  In modern scientific studies, it is often imperative to determine whether a
set of phenotypes is affected by a single factor. If such an influence is
identified, it becomes essential to discern whether this effect is contingent
upon categories such as sex or age group, and importantly, to understand
whether this dependence is rooted in purely non-environmental reasons. The
exploration of such dependencies often involves studying pleiotropy, a
phenomenon wherein a single genetic locus impacts multiple traits. This
heightened interest in uncovering dependencies by pleiotropy is fueled by the
growing accessibility of summary statistics from genome-wide association
studies (GWAS) and the establishment of thoroughly phenotyped sample
collections. This advancement enables a systematic and comprehensive
exploration of the genetic connections among various traits and diseases.
additive genetic correlation illuminates the genetic connection between two
traits, providing valuable insights into the shared biological pathways and
underlying causal relationships between them. In this paper, we present a novel
method to analyze such dependencies by studying additive genetic correlations
between pairs of traits under consideration. Subsequently, we employ matrix
comparison techniques to discern and elucidate sex-specific or
age-group-specific associations, contributing to a deeper understanding of the
nuanced dependencies within the studied traits. Our proposed method is
computationally handy and requires only GWAS summary statistics. We validate
our method by applying it to the UK Biobank data and present the results.
