  Recently more and more evidence suggests that rare variants with much lower
minor allele frequencies play significant roles in disease etiology. Advances
in next-generation sequencing technologies will lead to many more rare variants
association studies. Several statistical methods have been proposed to assess
the effect of rare variants by aggregating information from multiple loci
across a genetic region and testing the association between the phenotype and
aggregated genotype. One limitation of existing methods is that they only look
into the marginal effects of rare variants but do not systematically take into
account effects due to interactions among rare variants and between rare
variants and environmental factors. In this article, we propose the summation
of partition approach (SPA), a robust model-free method that is designed
specifically for detecting both marginal effects and effects due to gene-gene
(G-G) and gene-environmental (G-E) interactions for rare variants association
studies. SPA has three advantages. First, it accounts for the interaction
information and gains considerable power in the presence of unknown and
complicated G-G or G-E interactions. Secondly, it does not sacrifice the
marginal detection power; in the situation when rare variants only have
marginal effects it is comparable with the most competitive method in current
literature. Thirdly, it is easy to extend and can incorporate more complex
interactions; other practitioners and scientists can tailor the procedure to
fit their own study friendly. Our simulation studies show that SPA is
considerably more powerful than many existing methods in the presence of G-G
and G-E interactions.
