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  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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Efficient Computation of Nonparametric Survival Functions Via a Hierarchical Mixture Formulation

Wang, Y; Taylor, SM
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http://hdl.handle.net/10292/10711
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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.
Keywords
Nonparametric maximum likelihood; Survival function; Interval censoring; Clinical trial; Constrained Newton method; Disease-free survival
Date
2013
Source
Statistics and Computing, 23(6), 713-725.
Item Type
Journal Article
Publisher
Springer
DOI
10.1007/s11222-012-9341-9
Publisher's Version
https://link.springer.com/article/10.1007%2Fs11222-012-9341-9
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.

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