The first part of my dissertation focuses on post-randomization modification of intent-to-treat effects. For example, in the field of behavioral science, investigations involve the estimation of the effects of behavioral interventions on final outcomes for individuals stratified by post-randomization moderators measured during the early stages of the intervention (e.g., landmark analyses in cancer research). Motivated by this, we address several questions on the use of standard and causal approaches to assessing the modification of intent-to-treat effects of a randomized intervention by a post-randomization factor. First, we show analytically the bias of the estimators of the corresponding interaction and meaningful main effects for the standard regression model under different combinations of assumptions. Such results show that the assumption of independence between two factors involved in an interaction, which has been assumed in the literature, is not necessary for unbiased estimation. Then, we present a structural nested distribution model estimated with G-estimation equations, which does not assume that the post-randomization variable is effectively randomized to individuals. We show how to obtain efficient estimators of the parameters of the structural distribution model. Finally, we confirm with simulations the performance of these optimal estimators and further assess our approach with data from a randomized cognitive therapy trial. The second part of my dissertation is on optimal and adaptive designs for dose-finding experiments in clinical trials with multiple correlated responses. For instance, in phase I/II studies, efficacy and toxicity are often the primary endpoints which are observed simultaneously and need to be evaluated together. Accordingly, we focus on bivariate responses with one continuous and one categorical. We adopt the bivariate probit dose-response model and study locally optimal, two-stage optimal, and fully adaptive designs under different cost constraints. We assess the performance of the different designs through simulations and suggest that the two-stage designs are as efficient as and may be more efficient than the fully adaptive deigns under a moderate sample size in the initial stage. In addition, two-stage designs are easier to construct and implement, and thus can be a useful approach in practice.