On the magnitude, sign and ranking of recanting-twin path-specific effects

The framework of recanting twin path-specific effects has recently been propose to address the issue of intermediate confounding in causal mediation analysis, enabling the decomposition of the average treatment effect into identifiable fine-grained path-specific effects (PSEs). An open question, however, is the extent to which recanting-twin PSEs reflect the direction and relative magnitude of their corresponding natural PSEs. In this paper, we systematically characterize the behaviors of the recanting-twin PSEs in terms of magnitude, sign and ranking, benchmarking against natural PSEs. To achieve this, we first derive non-parametric, identifiable upper and lower bounds for the absolute difference between recanting-twin and natural PSEs in binary outcome settings. These bounds provide a practical way to assess whether discrepancies in magnitude between the two types of effects are substantial, thereby facilitating the use of recanting-twin PSEs as informative approximations of their natural counterparts. A simulation study is then conducted to evaluate frequency of disagreements in sign and ranking between recanting-twin and natural effects in non-linear, non-monotonic scenarios. Across four scenarios and 320 numerical settings, we find that disagreement ranges from 15% to 56% for ranking and from 5% to 43% for sign. Disagreement is strongly influenced by the non-observable correlation between counterfactual values of the intermediate confounder, suggesting that caution is needed when interpreting the magnitude and ranking of recanting-twin PSEs, and motivating future work to identify conditions under which the two types of PSEs yield consistent conclusions when non-monotonicity presents.