Some New Methods for Design and Analysis of Survival Data

For survival outcomes, usually, statistical equivalent tests to show a new treatment therapeutically equivalent to a standard treatment are based on the Cox (1972) proportional hazards assumption. We present an alternative method based on the linear transformation model (LTM) for two treatment arms, and show the advantages of using this equivalence test instead of tests based on the Cox's model. LTM is a very general class of models including models such as the proportional odds survival model (POSM). We presented a sufficient condition to check whether log-rank based tests have inflated Type I error rates. We show that POSM and some other commonly used survival models within the LTM class all satisfy this condition. Simulation studies show that repeated use of our test instead of using log-rank based tests will be a safer statistical practice. Our second goal is to develop a practical Bayesian model for survival data with high dimensional covariate vector. We develop the Information Matrix (IM) and Information Matrix Ridge (IMR) priors for commonly used survival models including the Cox's model and the cure rate model proposed by Chen et al. (1999), and examine many desirable theoretical properties including sufficient conditions for the existence of the moment generating functions for these priors and corresponding posterior distributions. The performance of these priors in practice is compared with some competing priors via the Bayesian analysis of a study that investigates the relationship between lung cancer survival time and a large number of genetic markers.