Markov model-based clustering for efficient patient care

Phase-type distributions were used to carry out model-based clustering of patients using the time spent by the patients in hospital, with maximum likelihood estimation of the model parameters. These parameters were allowed to vary with covariates so that the probability of cluster membership was dependent on these covariates. Expressions for the cluster membership probabilities and corresponding distributions of length of stay in care were found where the membership probabilities can be updated to take account of length of stay to date. The approach was applied to data on geriatric patients from an administrative database of a London hospital. The age of the patients at admission to care and the year of admission were included as covariates. Differential effects of these covariates on the various parameters of the fitted model were demonstrated, and interpretations of these effects made. The clusters here corresponded to patient pathways, with different length of stay distributions, varying care needs and different associated costs. By using the membership probabilities to assign patients to such clusters, care may thus be suited to their predicted pathway. Such an approach might be used in association with healthcare process improvement technologies, such as Lean Thinking or Six Sigma.