Generalized M-estimation for the accelerated failure time model

Abstract

The accelerated failure time (AFT) model is an important regression tool to study the association between failure time and covariates. In this paper, we propose a robust weighted generalized M (GM) estimation for the AFT model with right-censored data by appropriately using the Kaplan–Meier weights in the GM–type objective function to estimate the regression coefficients and scale parameter simultaneously. This estimation method is computationally simple and can be implemented with existing software. Asymptotic properties including the root-n consistency and asymptotic normality are established for the resulting estimator under suitable conditions. We further show that the method can be readily extended to handle a class of nonlinear AFT models. Simulation results demonstrate satisfactory finite sample performance of the proposed estimator. The practical utility of the method is illustrated by a real data example.

Keywords:

• accelerated failure time model
• generalized M-estimator
• influence function
• Kaplan–Meier weights
• right censoring
• robustness

Acknowledgements

We are grateful to Editor Prof. Roland Fried, an Associate Editor and two anonymous referees for their very constructive comments and suggestions which helped improve the paper greatly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Wang's research is supported by a grant for Young Ph.D. Researchers from CUFE (QBJ1423). Hu's research is partially supported by the Natural Science Foundation of China (11201317, 11371062). Xiang's research is partially supported by the Singapore MOE AcRF (RG30/12, ARC29/14).