Survival analysis deals with failure-time data. The analysis of failure-time data is usually complicated by the presence of censoring so that the regular parametric and nonparametric estimation methods need to be modified. A parametric model usually works well when it fits the data properly. It is less efficient when the parametric model deviates from the underlying distribution of the data. The nonparametric methods are preferred when it is difficult to find a parametric model which fits the data well.

Kouassi and Singh (1997) introduced a weighted linear mixture of parametric and nonparametric models to estimate the hazard function. Their semiparametric mixture model provides flexibility in estimation by assigning more weight to the component in the mixture that fits the data better. In the first part of this dissertation, we extend this methodology to the estimation of survival function that minimizes the mean-squared-error. However, we find the semiparametric mixture model computationally intensive and difficult to interpret. The choice of the parametric component and estimation of the nonparametric component remains to be justified.

This dissertation continues to propose a parametric mixture model framework for the analysis of survival data that are subject to censoring and multiple causes of failure. An Expectation-Maximization algorithm is implemented to achieve the maximum likelihood estimation of mixture model and a model selection statistic based on Bayesian Information Criterion is applied to find the mixture form that best fits the data. We exploit the asymptotic properties of the maximum likelihood method for statistical inference about the parameters. Furthermore, the parametric mixture model is extended to a regression framework for analyzing the survival data with covariates. The regression context allows us to adjust for covariates and to assess their effects on the joint distribution of survival time and type of failure. The methodology is judged by simulation and applied to real datasets. These applications indicate that the parametric mixture model with its flexibility is a good alternative tool in the analysis of survival data.