Genotype–covariate correlation and interaction disentangled by a whole-genome multivariate reaction norm model

The genomics era has brought useful tools to dissect the genetic architecture of complex traits. Here we propose a multivariate reaction norm model (MRNM) to tackle genotype–covariate (G–C) correlation and interaction problems. We apply MRNM to the UK Biobank data in analysis of body mass index using smoking quantity as a covariate, finding a highly significant G–C correlation, but only weak evidence for G–C interaction. In contrast, G–C interaction estimates are inflated in existing methods. It is also notable that there is significant heterogeneity in the estimated residual variances (i.e., variances not attributable to factors in the model) across different covariate levels, i.e., residual–covariate (R–C) interaction. We also show that the residual variances estimated by standard additive models can be inflated in the presence of G–C and/or R–C interactions. We conclude that it is essential to correctly account for both interaction and correlation in complex trait analyses.