Figure 1.

Methods flowchart for UK Biobank: participant exclusion, analysis groupings and scheme for interaction analysis. FEM, fixed effects model; LRT, likelihood ratio test; REM, random effects model; G–C, genotype‐covariate; MRNM, multivariate reaction norm model; R–C, residual‐covariate; $N_{\mathit{\text{ik}}}$, sample size for analysis group i, subgroup $k$; ${\underset{\mathit{¯}}{\mathit{C}}}_{\mathit{\text{ij}}}$ (${\underset{\mathit{¯}}{\mathit{C}}}_{\mathit{\text{ijk}}}$), vector of length $N_{\mathit{i}}$ ($N_{\mathit{\text{ijk}}}$) containing the $j\mathrm{th}$ standardised residual covariate trait from analysis group $i$ (and subgroup $k$); ${\underset{\mathit{¯}}{\mathit{Y}}}_{\mathit{\text{ij}}}$ (${\underset{\mathit{¯}}{\mathit{Y}}}_{\mathit{\text{ijk}}}$), vector of length $N_{\mathit{i}}$ ($N_{\mathit{\text{ik}}}$) containing the standardised residual outcome trait for interaction analysis with ${\underset{\mathit{¯}}{\mathit{C}}}_{\mathit{\text{ij}}}$ (${\underset{\mathit{¯}}{\mathit{C}}}_{\mathit{\text{ijk}}}$); ${\underset{¯}{\alpha }}_{0\mathit{,}\mathit{\text{ijk}}}$ (${\underset{\mathit{¯}}{\mathit{\beta }}}_{0\mathit{,}\mathit{\text{ijk}}}$), random effects vector of length $N_{\mathit{\text{ik}}}$ representing the contribution to the outcome (covariate) trait for each individual from the homogeneous polygenic component; ${\underset{¯}{\tau }}_{0,\mathit{\text{ijk}}}$ (${\underset{¯}{\epsilon }}_{0,\mathit{\text{ijk}}}$), random effects vector of length $N_{\mathit{\text{ik}}}$ representing the contribution to the outcome (covariate) trait for each individual from the homogeneous residual component; ${\underset{¯}{\alpha }}_{1\mathit{,}\mathit{\text{ijk}}}$ (${\underset{¯}{\tau }}_{1,\mathit{\text{ijk}}}$), random effects vector of length $N_{\mathit{\text{ik}}}$ representing the contribution to the outcome trait for each individual due to G–C (R–C) interaction