On set-based association tests: Insights from a regression using summary statistics

Motivated by, but not limited to, association analyses of multiple genetic variants, we propose here a summary statistics-based regression framework. The proposed method requires only variant-specific summary statistics, and it unifies earlier methods based on individual-level data as special cases. The resulting score test statistic, derived from a linear mixed-effect regression model, inherently transforms the variant-specific statistics using the precision matrix to improve power for detecting sparse alternatives. Furthermore, the proposed method can incorporate additional variant-specific information with ease, facilitating omic-data integration. We study the asymptotic properties of the proposed tests under the null and alternatives, and we investigate efficient P-value calculation in finite samples. Finally, we provide supporting empirical evidence from extensive simulation studies and two applications.