Analyses of data with missing values often require assumptions about missingness mechanisms that cannot be assessed empirically, highlighting the need for sensitivity analyses. However, universal recommendations for reporting missing data and conducting sensitivity analyses in empirical studies are scarce. Both steps are often neglected by practitioners due to the lack of clear guidelines for summarizing missing data and systematic explorations of alternative assumptions, as well as the typical attendant complexity of missing not at random (MNAR) models. We propose graphical displays that help visualize and systematize the results of sensitivity analyses, building upon the idea of "tipping-point" analysis for experiments with dichotomous treatment. The resulting "enhanced tipping-point displays" (ETP) are convenient summaries of conclusions drawn from using different modeling assumptions about the missingness mechanisms, applicable to a broad range of outcome distributions. We also describe a systematic way of exploring MNAR models using ETP displays, based on a pattern-mixture factorization of the outcome distribution, and present a set of sensitivity parameters that arises naturally from such a factorization. The primary goal of the displays is to make formal sensitivity analyses more comprehensible to practitioners, thereby helping them assess the robustness of experiments' conclusions. We also present an example of a recent use of ETP displays in a medical device clinical trial, which helped lead to FDA approval. The last part of the dissertation demonstrates another method of sensitivity analysis in the same clinical trial. The trial is complicated by missingness in outcomes "due to death", and we address this issue by employing Rubin Causal Model and principal stratification. We propose an improved method to estimate the joint posterior distribution of estimands of interest using a Hamiltonian Monte Carlo algorithm and demonstrate its superiority for this problem to the standard Metropolis-Hastings algorithm. The proposed methods of sensitivity analyses provide new collections of useful tools for the analysis of data sets plagued with missing values. / Statistics