multi-dimensional aspects of the resource allocation planning; and (3) allows for some degree of flexibility of decision-making with respect to resource allocation. The goals are decomposed and prioritized with respect to the corresponding criteria using the analytic hierarchy process (AHP). The model result is derived and discussed. This GP model facilitates decision-making planning process and managerial policy in health-care information resources planning and similar planning settings.     

A heuristic for direct consumer participation in primary health care planning

Recent attempts at consumer participation in the health care planning process have proved weak in their ability to responsively account for consumer health welfare. This can be attributed, in large part, to the mechanisms employed for identifying and utilizing the consumer's health care views and preferences. A heuristic planning procedure designed to overcome these problems by directly incorporating consumer preferences is developed. It identifies that (primary) health care delivery system which maximizes total incremental health benefit to a community subject to a prespecified budget constraint. The model assumes a methodology (previously developed by the author) for measuring, in aggregable units, the benefit, B_ip, from some health care facility p as perceived by some consumer i. Application of the procedure and subsequent sensitivity analyses demonstrate its ability to generate valid solutions that are robust to disturbances in the planning system.