The broad, long-term objectives of this research are the developments of non- and semi-parametric statistical methods for analyzing censored data commonly encountered in biomedical investigations. The specific aims of the next project period include: (1) generalization of the Cox regression model to allow non-proportional hazards structures; (2) construction of simple and reliable inference procedures for the semiparametric accelerated failure time model; (3) exploration of efficient estimation procedures for the marginal modellings of multivariate failure time data; (4) derivation of nonparametric tests and semiparametric regression methods for growth curves under informative heterogeneous censoring. These topics are motivated by and directly relevant to biomedical applications. The statistical models under investigation are highly flexible and versatile, imposing no parametric form on the distribution of any random variable. The proposed inference procedures are relatively simple and efficient. The asymptotic properties of the proposed estimators and test statistics will be studied rigorously with the use of counting-process martingale theory, modern empirical process theory and other probability tools. Their operating characteristics in practical settings will be evaluated extensively through computer simulation. Applications to real medical studies will be provided. The research results will be disseminated to practicing statisticians and medical investigators via publications, lectures and software distributions.