Refutable Exclusion Restrictions in Competing Risks with Categorical Covariates
Abstract
Competing-risks data do not identify latent marginal duration distributions or their dependence without additional restrictions. This paper asks whether restrictions introduced to restore identification themselves restrict the observable law. For a two-risk Archimedean model with categorical exclusion restrictions, we derive a necessary-and-sufficient observable characterization. A discrete single-crossing argument identifies the scalar copula parameter from cell-specific overall survival probabilities, while cause indicators recover the remaining allocation and generate additional specification restrictions. We construct an identification-robust, self-normalized quadratic statistic, invert it to obtain confidence sets, and use empty inverted sets as a conservative specification test. Simulations show that the cause indicator can be decisive: under the weakest contrast considered it converts a frequently uninformative survival-based confidence set into an informative joint set without loss of coverage, whereas excessive categorical contrast can eliminate causes from individual cells and make cause-specific recovery inadmissible. The results turn latent exclusion restrictions into refutable restrictions without estimating covariate derivatives.
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BibTeX
@misc{akhmedov2026refutable,
title = {{Refutable Exclusion Restrictions in Competing Risks with Categorical Covariates}},
author = {Isfandiyor Akhmedov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28866},
eprint = {2609.28866},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28866},
}
RIS
TY - UNPB
TI - Refutable Exclusion Restrictions in Competing Risks with Categorical Covariates
AU - Isfandiyor Akhmedov
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28866
UR - https://arxiv.org/abs/2609.28866
AB - Competing-risks data do not identify latent marginal duration distributions or their dependence without additional restrictions. This paper asks whether restrictions introduced to restore identification themselves restrict the observable law. For a two-risk Archimedean model with categorical exclusion restrictions, we derive a necessary-and-sufficient observable characterization. A discrete single-crossing argument identifies the scalar copula parameter from cell-specific overall survival probabilities, while cause indicators recover the remaining allocation and generate additional specification restrictions. We construct an identification-robust, self-normalized quadratic statistic, invert it to obtain confidence sets, and use empty inverted sets as a conservative specification test. Simulations show that the cause indicator can be decisive: under the weakest contrast considered it converts a frequently uninformative survival-based confidence set into an informative joint set without loss of coverage, whereas excessive categorical contrast can eliminate causes from individual cells and make cause-specific recovery inadmissible. The results turn latent exclusion restrictions into refutable restrictions without estimating covariate derivatives.
ER -