Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes

Performance evaluation of nursing homes is usually accomplished by the repeated administration of questionnaires aimed at measuring the health status of the patients during their period of residence in the nursing home. We illustrate how a latent Markov model with covariates may effectively be used for the analysis of data collected in this way. This model relies on a not directly observable Markov process, whose states represent different levels of the health status. For the maximum likelihood estimation of the model we apply an EM algorithm implemented by means of certain recursions taken from the literature on hidden Markov chains. Of particular interest is the estimation of the effect of each nursing home on the probability of transition between the latent states. We show how the estimates of these effects may be used to construct a set of scores which allows us to rank these facilities in terms of their efficacy in takingcare of the health conditions of their patients. The method is used within an application based on data concerning a set of nursing homes located in the Region of Umbria, Italy, which were followed for the period 2003–2005. 1. Introduction. Both in European countries and in the United States, elderly people with chronic conditions or functional limitations can access nursing homes whenever they are no longer able or choose not to remain in their own homes. These facilities provide a diverse array of services such as housing, support systems, nursing and medical care for a sustained period of time. These services range from minimal personal assistance to virtually total care for the patients. The challenge for the nursing homes is to provide the opportunity for elderly people to live with dignity even though they may be physically or cognitively impaired. The quality of the assistance and the

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