A robust fusion-extraction procedure with summary statistics in the presence of biased sources

Summary Information from multiple data sources is increasingly available. However, some may produce biased estimates due to sampling, corruption or model misspecification. Thus there a need for robust combination methods that can be used with sources. In this paper, fusion-extraction method proposed. Unlike existing methods, the proposed applied in important case where researchers have no knowledge of which are unbiased. The estimator easy compute and employs only summary statistics; hence it many different fields, such as meta-analysis, Mendelian randomization distributed systems. consistent, even if biased, asymptotically equivalent oracle uses unbiased data. Asymptotic normality also established. contrast meta-analysis theoretical properties guaranteed our estimator, number dimension parameter diverge sample size increases. Furthermore, provides consistent selection probability approaching 1. Simulation studies demonstrate efficiency robustness empirically. dataset evaluate surgical treatment moderate periodontal disease study risk factors head neck cancer.