Trend Analysis of Length of Stay Data via Phase-Type Models

The populations in many developed countries throughout the world are aging rapidly and the number of geriatric patients is expected to rise steeply in those countries. This will exert greater pressures on the management of hospital resources as a result. Hospital length of stay (LOS) is an important indicator of hospital activity and management because of its direct relation to resource consumption. Planning of hospital resources according to identified trends of LOS is, thus, an effective way to meet such future needs. In this paper, we propose a method to analyze the temporal trends of LOS based on the Coxian phase-type distributions, a special type of continuous-time Markov process. By fitting and regressing the probabilities of discharge from each phase of the distribution on time, we have found a growing trend in the proportion of long-staying patients in our sample of stroke patients from a general hospital in Singapore. We compare the yearly, quarterly and monthly trends over the same period to see the common pattern. The datasets were also robustified by bootstrapping to aid the analysis.