Dependent data methods are widely used in practice to conduct analyses for hierarchical and longitudinal studies. Formally, their use depends on a variety of assumptions, for example, parametric distributional assumptions or assumptions about the sampling mechanism. The overarching goal of our research program is to quantify sensitivity to these assumptions, identifying scenarios in which they are and are not important and developing new, more robust methods when necessary. Our focus is on assumptions surrounding the sampling mechanism, including missing data and outcome dependent sampling. Our research has four aims. Our first aim considers the performance of commonly used methods that are used to avoid cluster level confounding. However, they may be sensitive to data which are missing at random (MAR), but not missing completely at random (MCAR). Aims 2 through 4 consider outcome dependent sampling mechanisms that are frequently encountered in practice. In Aim 2 we consider the use of parametric mixed models in situations such as for outcome dependent family studies. Aim 3 considers the situation in which the timing of measurements may be dependent on previous results (e.g., more frequent exams in prostate cancer patients with rising prostate specific antigen (PSA) test results). Aim 4 considers a general and unifying context in which to imbed the work on Aims 2 and 3, derive optimality results, and develop a platform for creation of new statistical methods for outcome dependent sampling. Results from our research will directly inform current statistical practice for these commonly used methods.