Modelling hospital length of stay using convolutive mixtures distributions

Length of hospital stay (LOS) is an important indicator of the hospital activity and management of health care. The skewness in the distribution of LOS poses problems in statistical modelling because it fails to adequately follow the usual traditional distribution of positive variables such as the log-normal distribution. We present in this paper a model using the convolution of two distributions, a technique well known in the signal processing community. The specificity of that model is that the variable of interest is considered to be the resulting sum of two random variables with different distributions. One of the variables features the patient-related factors in terms of their need to recover from their admission condition, while the other models the hospital management process such as the discharging process. Two estimation procedures are proposed. One is the classical maximum likelihood, while the other relates to the expectation-maximization algorithm. We present some results obtained by applying this model to a set of real data from a group of hospitals in Victoria (Australia). Copyright © 2016 John Wiley & Sons, Ltd.