Regularized Estimation for the Accelerated Failure Time Model

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Abstract
SummaryIn the presence of high‐dimensional predictors, it is challenging to develop reliable regression models that can be used to accurately predict future outcomes. Further complications arise when the outcome of interest is an event time, which is often not fully observed due to censoring. In this article, we develop robust prediction models for event time outcomes by regularizing the Gehan's estimator for the accelerated failure time (AFT) model (Tsiatis, 1996,Annals of Statistics18, 305–328) with least absolute shrinkage and selection operator (LASSO) penalty. Unlike existing methods based on the inverse probability weighting and the Buckley and James estimator (Buckley and James, 1979,Biometrika66, 429–436), the proposed approach does not require additional assumptions about the censoring and always yields a solution that is convergent. Furthermore, the proposed estimator leads to a stable regression model for prediction even if the AFT model fails to hold. To facilitate the adaptive selection of the tuning parameter, we detail an efficient numerical algorithm for obtaining the entire regularization path. The proposed procedures are applied to a breast cancer dataset to derive a reliable regression model for predicting patient survival based on a set of clinical prognostic factors and gene signatures. Finite sample performances of the procedures are evaluated through a simulation study.

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