Dual and simultaneous sensitivity analysis for matched pairs

When a study shows an association between a treatment and a response, before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable, U,might explain the observed association. Sensitivity analysis clarifies the properties U must have in terms of its relationship to the response and its imbalance in the groups being compared. A substantial literature has investigated the imbalance or association between U and group assignment. This paper develops a dual sensitivity analysis for matched pairs, focusing on the strength of the relationship between U and the response required to reduce an observed association to non-significance. A third simultaneous form of sensitivity analysis models both relationships between U and treatment assignment and U and response. The simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships. The methods are illustrated by several examples.