Generalized Unified Approach to Regression Models with Covariates Missing in Nonmonotone Patterns
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Complicated designs (eg. partially questionnaire design), which are often used in epidemiologic studies to reduce the cost of data collection while at the same time improving data quality, generate data with nonmonotone missing patterns. This thesis focuses on statistical inference for regression models with nonmonotone missing covariate data under some designs that generate nonmonotone missing data in covariates. Proposed methods in this scenario often depend on additional assumptions about covariates, for example, the covariates need to be categorical or follow a particular semiparametric joint distribution. This thesis describes a generalized unified estimation method for regression models with covariates missing in nonmonotone patterns which use a sequence of working regression models to extract information from incomplete observations. It can deal with both continuous and categorical variables. We consider both cross-sectional and longitudinal studies. The asymptotic theory and variance estimator for the generalized unified estimator are provided. Simulation studies in different settings are used to examine the proposed method. Finally we applied the generalized unified approach to the two real examples. One is a cross-sectional study, and the other is a longitudinal study.