An Optimal Bahadur-Efficient Method in Detection of Sparse Signals with Applications to Pathway Analysis in Sequencing Association Studies

Next-generation sequencing data pose a severe curse of dimensionality, complicating traditional "single marker—single trait" analysis. We propose a two-stage combined p-value method for pathway analysis. The first stage is at the gene level, where we integrate effects within a gene using the Sequence Kernel Association Test (SKAT). The second stage is at the pathway level, where we perform a correlated Lancaster procedure to detect joint effects from multiple genes within a pathway. We show that the Lancaster procedure is optimal in Bahadur efficiency among all combined p-value methods. The Bahadur efficiency,limε→0N(2)/N(1)=ϕ12(θ), compares sample sizes among different statistical tests when signals become sparse in sequencing data, i.e. ε →0. The optimal Bahadur efficiency ensures that the Lancaster procedure asymptotically requires a minimal sample size to detect sparse signals (PN(i)