A Gaussian Mixture Model Approach to Grouping Patients According to their Hospital Length of Stay

In this paper we propose a new approach capable of determining clinically meaningful patient groups from a given dataset of patient spells. We hypothesise that the skewed distribution of length of stay (LOS) observations, often modelled in the past using mixed exponential equations, is composed of several homogeneous groups that together form the overall skewed LOS distribution. We show how the Gaussian mixture model (GMM) can be used to approximate each group, and discuss each group's possible clinical interpretation and statistical significance. In addition, we show how the health professional can use the outcome of the grouping approach to answer several questions about individual patients and their likely LOS in hospital. Our results demonstrate that the grouping of stroke patient spells estimated by the GMM resembles the clinical experience of stroke patients and the different stroke recovery patterns.