Pitfalls in performing genome-wide association studies on ratio traits

Genome-wide association studies (GWASs) are often performed on ratios composed of a numerator trait divided by a denominator trait. Examples include body mass index (BMI) and the waist-to-hip ratio, among many others. Explicitly or implicitly, the goal of forming the ratio is typically to adjust for an association between the numerator and denominator. While forming ratios may be clinically expedient, there are several important issues with performing GWAS on ratios. Forming a ratio does not "adjust" for the denominator in the sense of conditioning on it, and it is unclear whether associations with ratios are attributable to the numerator, the denominator, or both. Here we demonstrate that associations arising in ratio GWAS can be entirely denominator driven, implying that at least some associations uncovered by ratio GWAS may be due solely to a putative adjustment variable. In a survey of 10 common ratio traits, we find that the ratio model disagrees with the adjusted model (performing GWAS on the numerator while conditioning on the denominator) at around 1/3 of loci. Using BMI as an example, we show that variants detected by only the ratio model are more strongly associated with the denominator (height), while variants detected by only the adjusted model are more strongly associated with the numerator (weight). Although the adjusted model provides effect sizes with a clearer interpretation, it is susceptible to collider bias. We propose and validate a simple method of correcting for the genetic component of collider bias via leave-one-chromosome-out polygenic scoring.