🤖 AI Summary
This study addresses the non-identifiability of conventional single-index time-to-event models under unknown dependent censoring or competing risks. By introducing an exclusion restriction, the authors establish—within a nonparametric framework—the first identification result for the ratio of marginal covariate effects, thereby circumventing reliance on strong and untestable assumptions. The proposed nonparametric estimation approach is compatible with widely used semiparametric models, including Cox proportional hazards, accelerated failure time, and proportional odds models, and yields a suite of estimators applicable to general settings. Numerical experiments demonstrate that the method provides robust and efficient estimation of relative covariate effects even when the censoring mechanism is misspecified.
📝 Abstract
Single-index models or time-to-event models are frequently applied in empirical research. These models are non-identifiable in presence of unknown (dependent) censoring or competing risks and do not give informative results in empirical analysis unless rather strong, non-testable restrictions hold. Little is known, whether the known robustness properties of the single-index model carry over to models with dependent censoring or competing risks. This paper shows that the ratio of partial covariate effects on the margins is identifiable in nonparametric models with unknown dependent censoring or nonparametric competing risks models with nonparametric dependence structure, provided an exclusion restriction holds. Commonly used (semi)parametric models for the margin and independent censoring, such as Cox proportional hazards, accelerated failure time or proportional odds models, can be used to obtain relative covariate effects despite their misspecified censoring mechanism. Several nonparametric estimators for the general model are introduced and their numerical properties are studied.