NDLI: A tutorial on rank-based coefficient estimation for censored data in small- and large-scale problems

Content Provider	Springer Nature Link
Author	Chung, Matthias Long, Qi Johnson, Brent A.
Copyright Year	2012
Abstract	The analysis of survival endpoints subject to right-censoring is an important research area in statistics, particularly among econometricians and biostatisticians. The two most popular semiparametric models are the proportional hazards model and the accelerated failure time (AFT) model. Rank-based estimation in the AFT model is computationally challenging due to optimization of a non-smooth loss function. Previous work has shown that rank-based estimators may be written as solutions to linear programming (LP) problems. However, the size of the LP problem is O(n $^{2}$+p) subject to n $^{2}$ linear constraints, where n denotes sample size and p denotes the dimension of parameters. As n and/or p increases, the feasibility of such solution in practice becomes questionable. Among data mining and statistical learning enthusiasts, there is interest in extending ordinary regression coefficient estimators for low-dimensions into high-dimensional data mining tools through regularization. Applying this recipe to rank-based coefficient estimators leads to formidable optimization problems which may be avoided through smooth approximations to non-smooth functions. We review smooth approximations and quasi-Newton methods for rank-based estimation in AFT models. The computational cost of our method is substantially smaller than the corresponding LP problem and can be applied to small- or large-scale problems similarly. The algorithm described here allows one to couple rank-based estimation for censored data with virtually any regularization and is exemplified through four case studies.
Starting Page	601
Ending Page	614
Page Count	14
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	23
Issue Number	5
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2012-05-26
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Accelerated failure time model Ill-posed problems Regularization Survival analysis Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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