Statistical Methods for the Analysis of Lqjgitudinal Data with Binary

Hideki ORIGASA. Statistical methods for the analysis of longitudinal data with binary responses. (Under the direction of JAMES D. KNOKE). Medical researches often involve a time factor. Each subject has observations at several occasions. These are called longitudinal data. This work is only concerned with those with binary responses. The main issue of interest is to test the treatment effect incorporating the time factor with respect to the frequency of having responses. The purpose of this work is to present two models for longitudinal data with binary responses and develop statistical methodology for analysis under these models. The first model is referred to as a Markov Logistic Regression Model (MLRM) which models the transition probabilities as a logistic function of covariates including the previous outcome. This model has advantages over other models in a different way. Its advantage over the multivariate linear model is to delete less incomplete observations. Allowing time dependent covariates is the advantage over the Zeger, Liang, and Self's (1985) model (abbreviated as ZLS model). Finally, the advantage over the Grizzle, Starmer, and Koch's (1969) model (abbreviated as GSK model) is to allow continuous covariates as well as discrete ones. Based on thiS model, the maximum likelihood estimate and the likelihood ratio test criterion are derived. Some asymptotic theorems are also proved.