Abstract
This paper considers regression models with censored data where the dependent variable T and the censoring variable C are both assumed to follow a multi-index structure with the covariates. An iterative and structure-adaptive procedure is proposed to estimate the sufficient dimension reduction (SDR) spaces for T and C, as well as their joint SDR space, simultaneously. A cross-validation procedure is used to determine the structural dimensions of the individual SDR spaces. Simulation study shows that in terms of estimation efficiency, the proposed method is comparable to parametric models such as the Cox proportional hazards model when the latter is supposed to benefit from correct model specification, and outperforms the latter otherwise. When applied to the popular primary biliary cirrhosis data, the new approach is able to identify an important predictor for the patients’ survival time, which has long been noted by clinicians as a critical indicator but has so far not been picked up by existing statistical analysis.
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