  Studying phenotype-gene association can uncover mechanism of diseases and
develop efficient treatments. In complex disease where multiple phenotypes are
available and correlated, analyzing and interpreting associated genes for each
phenotype respectively may decrease statistical power and lose intepretation
due to not considering the correlation between phenotypes. The typical
approaches are many global testing methods, such as multivariate analysis of
variance (MANOVA), which tests the overall association between phenotypes and
each gene, without considersing the heterogeneity among phenotypes. In this
paper, we extend and evaluate two p-value combination methods, adaptive
weighted Fisher's method (AFp) and adaptive Fisher's method (AFz), to tackle
this problem, where AFp stands out as our final proposed method, based on
extensive simulations and a real application. Our proposed AFp method has three
advantages over traditional global testing methods. Firstly, it can consider
the heterogeneity of phenotypes and determines which specific phenotypes a gene
is associated with, using phenotype specific 0-1 weights. Secondly, AFp takes
the p-values from the test of association of each phenotype as input, thus can
accommodate different types of phenotypes (continuous, binary and count).
Thirdly, we also apply bootstrapping to construct a variability index for the
weight estimator of AFp and generate a co-membership matrix to categorize
(cluster) genes based on their association-patterns for intuitive biological
investigations. Through extensive simulations, AFp shows superior performance
over global testing methods in terms of type I error control and statistical
power, as well as higher accuracy of 0-1 weights estimation over AFz. A real
omics application with transcriptomic and clinical data of complex lung
diseases demonstrates insightful biological findings of AFp.
