Efficient Computation of Nonparametric Survival Functions Via a Hierarchical Mixture Formulation

Date
2013
Authors
Wang, Y
Taylor, SM
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract

We propose a new algorithm for computingthe maximum likelihood estimate of a nonparametric survivalfunction for interval-censored data, by extending therecently-proposed constrained Newton method in a hierarchicalfashion. The new algorithm makes use of the fact thata mixture distribution can be recursively written as a mixtureof mixtures, and takes a divide-and-conquer approach tobreak down a large-scale constrained optimization probleminto many small-scale ones, which can be solved rapidly.During the course of optimization, the new algorithm, whichwe call the hierarchical constrained Newton method, can efficientlyreallocate the probability mass, both locally andglobally, among potential support intervals. Its convergenceis theoretically established based on an equilibrium analysis.Numerical study results suggest that the new algorithmis the best choice for data sets of any size and for solutionswith any number of support intervals.

Description
Keywords
Nonparametric maximum likelihood , Survival function , Interval censoring , Clinical trial , Constrained Newton method , Disease-free survival
Source
Statistics and Computing, 23(6), 713-725.
Rights statement
Authors may self-archive the author’s accepted manuscript of their articles on their own websites. Authors may also deposit this version of the article in any repository, provided it is only made publicly available 12 months after official publication or later. He/ she may not use the publisher's version (the final article), which is posted on SpringerLink and other Springer websites, for the purpose of self-archiving or deposit. Furthermore, the author may only post his/her version provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website.