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Accelerated failure time models with nonlinear covariates effects. (English) Zbl 1117.62113

Summary: As a flexible alternative to the Cox model, the accelerated failure time (AFT) model assumes that the event time of interest depends on the covariates through a regression function. The AFT model with nonparametric covariate effects is investigated, when variable selection is desired along with estimation. Formulated in the framework of the smoothing spline analysis of variance model, the proposed method based on the W. Stute estimate [Consistent estimation under random censorship when covariables are present. J. Multivariate Anal. 45, No. 1, 89–103 (1993; Zbl 0767.62036)] can achieve a sparse representation of the functional decomposition, by utilizing a reproducing kernel Hilbert norm penalty. Computational algorithms and theoretical properties of the proposed method are investigated. The finite sample size performance of the proposed approach is assessed via simulation studies. The primary biliary cirrhosis data is analyzed for demonstration.

MSC:

62N05 Reliability and life testing
62G08 Nonparametric regression and quantile regression
62J10 Analysis of variance and covariance (ANOVA)
62G05 Nonparametric estimation
46N30 Applications of functional analysis in probability theory and statistics
65C60 Computational problems in statistics (MSC2010)
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 0767.62036

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