During the next funding period of this grant, we will examine some important questions in regression models for right-censored data. The issues we have chosen extend work conducted during the current project period, and epidemiologic studies in cancer research. More specifically, we will investigate the following topics: 1. A study of properties of methods for fitting nonlinear models for covariate effects in proportional hazards regression. In particular, we will examine the loss of efficiency when overfitting nonlinear models, and the effect on inference of adaptive knot placement of regression splines. 2. Methods for inference in proportional hazards or relative risk regression models when either outcome variables or covariates are either measured with error, or are replaced by surrogate variables that are easier to measure. 3. Methods for parsimonious modeling of the association of survival data and covariates when different covariate values do not produce proportional conditional hazard functions. 4. A study of significance tests that are sensitive to a wide range of relationships between survival data and smooth (i.e. continuous) covariates.