A tutorial on the inheritance procedure for multiple testing of tree-structured hypotheses

In a candidate gene association study the goal is to find associations between a trait of interest and genetic variation at markers, such as single-nucleotide polymorphisms, or SNPs. SNPs are grouped within candidate genes thought to influence the trait. Such grouping imposes a tree structure on the hypotheses, with hypotheses about single-SNP associations nested within gene-based associations. In this project we give a tutorial on the inheritance procedure, a powerful new method for testing tree-structured hypotheses. We define sequentially rejective procedures and show that the inheritance procedure is a sequentially rejective procedure that strongly controls the family-wise error rate under so-called monotonicity and single step conditions. We also show how to further improve power by taking advantage of the logical implications among the nested hypotheses. The resulting testing strategy enables more powerful detection of gene- and SNP-based associations, while controlling the chance of incorrectly claiming that such associations exist.