A Methodology to Monitor the Changing Trends in Health Status of an Elderly Person by Developing a Markov Model

Abstract

In this paper we are proposing a statistical testing methodology to monitor changing trends in the health status of elderly people. The occupancy pattern of elderly people can be modeled using a Markov chain, estimating transition probabilities of the chain and test hypotheses about them. The profile of the person for a given period can be stored as a transition matrix of a discrete, regular, ergodic Markov chain. The observation of the occupancy pattern for a given test period can be established as a test Markov chain using information from sensors such as infrared sensors, magnetic switches etc. In the absence of real time data, we have used uniformly distributed transition probabilities to define the profile of the Markov chain and then generated test Markov chain based on this model. The transition probabilities are extracted for the test and profile Markov chain using Maximum Likelihood Estimates (MLE). The statistical testing of occupancy monitoring establishes a basis for statistical inference about the system performance without generating any real time statistics for the occupancy pattern. Chi square test and likelihood ratio tests ensure that the sequences generated from the two Markov chains are statistically same. Any difference in profile Markov chain and test Markov chain could indicate a changed health status of the elderly person.