The critical barrier in interaction analysis for rare variants is that most traditional statistical methods for testing interactions were originally designed for testing the interaction between common variants and are difficult to apply to rare variants because of their prohibitive computational time and poor ability. The great challenges for successful detection of interactions with next-generation sequencing (NGS) data are (1) lack of methods for interaction analysis with rare variants, (2) severe multiple testing, and (3) time-consuming computations. To meet these challenges, we shift the paradigm of interaction analysis between two loci to interaction analysis between two sets of loci or genomic regions and collectively test interactions between all possible pairs of SNPs within two genomic regions. In other words, we take a genome region as a basic unit of interaction analysis and use high-dimensional data reduction and functional data analysis techniques to develop a novel functional regression model to collectively test interactions between all possible pairs of single nucleotide polymorphisms (SNPs) within two genome regions. By intensive simulations, we demonstrate that the functional regression models for interaction analysis of the quantitative trait have the correct type 1 error rates and a much better ability to detect interactions than the current pairwise interaction analysis. The proposed method was applied to exome sequence data from the NHLBI's Exome Sequencing Project (ESP) and CHARGE-S study. We discovered 27 pairs of genes showing significant interactions after applying the Bonferroni correction (P-values < 4.58 × 10) in the ESP, and 11 were replicated in the CHARGE-S study
