Represents the expanded causal network involving two traits and the various estimated causal paths from trait X of an index case ((X_{i})) to a phenotype Y in the partner ((Y_{p})) given by ω, γ and ρ. Cross-trait causal effects from (X_{i}) to (Y_{p}) (ω) can be summarized by three possible (non-independent) scenarios: (1) (X_{i}) could exert a causal effect on (X_{p}), followed by (X_{p}) having a causal effect on (Y_{p}) in the partner alone (γ); (2) the reverse could occur whereby (X_{i}) has a causal effect on (Y_{i}) in the index alone, followed by a causal effect of (Y_{i}) case on (Y_{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_{i}) on (Y_{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.
