Bayesian local sensitivity to non-ignorable concurrent missing outcome and covariates: an application to the NHANES data

A major concern in statistical analysis is missing data. Analysis frequently operates under the presumption that missingness is ignorable when it occurs in the study. It is critical to evaluate the effect of missingness on the most important Bayesian inferences because ignorability is an untestable assumption in the absence of data augmentation. Previously, in a Bayesian framework, the influence of missing outcomes' non-ignorability was studied using local sensitivity indices. In this paper, for the first time, the Bayesian first and second-order indices of local sensitivity to non-ignorability for data exposed to concurrent missingness in both outcome and covariates will be extended. These indices are calculated via the first and second-order derivatives of the Bayes estimators with respect to the non-ignorability parameter(s). Our results indicate that there are parameters where the Bayes estimates have high nonlinearity in the neighbourhood of the ignorable model and the first-order sensitivity analysis cannot detect their sensitivity to non-ignorability assumption. These parameters are related to the slope of covariates in which there is concurrent missingness and the error variance. We will evaluate the features of our proposed indices through several simulated studies. Finally, a real dataset derived from the National Health and Nutrition Examination Survey (NHANES) is used to demonstrate the applicability of these indices.