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An adaptive and robust method for multi-trait analysis of genome-wide association studies using summary statistics


Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with human traits or diseases in the past decade. Nevertheless, much of the heritability of many traits is still unaccounted for. Commonly used single-trait analysis methods are conservative, while multi-trait methods improve statistical power by integrating association evidence across multiple traits. In contrast to individual-level data, GWAS summary statistics are usually publicly available, and thus methods using only summary statistics have greater usage. Although many methods have been developed for joint analysis of multiple traits using summary statistics, there are many issues, including inconsistent performance, computational inefficiency, and numerical problems when considering lots of traits. To address these challenges, we propose a multi-trait adaptive Fisher method for summary statistics (MTAFS), a computationally efficient method with robust power performance. We applied MTAFS to two sets of brain imaging derived phenotypes (IDPs) from the UK Biobank, including a set of 58 Volumetric IDPs and a set of 212 Area IDPs. Through annotation analysis, the underlying genes of the SNPs identified by MTAFS were found to exhibit higher expression and are significantly enriched in brain-related tissues. Together with results from a simulation study, MTAFS shows its advantage over existing multi-trait methods, with robust performance across a range of underlying settings. It controls type 1 error well and can efficiently handle a large number of traits.

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Fig. 1: Power comparison and ROC curves of UKCOR1 and M1.
Fig. 2: Power comparison and ROC curves of UKCOR1 and M2.
Fig. 3: Analysis results of the 58 Volumetric IDPs.

Data availability

The author states that all data necessary for confirming the conclusions presented in the article are represented fully within the article. The UK Biobank summary statistics are available in the

Code availability

The software for our proposed method MTAFS is available at All results for the real data analyses are at


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We would like to thank the Section Editor and two anonymous reviewers for their valuable comments and suggestions. We would also like to acknowledge the Ohio Supercomputer Center for providing resources that have contributed to the research results reported within this paper.


This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations



QD conceived the study design, performed analyses, developed methodology and drafted the manuscript. CS and SL provided extensive feedback regarding the study design, methodology and analyses, and revised the manuscript.

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Correspondence to Shili Lin.

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The authors declare no competing interests.

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The UK Biobank brain imaging data ( were publicly available without identifying information.

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Deng, Q., Song, C. & Lin, S. An adaptive and robust method for multi-trait analysis of genome-wide association studies using summary statistics. Eur J Hum Genet (2023).

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