Models for Longitudinal Analysis of Binary Response Data for Identifying the Effects of Different Treatments on Insomnia

In this paper some models are applied to analyze insomnia data. Insomnia is a sleep disorder in which the patient does not get enough or satisfactory sleep and investigating the use of hypnotic drug for its cure is so important. For studying the effect of drugs on insomnia, it is useful to observe the response of interest (cured or not cured) for each subject repeatedly at several times. So, a longitudinal study of repeated binary responses along with a treatment variable (with two levels hypnotic or placebo) are used for some individuals on two times. A very important feature of the data is that the correlation between the two longitudinal responses depends on the level of hypnotic drug. This is, firstly, shown by an exploratory data analysis. Then, as an option, Dale’s bivariate model for analyzing longitudinal or repeated measurements of binary responses, considering the effect of treatment on the responses and the correlation structure, is used to find an overall population effect on the responses. As other options, transition and random effect models for analyzing these data are used to investigate, respectively, the reasons for 3068 Z. Rezaei Ghahroodi, M. Ganjali and I. Kazemi the change of the responses and to find the subject-specific variations. How the interpretation of the results is different with the use of the Dale’s model and how one may find out the effect of the drug on the correlation structure by a transition or random effect model are also discussed.