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

TL;DR

This paper introduces a robust fusion-extraction method using summary statistics that remains consistent and reliable even when many data sources are biased, applicable across various fields like meta-analysis and Mendelian randomization.

Contribution

It proposes a new estimator that is robust to biased sources, easy to compute, and asymptotically equivalent to an oracle estimator under mild conditions.

Findings

Estimator is consistent despite biased sources.

Method performs well with diverging number of sources and parameters.

Simulation studies confirm robustness and oracle property.

Abstract

Information from various data sources is increasingly available nowadays. However, some of the data sources may produce biased estimation due to commonly encountered biased sampling, population heterogeneity, or model misspecification. This calls for statistical methods to combine information in the presence of biased sources. In this paper, a robust data fusion-extraction method is proposed. The method can produce a consistent estimator of the parameter of interest even if many of the data sources are biased. The proposed estimator is easy to compute and only employs summary statistics, and hence can be applied to many different fields, e.g. meta-analysis, Mendelian randomisation and distributed system. Moreover, the proposed estimator is asymptotically equivalent to the oracle estimator that only uses data from unbiased sources under some mild conditions. Asymptotic normality of the proposed estimator is also established. In contrast to the existing meta-analysis methods, the theoretical properties are guaranteed even if both the number of data sources and the dimension of the parameter diverge as the sample size increases, which ensures the performance of the proposed method over a wide range. The robustness and oracle property is also evaluated via simulation studies. The proposed method is applied to a meta-analysis data set to evaluate the surgical treatment for the moderate periodontal disease, and a Mendelian randomization data set to study the risk factors of head and neck cancer.