Local sensitivity analysis and bias model selection

Abstract

Incomplete data analysis is often considered with other problems such as model uncertainty or non-identi ability. In this thesis I will use the idea of the local sensitivity analysis to address problems under both ignorable and non-ignorable missing data assumptions. One problem with ignorable missing data is the uncertainty for covariate density. At the mean time, the misspeci cation for the missing data mechanism may happen as well. Incomplete data biases are then caused by di erent sources and we aim to evaluate these biases and interpret them via bias parameters. Under non-ignorable missing data, the bias analysis can also be applied to analyse the di erence from ignorability, and the missing data mechanism misspeci cation will be our primary interest in this case. Monte Carlo sensitivity analysis is proposed and developed to make bias model selection. This method combines the idea of conventional sensitivity analysis and Bayesian sensitivity analysis, with the imputation procedure and the bootstrap method used to simulate the incomplete dataset. The selection of bias models is based on the measure of the observation dataset and the simulated incomplete dataset by using K nearest neighbour distance. We further discuss the non-ignorable missing data problem under a selection model, with our developed sensitivity analysis method used to identify the bias parameters in the missing data mechanism. Finally, we discuss robust con dence intervals in meta-regression models with publication bias and missing confounder.