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Analyzing treatment or exposure effect is a major research theme in scientific studies. In the current big-data era where multiple sources of data are available, it is of interest to perform a synthesized analysis of treatment effects by integrating information from different data sources or studies. However, studies may contain heterogeneous and incomplete covariate sets, and individual data therein may not be accessible. We apply and extend the generalized meta-analysis method to integrate summary results (e.g., regression coefficients) of outcome and treatment (propensity score, PS) regression analyses across different datasets that may contain heterogeneous covariate sets. The proposed integrated analysis utilizes a reference dataset, which contains data on the complete set of covariates. The asymptotic distribution for the proposed integrated estimator is established. Simulations reveal that the proposed estimator performs well. We apply the proposed method to obtain the causal effect of waist circumference on hypertension by integrating two existing outcomes and PS regression analyses with different sets of covariates. [ABSTRACT FROM AUTHOR]

For a linear regression model with two-predictor variables, the effects of the correlation between the two predictors on estimated standardized regression coefficients and R 2 have been well studied. However, the role the correlation plays may sometimes be overstated, such that confusion and misconceptions may arise. In this article, we revisit the issue from the perspective of a semipartial correlation coefficient. We find that by taking this perspective we are not only able to reach the same conclusions while avoiding those misunderstandings, we are also able to gain more insight. In addition, we also take a geometrical approach to illustrate how estimated standardized regression coefficients and R 2 behave as the correlation varies. Geometrical displays provide readers with a way to visualize the behavior changes and to understand the reasons behind those changes more easily. Although we focus mainly on two predictors in this article, the conclusions can be easily extended to a general k-predictor case. [ABSTRACT FROM AUTHOR]