A New Functional F-Statistic for Gene-Based Inference Involving Multiple Phenotypes

Genetic pleiotropy is the phenomenon where a single gene or genetic variant influences multiple traits. Numerous statistical methods exist for testing for genetic pleiotropy at the variant level, but fewer methods are available for testing genetic pleiotropy at the gene-level. In the current study, we derive an exact alternative to the Shen and Faraway functional F-statistic for functional-on-scalar regression models. Through extensive simulation studies, we show that this exact alternative performs similarly to the Shen and Faraway F-statistic in gene-based, multi-phenotype analyses and both F-statistics perform better than existing methods in small sample, modest effect size situations. We then apply all methods to real-world, neurodegenerative disease data and identify novel associations.