# DOT: Gene-set analysis by combining decorrelated association statistics

## TL;DR

This paper introduces DOT, a decorrelation method for gene-set analysis that significantly improves power over traditional sum-of-squares tests, especially in heterogeneous genetic data, demonstrated through breast cancer data analysis.

## Contribution

The paper proposes a novel decorrelation approach for gene-set analysis that enhances statistical power in complex genetic datasets compared to traditional methods.

## Key findings

- DOT yields higher power than traditional methods in diverse LD and effect size scenarios.
- Theoretical analysis explains the power gains of DOT over sum of squared scores.
- Application to breast cancer data reveals new potential genetic associations.

## Abstract

Historically, the majority of statistical association methods have been designed assuming availability of SNP-level information. However, modern genetic and sequencing data present new challenges to access and sharing of genotype-phenotype datasets, including cost management, difficulties in consolidation of records across research groups, etc. These issues make methods based on SNP-level summary statistics for a joint analysis of variants in a group particularly appealing. The most common form of combining statistics is a sum of SNP-level squared scores, possibly weighted, as in burden tests for rare variants. The overall significance of the resulting statistic is evaluated using its distribution under the null hypothesis. Here, we demonstrate that this basic approach can be substantially improved by decorrelating scores prior to their addition, resulting in remarkable power gains in situations that are most commonly encountered in practice; namely, under heterogeneity of effect sizes and diversity between pairwise LD. In these situations, the power of the traditional test, based on the added squared scores, quickly reaches a ceiling, as the number of variants increases. Thus, the traditional approach does not benefit from information potentially contained in any additional SNPs, while our decorrelation by orthogonal transformation (DOT) method yields steady gain in power. We present theoretical and computational analyses of both approaches, and reveal causes behind sometimes dramatic difference in their respective powers. We showcase DOT by analyzing breast cancer data, in which our method strengthened levels of previously reported associations and implied the possibility of multiple new alleles that jointly confer breast cancer risk.