Assess treatment–mediator interaction and conditional independent censoring in the illustrative UDCA analysis

Determine whether an interaction exists between Ursodeoxycholic acid treatment and histological progression, and whether censoring is independent conditional on the covariates included in the illustrative mediation analysis of liver transplant-free survival in primary biliary cholangitis patients.

Background

The illustrative analysis estimates direct and indirect effects of Ursodeoxycholic acid on liver transplant-free survival through time-dependent histological progression. The authors note that the small sample size prevented reliable assessment of several assumptions relevant to both the difference method and the parametric mediational g-formula.

In particular, the presence of treatment–mediator interaction and the validity of conditional independent censoring were not investigated. Either issue could bias the estimated mediation effects and could help explain why the two methods produced similar estimates in the example.

References

Further, we were unable to investigate whether an interaction between UDCA and histological progression is present, or whether censoring truly is independent, conditional on the included covariates.

— Causal Mediation Analysis with a Time-Dependent Mediator, Time-Dependent Confounders and a Time-to-Event Outcome: Revisiting the Difference Method  (2608.13094 - Denz et al., 13 Aug 2026) in Results for the motivating example, Section 5