Open Access Methodology article

Properties of permutation-based gene tests and controlling type 1 error using a summary statistic based gene test

David M Swanson1*, Deborah Blacker2, Taofik AlChawa3, Kerstin U Ludwig34, Elisabeth Mangold3 and Christoph Lange15

Author Affiliations

1 Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts

2 Departments of Psychiatry and Epidemiology, Massachusetts General Hospital, Boston, Massachusetts

3 Institute of Human Genetics, University of Bonn, Bonn, Germany

4 Department of Genomics, Life and Brain Center, University of Bonn, Bonn, Germany

5 Institute for Genomic Mathematics; German Center for Neurodegenerative Diseases, University of Bonn, Bonn, Germany

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BMC Genetics 2013, 14:108  doi:10.1186/1471-2156-14-108

Published: 7 November 2013



The advent of genome-wide association studies has led to many novel disease-SNP associations, opening the door to focused study on their biological underpinnings. Because of the importance of analyzing these associations, numerous statistical methods have been devoted to them. However, fewer methods have attempted to associate entire genes or genomic regions with outcomes, which is potentially more useful knowledge from a biological perspective and those methods currently implemented are often permutation-based.


One property of some permutation-based tests is that their power varies as a function of whether significant markers are in regions of linkage disequilibrium (LD) or not, which we show from a theoretical perspective. We therefore develop two methods for quantifying the degree of association between a genomic region and outcome, both of whose power does not vary as a function of LD structure. One method uses dimension reduction to “filter” redundant information when significant LD exists in the region, while the other, called the summary-statistic test, controls for LD by scaling marker Z-statistics using knowledge of the correlation matrix of markers. An advantage of this latter test is that it does not require the original data, but only their Z-statistics from univariate regressions and an estimate of the correlation structure of markers, and we show how to modify the test to protect the type 1 error rate when the correlation structure of markers is misspecified. We apply these methods to sequence data of oral cleft and compare our results to previously proposed gene tests, in particular permutation-based ones. We evaluate the versatility of the modification of the summary-statistic test since the specification of correlation structure between markers can be inaccurate.


We find a significant association in the sequence data between the 8q24 region and oral cleft using our dimension reduction approach and a borderline significant association using the summary-statistic based approach. We also implement the summary-statistic test using Z-statistics from an already-published GWAS of Chronic Obstructive Pulmonary Disorder (COPD) and correlation structure obtained from HapMap. We experiment with the modification of this test because the correlation structure is assumed imperfectly known.

Dimension reduction; Eigenvector; Gene-based testing; Permutation tests