Local sensitivity approximations for selectivity bias

Observational data analysis is often based on tacit assumptions of ignorabi lity or randomness. The paper develops a general approach to local sensitiv ity analysis for selectivity bias, which aims to study the sensitivity of i nference to small departures from such assumptions. If M is a model assumin g ignorability, we surround M by a small neighbourhood Ar defined in the se nse of Kullback-Leibler divergence and then compare the inference for model s in Ar with that for M. Interpretable bounds for such differences are deve loped. Applications to missing data and to observational comparisons are di scussed. Local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems.