Fig. 2: MR schematic within couples.

a, Illustrates the causal effect among couples with a single trait \((\alpha _{x_{\mathrm{i}} \to x_{\mathrm{p}}})\), where G represents genetic variant(s), X represents a single trait (in an index individual (X_i) and a partner (X_p)) and U represents confounding factors that are not associated with genetic variance owing to the random distribution of alleles at conception. Throughout the paper subscript i and p refer to the index and the partner, respectively. b, Directed acyclic graph illustrates the impact a confounder (trait Y) could have on the phenotypic correlation between partners for a given trait X (\(r_{x_{\mathrm{i}}x_{\mathrm{p}}}\)). Correlation due to confounding can be calculated as \(C = \alpha _{y \to x}^2 \times \alpha _y\). c, Represents the expanded causal network involving two traits and the various estimated causal paths from trait X of an index case (\(X_{\mathrm{i}}\)) to a phenotype Y in the partner (\(Y_{\mathrm{p}}\)) given by ω, γ and ρ. Cross-trait causal effects from \(X_{\mathrm{i}}\) to \(Y_{\mathrm{p}}\) (ω) can be summarized by three possible (non-independent) scenarios: (1) \(X_{\mathrm{i}}\) could exert a causal effect on \(X_{\mathrm{p}}\), followed by \(X_{\mathrm{p}}\) having a causal effect on \(Y_{\mathrm{p}}\) in the partner alone (γ); (2) the reverse could occur whereby \(X_{\mathrm{i}}\) has a causal effect on \(Y_{\mathrm{i}}\) in the index alone, followed by a causal effect of \(Y_{\mathrm{i}}\) case on \(Y_{\mathrm{p}}\) (ρ); or (3) there could be other mechanisms, either acting directly or through other unmeasured or unconsidered variables. To quantify ρ, we first estimated the causal effect of \(Y_{\mathrm{i}}\) on \(Y_{\mathrm{p}}\) in MVMR (not illustrated) to exclude any residual effect of X on phenotype Y from index to partner. These three scenarios could also act in some combination. Therefore, the ω estimate would capture the paths of γ, ρ and other mechanisms combined. In both a and c, cross-partner causal effects are given by blue arrows and same-person causal effects are given by green arrows.