Phase-Type Survival Trees and Mixed Distribution Survival Trees for Clustering Patients' Hospital Length of Stay

Clinical investigators, health professionals and managers are often interested in developing criteria for clustering patients into clinically meaningful groups according to their expected length of stay. In this paper, we propose two novel types of survival trees; phase-type survival trees and mixed distribution survival trees, which extend previous work on exponential survival trees. The trees are used to cluster the patients with respect to length of stay where partitioning is based on covariates such as gender, age at the time of admission and primary diagnosis code. Likelihood ratio tests are used to determine optimal partitions. The approach is illustrated using nationwide data available from the English Hospital Episode Statistics (HES) database on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period.