  Polygnicity refers to the phenomenon that multiple genetic variants have a
non-zero effect on a complex trait. It is defined as the proportion of genetic
variants that have a nonzero effect on the trait. Evaluation of polygenicity
can provide valuable insights into the genetic architecture of the trait.
Several recent works have attempted to estimate polygenicity at the SNP level.
However, evaluating polygenicity at the gene level can be biologically more
meaningful. We propose the notion of gene-level polygenicity, defined as the
proportion of genes having a non-zero effect on the trait under the framework
of transcriptome-wide association study. We introduce a Bayesian approach
polygene to estimate this quantity for a trait. The method is based on spike
and slab prior and simultaneously provides an optimal subset of non-null genes.
Our simulation study shows that polygene efficiently estimates gene-level
polygenicity. The method produces downward bias for small choices of trait
heritability due to a non-null gene, which diminishes rapidly with an increase
in the GWAS sample size. While identifying the optimal subset of non-null
genes, polygene offers a high level of specificity and an overall good level of
sensitivity -- the sensitivity increases as the sample size of the reference
panel expression and GWAS data increase. We applied the method to seven
phenotypes in the UK Biobank, integrating expression data. We find height to be
most polygenic and asthma to be the least polygenic. Our analysis suggests that
both HDL and triglycerides are more polygenic than LDL.
