Grant: Discovery Grants Program - Individual

Regression models are commonly used to study the association between a response variable and a set of covariates. Standard inference methods can be directly applied when there is no selection bias (e.g. in simple random sampling design) and the objects selected in the sample are fully observed. However in practice many studies involve some combination of selection bias, missing or mismeasured data. The objectives of the proposed research program are: (i) development and application of estimation methods which can deal with missing or mismeaured data with selection bias; and (ii) investigation of optimal sampling strategies for two-phase or multi-phase studies which maximize the information in observed data. Models explored under (i) will include the generalized linear models and partially linear models where certain variables (response or covariates) are missing either by design (e.g. two-phase study) or happenstance and auxiliary information is sometime available. Our recent work in this area based on semiparametric models and an expectation-maximization (EM) algorithm has several promising results for both response and covariates missing problems, and it can efficiently use auxiliary information to improve estimation efficiency and at the same time reduce estimation bias. Further investigation in this area will considerably enhance statistical inference both in theory and application. Two-phase or multi-phase studies produce data with certain variables missing by design. Research topics under (ii) will be conducted jointly with the efficient estimation methods under (i). In the proposed research we will consider numerical methods to investigate potential improvements of optimal design over the balanced design for different settings and develop optimal sampling strategies for more general settings. If successfully developed and implemented the methodology will be widely used.