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Family-based tests of association between a genetic marker and a disease constitute a common design to dissect the genetic architecture of complex traits. The FBAT software is one of the most popular tools to perform such studies. However, researchers are also often interested in the genetic contribution to a more specific manifestation of the phenotype (e.g. severe vs. non-severe form) known as a secondary outcome. Here, what we demonstrate is the limited power of the classical formulation of the FBAT statistic to detect the effect of genetic variants that influence a secondary outcome, in particular when these variants also impact on the onset of the disease, the primary outcome. We prove that this loss of power is driven by an implicit hypothesis, and we propose a derivation of the original FBAT statistic, free from this implicit hypothesis. Finally, we demonstrate analytically that our new statistic is robust and more powerful than FBAT for the detection of association between a genetic variant and a secondary outcome.

Implicit Hypotheses Are Hidden Power Droppers in Family-Based Association Studies of Secondary Outcomes