A review of tensor-based methods and their application to hospital care data

In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at different occasions. The occasions can be time-varying or refer to different conditions. In such cases, the data can be stored in a 3-way array or tensor. The Candecomp/Parafac and Tucker3 methods represent the most common methods for analyzing 3-way tensors. In this work, a review of these methods is provided, and then this class of methods is applied to a 3-way data set concerning hospital care data for a hospital in Rome (Italy) during 15 years distinguished in 3 groups of consecutive years (1892-1896, 1940-1944, 1968-1972). The analysis reveals some peculiar aspects about the use of health services and its evolution along the time.