Analysing and Predicting Patient Arrival Times

Abstract

We fit a Hidden Markov Model (HMM) to patient arrivals data, represented as a discrete data trace. The processing of the data trace makes use of a simple binning technique, followed by clustering, before it is input into the Baum-Welch algorithm, which estimates the parameters of the underlying Markov chain’s state-transition matrix. Upon convergence, the HMM predicts its own synthetic traces of patient arrivals, behaving as a fluid input model. The Viterbi algorithm then decodes the hidden states of the HMM, further explaining the varying rate of patient arrivals at different times of the hospital schedule. The HMM is validated by comparing means, standard deviations and autocorrelation functions of raw and synthetic traces. Finally, we explore an efficient optimal parameter initialization for the HMM, including choosing the number of hidden states. We summarize our findings, comparing results with other work in the field, and proposals for future work.