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Information from various data sources is increasingly available nowadays.However, some of the data sources may produce biased estimation due to commonlyencountered biased sampling, population heterogeneity, or modelmisspecification. This calls for statistical methods to combine information inthe presence of biased sources. In this paper, a robust data fusion-extractionmethod is proposed. The method can produce a consistent estimator of theparameter of interest even if many of the data sources are biased. The proposedestimator is easy to compute and only employs summary statistics, and hence canbe applied to many different fields, e.g. meta-analysis, Mendelianrandomisation and distributed system. Moreover, the proposed estimator isasymptotically equivalent to the oracle estimator that only uses data fromunbiased sources under some mild conditions. Asymptotic normality of theproposed estimator is also established. In contrast to the existingmeta-analysis methods, the theoretical properties are guaranteed even if boththe number of data sources and the dimension of the parameter diverge as thesample size increases, which ensures the performance of the proposed methodover a wide range. The robustness and oracle property is also evaluated viasimulation studies. The proposed method is applied to a meta-analysis data setto evaluate the surgical treatment for the moderate periodontal disease, and aMendelian randomization data set to study the risk factors of head and neckcancer.

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