Right-censored competing-risks extension

Develop and validate an extension of the categorical-exclusion Archimedean competing-risks identification and inference procedure to independently right-censored observations, including recomputation of the effective-size and largest-observation diagnostics for censored influence functions and a separate finite-sample analysis.

Background

The paper’s analysis assumes complete observation of the competing-risks duration and cause. It notes that independent right censoring should preserve the population cross-difference identification logic, while changing estimation, influence functions, and the usable time horizon.

Under right censoring, cell survival and cause-specific cumulative incidence could be estimated using Kaplan–Meier and Aalen–Johansen methods, with martingale influence functions propagated through the finite-dimensional moment map. However, inverse censoring survival weights interact with the generator-induced tail behavior, potentially shrinking the admissible cause-specific horizon. The paper therefore leaves the development and finite-sample validation of this censored-data extension unresolved.

References

This extension is not mechanically innocuous. Inverse censoring survival enters the influence functions and multiplies the generator-induced tail load. The admissible cause-specific horizon may therefore contract more than suggested by event survival alone, especially in portfolios with many recent entries and a common administrative extraction date: the distribution of contract inception dates determines the censoring survival G_c, which can fall rapidly in a fast-growing portfolio. The effective-size and largest-observation diagnostics must be recomputed for the censored influence functions; values calibrated under complete observation cannot be carried over. Developing and validating this extension is left for subsequent work rather than appended without a separate finite-sample analysis.

— Refutable Exclusion Restrictions in Competing Risks with Categorical Covariates  (2609.28866 - Akhmedov, 24 Sep 2026) in Section 5.5, “Right censoring”