Making valid inferences about effects attributable to a particular treatment condition on a health outcome of interest is an important goal in many epidemiological studies and is also a challenging topic for biostatistical research. Almost all the currently available biostatistical methodologies make the inference under the assumption that all the confounding variables between treatment and outcome are known, observed, and measured, excluding the possibility of unmeasured confounding variables. Although many investigators have recognized that the failure to take unmeasured confounding variables into account leads to substantially biased estimates of treatment effect, until now there lacks analytic techniques that properly addresses the challenge of unmeasured confounding variables in observational studies and randomized experimental studies with missing data.;A method of accounting for unmeasured confounding variables that we call latent variable analysis of unmeasured confounding variables (LVAUC) is developed in this dissertation. The LVAUC approach aims at estimating effects attributable to a treatment condition in the presence of unmeasured confounding variables. The method applies to general observational studies, including longitudinal studies with time-varying treatments. Moreover, this method is extended to deal with non-ignorable missing data. The estimator of treatment effect derived from the method is shown to be consistent and the performance of the method is tested with various simulations studies. The method is also illustrated with a data set from a health services research study entitled Access to Community Care and Effective Services and Supports (ACCESS) program and a longitudinal antipsychotic trial-Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) schizophrenia study.
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