  Identifying causal treatment (or exposure) effects in observational studies
requires the data to satisfy the unconfoundedness assumption which is not
testable using the observed data. With sensitivity analysis, one can determine
how the conclusions might change if assumptions are violated to a certain
degree. In this paper, we propose a new technique for sensitivity analysis
applicable to clusters observational data with a normally distributed or binary
outcome. The proposed methods aim to assess the robustness of estimated
treatment effects in a single study as well as in multiple studies, i.e.,
meta-analysis, against unmeasured confounders. Simulations with various
underlying scenarios were conducted to assess the performance of our methods.
Unlike other existing sensitivity analysis methods, our methods have no
restrictive assumptions on the number of unmeasured confounders or on the
relationship between measured and unmeasured confounders, and do not exclude
possible interactions between measured confounders and the treatment. Our
methods are easy to implement using standard statistical software packages.
