Adjusting for Bias due to Partially or Fully Unobserved Data

It is a well known fact that incomplete data could lead to efficiency loss in parameter estimation. Examples of incomplete data include when there are not enough data observations to allow valid inferences be drawn from an analysis or when a statistical model is misspecified so that an important covariate is omitted from the analysis model. The assumption that the missing data observations or missing covariate, however, is not verifiable. It is therefore necessary to evaluate the magnitude of bias due to the incomplete or unobserved data and if needed, to properly adjust the parameter estimation for this bias. In this dissertation, we first derived a local sensitivity index formula that can easily approximate the resulting bias of the maximum likelihood estimates in the location-scale model with nonignorable missing outcome data. Then, we developed a local sensitivity index formula that can easily quantify the impact of a potentially unobserved confounder on the maximum likelihood estimates in a generalized linear model setting. Last, we extended this local sensitivity index formula to the survival analysis when the hazard ratio is assumed to be constant over time. We were able to demonstrate the use and effectiveness of these simple formula in reestimating the treatment effect estimates using simulation studies as well as real data applications.