Capturing the re-admission process: focus on time window

In the majority of studies on patient re-admissions, a re-admission is deemed to have occurred if a patient is admitted within a time window of the previous discharge date. However, these time windows have rarely been objectively justified. We capture the re-admission process from the community using a special case of a Coxian phase-type distribution, expressed as a mixture of two generalized Erlang distributions. Using the Bayes theorem, we compute the optimal time windows in defining re-admission. From the national data set in England, we defined re-admission for chronic obstructive pulmonary disease (COPD), stroke, congestive heart failure, and hip- and thigh-fractured patients as 41, 9, 37, and 8 days, respectively. These time windows could be used to classify patients into two groups (binary response), namely those patients who are at high risk (e.g. within 41 days for COPD) and low risk of re-admission group (respectively, greater than 41 days). The generality of the modelling framework and the capability of supporting a broad class of distributions enables the applicability into other domains, to capture the process within the field of interest and to determine an appropriate time window (a cut-off value) based on evidence objectively derived from operational data.