The use of a semi-Markov model for describing sleep patterns.

The Markov chain model proposed by Zung et al. [1965] for sleep patterns was tested with more data, and found inadequate for describing sleep stage sequences because the data do not fit the geometric distribution required by the model. Instead, a semi-Markov process was shown to adequately represent the data. Predictive ability was illustrated. The parameters generated by a semi-Markov model correctly distinguished 11 out of 12 insomniacs from 11 out of 12 normal subjects. The transition probability for the progression from stage 1 to stage 2 is consistent over the night for subjects age 3 to 69. The transition probability for progression from stage 2 to stage 3, however, changes each hour during the night for the ages tested (20 to 69). The curve of these changes has the same general form except for ages 40-49 years. This age is well known for a high incidence of insomnia.