In observational studies, identifying assumptions may fail, often quietly and without notice, leading to biased causal estimates. Although less of a concern in randomized trials where treatment is assigned at random, bias may still enter the equation through other means. This dissertation has three parts, each developing new methods to address a particular pattern or source of bias in the setting being studied. In the first part, we extend the conventional sensitivity analysis methods for observational studies to better address patterns of heterogeneous confounding in matched-pair designs. We illustrate our method with two sibling studies on the impact of schooling on earnings, where the presence of unmeasured, heterogeneous ability bias is of material concern. The second part develops a modified difference-in-difference design for comparative interrupted time series studies. The method permits partial identification of causal effects when the parallel trends assumption is violated by an interaction between group and history. The method is applied to a study of the repeal of Missouri's permit-to-purchase handgun law and its effect on firearm homicide rates. In the final part, we present a study design to identify vaccine efficacy in randomized control trials when there is no gold standard case definition. Our approach augments a two-arm randomized trial with natural variation of a genetic trait to produce a factorial experiment. The method is motivated by the inexact case definition of clinical malaria.