Statistics and Computing

, Volume 23, Issue 6, pp 713–725

Efficient computation of nonparametric survival functions via a hierarchical mixture formulation



We propose a new algorithm for computing the maximum likelihood estimate of a nonparametric survival function for interval-censored data, by extending the recently-proposed constrained Newton method in a hierarchical fashion. The new algorithm makes use of the fact that a mixture distribution can be recursively written as a mixture of mixtures, and takes a divide-and-conquer approach to break down a large-scale constrained optimization problem into many small-scale ones, which can be solved rapidly. During the course of optimization, the new algorithm, which we call the hierarchical constrained Newton method, can efficiently reallocate the probability mass, both locally and globally, among potential support intervals. Its convergence is theoretically established based on an equilibrium analysis. Numerical study results suggest that the new algorithm is the best choice for data sets of any size and for solutions with any number of support intervals.


Nonparametric maximum likelihood Survival function Interval censoring Clinical trial Constrained Newton method Disease-free survival 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of StatisticsThe University of AucklandAucklandNew Zealand
  2. 2.Auckland University of TechnologyAucklandNew Zealand

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