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.

The simplest analysis of biomarker data is based on a series of single biomarker hypothesis tests, followed by correction for multiple testing. However, it is intuitively plausible that a joint analysis of multiple biomarkers will have higher statistical power and promise improved discrimination over tests based on single markers. In this article, we study analytical properties of the approach for joint analysis of correlated summary statistics based on the test for quadratic forms (TQ). Based on the derivation of the TQ-distribution, we proposed a scale-location approximation of the TQ statistic, which we call approximate TQ. We show that the approximate TQ has very similar power to the traditional TQ test under varying correlation structures among biomarkers. Our application of both the TQ and the approximate TQ test to data on biomarkers for inflamm-aging -an agerelated low-grade chronic inflammation -reveals an association between the percentage of IFNγ positive lymphocytes and overall muscle condition in senior horses.