Improving applicability of the non-monotone unified estimate for missing data

Abstract

In applied statistics missing data are a common problem. Performing a "complete case analysis" by removing individuals with missing data causes a loss of statistical power and can cause non-response bias. Inverse probability weighting is one method used to avoid non-response bias. However, when some individuals have partially observed data inverse probability weighting has only a limited ability to use this data. The unified approach (Zhao and Liu, 2021) is a modification of inverse probability weighting that uses "working models" to extract information from individuals with partially observed data. When the probability an individual has missing data can be accurately modeled but the distribution of the data is difficult to model the unified approach is an attractive option. In this thesis we review the theory of the unified estimate and its application to the Cox proportional hazards model for survival data. We present a new R program which can be used to easily fit the unified estimate for generalized linear models or Cox proportional hazards models. Possible hypothesis tests for the fit of the unified estimate and directions for future research are suggested.