Figure 1.

Causal directed acyclic graphs for linear data-generating models with one-sided exposure-to-outcome sibling spillover. Subscripts i and j denote family and sibling, respectively. T_ij is the exposure, Y_ij is the outcome, D_i is the gain-score, and U_i is an unobserved family-level confounder. Greek letters denote effects. (1A) does not have exposure-to-exposure spillover, whereas (1B) and (1C) have exposure-to-exposure spillovers. The gain-score method precisely identifies the spillover effect θ (T_i1 → Y_i2) in all three models.