Asymptotic tests of association with multiple SNPs in linkage disequilibrium

We consider detecting associations between a trait and multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium (LD). To maximize the use of information contained in multiple SNPs while minimizing the cost of large degrees of freedom (DF) in testing multiple parameters, we first theoretically explore the sum test derived under a working assumption of a common association strength between the trait and each SNP, testing on the corresponding parameter with only one DF. Under the scenarios that the association strengths between the trait and the SNPs are close to each other (and in the same direction), as considered by Wang and Elston [Am. J. Hum. Genet. [2007] 80:353-360], we show with simulated data that the sum test was powerful as compared to several existing tests; otherwise, the sum test might have much reduced power. To overcome the limitation of the sum test, based on our theoretical analysis of the sum test, we propose five new tests that are closely related to each other and are shown to consistently perform similarly well across a wide range of scenarios. We point out the close connection of the proposed tests to the Goeman test. Furthermore, we derive the asymptotic distributions of the proposed tests so that P-values can be easily calculated, in contrast to the use of computationally demanding permutations or simulations for the Goeman test. A distinguishing feature of the five new tests is their use of a diagonal working covariance matrix, rather than a full covariance matrix as used in the usual Wald or score test. We recommend the routine use of two of the new tests, along with several other tests, to detect disease associations with multiple linked SNPs.