A case-cohort study is a two-phase study where at the first phase a representative sample, referred to as the study cohort, is selected from the target population. At the second phase, a subsample is selected from the cohort based on the case status. All cases are included in the subsample whereas only a random sample of controls is included. The endpoint of interest in such studies is usually the failure time. Several methods have been proposed to estimate the relative risk or hazard ratio from a case-cohort study. These methods almost always disregard the covariate information that is not included in the sampled study sub-cohort, and therefore, results in the loss of efficiency. While there have been attempts to derive the most efficient estimators, the resulting estimators were challenging from the data analysis point of view. We propose a locally efficient estimator (LEE) by restricting the estimator to a class of regular asymptotically linear estimators. The properties of this estimator are investigated through simulation and application to the Wilm's tumor study. The public health relevance of this dissertation is the use of innovative methodology to reduce cost associated with research
