Failure time data are commonly encountered in epidemiological and biomedical studies, where the exact time of an event may be unknown or incomplete. Many semiparametric models have been developed in the literature to analyze such data; however, they may not always be effective in dealing with the diverse complexities that arise in practice. This motivated us to develop a more comprehensive class of semiparametric models for analyzing censored failure time data, with the ultimate goal of addressing the limitations of existing models and improving the accuracy of statistical inference.In the first project, we propose a broad class of so-called Cox-Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function through a transformation framework. The proposed model offers a high degree of flexibility and versatility, encompassing the Cox-Aalen model and transformation models as special cases. For right-censored data, we propose an estimating equation approach and devise an Expectation-Solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via empirical process techniques. Moreover, the ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we assess the performance of the proposed procedures by conducting extensive simulation studies and applying them in two randomized, placebo-controlled HIV prevention efficacy trials. The data example shows the utility of the proposed Cox-Aalen transformation models in enhancing statistical power for discovering covariate effects.In the second project, we consider the regression analysis of the Cox-Aalen transformation models with partly interval-censored data, which comprise exact and interval-censored observations. We formulate a set of estimating equations and utilize an ES algorithm that guarantees stability and rapid convergence. Under regularity assumptions, we demonstrate that resulting estimators are consistent and asymptotically normal, and we propose the use of weighted bootstrapping techniques to estimate their variance consistently. To evaluate the proposed methods, we perform thorough simulation experiments and applied them to the analysis of the data from a randomized HIV/AIDS trial.