This research is concerned with the generalization of the two well known regression models for duration times, the proportional hazards model ant the accelerated failure time model, to a mixed model with both fixed effects and a random effect. In particular, the objective of this research is to consider score and likelihood ratio tests for the presence of the random effect in the proportional hazards model and to consider both a method of estimation for the regression coefficient and nonparametric likelihood estimation of the error distribution in the mixed effects, accelerated failure time model. Many areas of scientific endeavor, such as demography, duration analysis in economics, reliability in manufacturing, and survival analysis in medical studies, are confronted with dependent duration times. This research is concerned with a generalization of two often used models to a model which is more realistic.
