🤖 AI Summary
When unobserved confounding affects the mediator, the natural path-specific effect (PSE) is generally non-identifiable, and the recanting-twin effect is commonly used as a proxy. This study establishes, for the first time, nonparametric sharp bounds on the absolute difference between these two effects for binary outcomes and systematically evaluates their agreement in magnitude, sign, and ranking. Leveraging causal path decomposition, bound derivation, and extensive Monte Carlo simulations across 320 configurations, we find that ranking discrepancies occur in 15%–56% of cases and sign disagreements in 5%–43%. The extent of disagreement is strongly influenced by the counterfactual correlation of the mediator, revealing notable limitations of the recanting-twin approximation in non-monotonic settings.
📝 Abstract
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.