Meta‐analysis with sample‐standardization in multi‐site studies.

Purpose: To conceptualize a particular target population and estimand for multi‐site pharmacoepidemiologic studies within data networks and to analytically examine sample‐standardization as a meta‐analytic method compared with inverse‐variance weighted meta‐analyses. Methods: The target population of interest is all and only all individuals from the data‐contributing sites. Standardization, a general conditioning technique frequently employed for confounding control, was adopted to estimate the network‐wide causal treatment effect. Specifically, the proposed sample‐standardization yields a meta‐analysis estimator, that is, a weighted summation of site‐specific results, where the weight for a site is the proportion of its size in the entire network. This sample‐standardization estimator was evaluated analytically in comparison to estimators from inverse‐variance weighted fixed‐effect and random‐effects meta‐analyses in terms of statistical consistency. Results: A proof is reported to justify the consistency of the sample‐standardization estimator with and without treatment effect heterogeneity by site. Both inverse‐variance weighted fixed‐effect and random‐effects meta‐analyses were found to generally result in inconsistent estimators in the presence of treatment effect heterogeneity by site for this particular target population and estimand. Conclusions: Sample‐standardization is a valid approach to generate causal inference in multi‐site studies when the target population comprises all and only all individuals within the network, even in the presence of heterogeneity of treatment effect by site. Multi‐site studies should clearly specify the target population and estimand to help select the most appropriate meta‐analytic methods. [ABSTRACT FROM AUTHOR]