TREATMENT COMPARISON IN BIOMEDICAL STUDIES USING SURVIVAL FUNCTION by

In the dissertation, we study the statistical evaluation of treatment comparisons by evaluat-ing the relative comparison of survival experiences between two treatment groups. We construct confidence interval and simultaneous confidence bands for the ratio and odds ratio of two survival functions through both parametric and nonparametric approaches. We first construct empirical likelihood confidence interval and simultaneous confidence bands for the odds ratio of two survival functions to address small sample efficacy and sufficiency. The empirical log-likelihood ratio is developed, and the corresponding asymptotic distribution is derived. Simulation studies show that the proposed empirical likelihood band has outperformed the normal approximation band in small sample size cases in the sense that it yields closer coverage probabilities to chosen nominal levels. Furthermore, in order to incorporate prognostic factors for the adjustment of survival func-tions in the comparison, we construct simultaneous confidence bands for the ratio and odds ratio of survival functions based on both the Cox model and the additive risk model. We develop simulta-neous confidence bands by approximating the limiting distribution of cumulative hazard function