Local Nonlinear Sensitivity to Nonigorable Selection

An untestable ignorable missingness assumption is often used in reality. Assessing the impact of nonignorability in the standard analyses results is needed. Developing simple and principled measures to quantify the sensitivity to nonigorability is an increasing interest. Past developments assume linearity assumptions and demonstrate their usefulness in a range of important statistical applications. In this thesis, we develop general formula for nonlinear sensitivity index measures to nonignorability. These nonlinear index measures maintain the computational simplicity of the linear sensitivity index measures and avoid ftting complicated nonignorable models. The proposed nonlinear sensitivity measures can effectively detect the impact of nonignorability comparing to the linear index measures in some important situations. These situations include when the parameters of interest concerns with fi ner distributional features such as variance and tail percentiles, as well as when the outcome and covariates in a regression model are subject to simultaneous missingness (e.g., EMA studies). The nonlinear sensitivity index measures have been evaluated in simulated and real collected datasets.