Dual and simultaneous sensitivity analysis for matched pairs

When a study shows an association between a treatment and a response, befor e concluding that there is a causal relationship it is useful to assess whe ther or not an unobserved variable, U,might explain the observed associatio n. Sensitivity analysis clarifies the properties U must have in terms of it s relationship to the response and its imbalance in the groups being compar ed. A substantial literature has investigated the imbalance or association between U and group assignment. This paper develops a dual sensitivity anal ysis for matched pairs, focusing on the strength of the relationship betwee n U and the response required to reduce an observed association to non-sign ificance. A third simultaneous form of sensitivity analysis models both rel ationships between U and treatment assignment and U and response. The simul taneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships. The methods are illustr ated by several examples.