Variable selection in observational studies

Observational studies are nonrandomized experiments in which treated and control groups may differ with respect to pretreatment covariate. Covariance adjustment is used in observational studies to adjust for imbalances in observed covariates. Often treatment effects are modeled as an additive constant, but it is quite possible that the treatment effect varies with the covariates X. In this thesis, I consider how to identify covariates that are either needed for adjustment or are related to the size of the treatment effect. The idea is to use Mallow\u27s generalized $C\sb{P}$ statistic in such a way that it measures our ability to estimate treatment effects. This thesis defined a statistics named $L\sb{P}$, as a measure of the standardized mean square error of the treatment effects. The $L\sb{P}$ statistics is a criterion for selecting an appropriate subset of the covariates and it is used to compare covariance models graphically, where both bias and random errors are considered