The paper develops a Markov model in continuous time for the length of stay of elderly people moving within and between residential home care and nursing home care. A procedure to determine the structure of the model and to estimate parameters by maximum likelihood is presented. The modelling approach was applied to 4 years' placement data from the social services department of a London borough. The results in this London borough suggest that, for residential home care, a single-exponential distribution with mean 923 days is adequate to provide a good description of the pattern of the length of stay, whereas, for nursing home care, a mixed exponential distribution with means 59 days (short stay) and 784 days (long stay) is required, and that 64% of admissions to nursing home care will become long-stay residents. The implications of these findings and the advantages of the proposed modelling approach in the general context of long-term care are discussed. Copyright 2005 Royal Statistical Society.

The main aim of this paper is to derive a solution to the capacity problem faced by many perinatal networks in the United Kingdom. We propose a queueing model to determine the number of cots at all care units for any desired overflow and rejection probability in a neonatal unit. The model formulation is developed, being motivated by overflow models in telecommunication systems. Exact expressions for the overflow and rejection probabilities are derived. The model is then applied to a neonatal unit of a perinatal network in the UK.

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Abstract-Understanding the pattern of length of stay in institutional long-term care has important practical implications in the management of long-term care. Furthermore, residents' attributes are believed to have significant effects on these patterns. In this paper, we present a model-based approach to extract, from a routinely gathered administrative social care dataset, high-level length-of-stay patterns of residents in long-term care. This approach extends previous work by the authors to incorporate residents' features. Two applications using data provided by a local authority in England are presented to demonstrate the potential use of this approach.Index Terms-Covariate, length-of-stay analysis, long-term care, Markov model, survival analysis.

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