Model assisted sensitivity analyses for hidden bias with binary outcomes

In medical and health sciences, observational studies are a major data source for inferring causal relationships. Unlike randomized experiments, observational studies are vulnerable to the hidden bias introduced by unmeasured confounders. The impact of unmeasured covariates on the causal effect can be assessed by conducting a sensitivity analysis. A comprehensive framework of sensitivity analyses has been developed for matching designs. Sensitivity parameters are introduced to capture the association between the missing covariates and the exposure or the outcome. Fixing sensitivity parameter values, it is possible to compute the bounds of the p-value of a randomization test on causal effects. We propose a model assisted sensitivity analysis with binary outcomes for the general 1:k matching design, which provides results equivalent to the conventional nonparametric approach in large sample. By introducing a conditional logistic outcome model, we substantially simplify the implementation and interpretation of the sensitivity analysis. More importantly, we are able to provide a closed form representation for the set of sensitivity parameters for which the maximum p-values are non-significant. This methodology can be easily extended to matching designs with multilevel treatments. We illustrate our method using a U.S. trauma care database to examine mortality difference between trauma care levels.