Navigating the bias from unobserved or residual confounding in observational studies in research is a complex and nuanced endeavor. In evaluating the impact of a specific intervention or treatment, researchers aim to isolate the genuine causal relationship between the treatment and observed outcomes. Yet, bias from unobserved or residual confounding in the study design, can complicate these analyses. These biases may encompass unobservable patient characteristics, variations in adherence to the treatment protocol, or contextual factors influencing both treatment assignment and outcomes. Hence, the imperative arises for the development of robust methodologies that effectively address bias from unobserved or residual confounding, ensuring the integrity and accuracy of research findings. In the first paper, we develop two generic classes of exact statistical tests for a biased randomization assumption. One important by-product of our testing framework is a quantity called \emph{residual sensitivity value} (RSV), which provides a means to quantify the level of residual confounding or hidden bias due to imperfect matching of observed covariates in a matched sample. We advocate taking into account RSV in the downstream primary analysis. In the second paper, we propose a new approach to reduce sensitivity to hidden bias for conducting statistical inference on the attributable fraction among the exposed (\textbf{AF}$_e$) by leveraging case description information. Case description information is information that describes the case, e.g., the subtype of cancer. The exposure may have more of an effect on some types of cases than other types. We explore how leveraging case description information can reduce sensitivity to bias from unmeasured confounding through an asymptotic tool, design sensitivity, and simulation studies. We allow for the possibility that leveraging case definition information may introduce additional selection bias through an additional sensitivity parameter. In the third paper, we consider identification and inference for the average treatment effect and heterogeneous treatment effect conditional on observable covariates in the presence of unmeasured confounding. Since point identification of these treatment effects is not achievable without strong assumptions, we obtain bounds on these treatment effects by leveraging differential effects, a tool that allows for using a second treatment to learn the effect of the first treatment. The differential effect is the effect of using one treatment in lieu of the other. We provide conditions under which differential treatment effects can be used to point identify or partially identify treatment effects. Under these conditions, we develop a flexible and easy-to-implement semi-parametric framework to estimate bounds and leverage a two-stage approach to conduct statistical inference on the effects of interest.