cLD: Rare-variant linkage disequilibrium between genomic regions identifies novel genomic interactions

Linkage disequilibrium (LD) is a fundamental concept in genetics; critical for studying genetic associations and molecular evolution. However, LD measurements are only reliable for common genetic variants, leaving low-frequency variants unanalyzed. In this work, we introduce cumulative LD (cLD), a stable statistic that captures the rare-variant LD between genetic regions, which reflects more biological interactions between variants, in addition to lack of recombination. We derived the theoretical variance of cLD using delta methods to demonstrate its higher stability than LD for rare variants. This property is also verified by bootstrapped simulations using real data. In application, we find cLD reveals an increased genetic association between genes in 3D chromatin interactions, a phenomenon recently reported negatively by calculating standard LD between common variants. Additionally, we show that cLD is higher between gene pairs reported in interaction databases, identifies unreported protein-protein interactions, and reveals interacting genes distinguishing case/control samples in association studies. Linkage disequilibrium (LD) is a crucial concept in genetics, but current methods of measuring LD are not reliable for rare variants. In our study, we introduce a new statistic called cumulative LD (cLD) that captures the linkage disequilibrium between genetic regions containing rare variants, which are often unanalyzed. We demonstrate that cLD is a stable statistic and show through simulations using real data that it is more reliable than traditional LD for rare variants.Our findings show that cLD is a valuable tool for studying genetic associations and molecular evolution. We use cLD to reveal increased genetic association between genes in 3D chromatin interactions, which standard LD failed to detect. Additionally, we show that cLD identifies unreported protein-protein interactions and distinguishes case/control samples in association studies. Our work is significant because it provides a stable and reliable method for analyzing rare variants, which were previously overlooked due to unreliable LD measurements. Our findings have implications for future genetic association studies and molecular evolution research, particularly in understanding rare variant interactions and their biological significance.