Permutation methods for assessing significance in binary trait association mapping with structured samples

In genetic association analysis of complex traits, permutation testing can be a valuable tool for assessing significance when the asymptotic distribution of the test statistic is unknown or not well-approximated. This commonly arises when the association test statistic is itself a function of multiple correlated statistics. e.g, in tests of gene-set, pathway or genome-wide significance, as well as omnibus tests that combine test statistics that perform well in different scenarios. For genetic association testing in samples with population structure and/or relatedness, use of naive permutation can lead to inflated type 1 error. To address this in quantitative traits, the MVNpermute method was developed. However, for association mapping of a binary trait, the relationship between the mean and variance makes both naive permutation and the MVNpermute method invalid. We propose BRASS, a permutation method for binary trait association mapping in samples that have related individuals and/or population structure. BRASS allows for covariates ascertainment andsimultaneous testing of multiple markers, and it accommodates a wide range of test statistics. We use an estimating equation approach that can be viewed as a hybrid of logistic regression and linear mixed-effects model methods, and we use a combination of principal components and a genetic relatedness matrix to account for sample structure. We show in simulation studies that BRASS maintains correct control of type 1 error in a range of scenarios that include population structure, familial relatedness, ascertainment and phenotype model misspecification. In these settings, only BRASS maintains correct control of type 1 error, performing far better than all other methods. We apply BRASS to two genome-wide analyses in domestic dog, one for elbow dysplasia (ED) in 82 breeds and another for idiopathic epilepsy (IE) in the Irish Wolfhound breed. We detect significant association of IE with SNPs in a previously-identified chromosome 4 region that contains multiple candidate genes.Author summaryPermutation testing is commonly used when distributional assumptions cannot be made or do not apply, or when performing a multiple testing correction, e.g., to assess region-wide or genome-wide significance in association mapping studies. Naively permuting the data is only valid under the assumption of exchangeability, which, in the presence of sample structure and polygenicity, typically does not hold. Linear mixed-model based approaches have been proposed for permutation-based tests with continuous traits that can also adjust for sample structure; however, these may not remain valid when applied to binary traits, as key features of binary data are not well accounted for. We propose BRASS, a permutation-based testing method for binary data that incorporates important characteristics of binary data in the trait model, can accommodate relevant covariates and ascertainment, and adjusts for the presence of structure in the sample. We demonstrate the use of this approach in the context of correcting for multiple testing in two genome-wide association studies in domestic dog: one for elbow dysplasia and one for idiopathic epilepsy.