Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions

In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have c...

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Bibliographic Details
Published in:Biometrika 2012-06, Vol.99 (2), p.327-343
Main Authors: PARK, YONGSEOK, TAYLOR, JEREMY M. G., KALBFLEISCH, JOHN D.
Format: Article
Language:English
Subjects:
Algorithms
Applications
Asymptotic methods
Biology, psychology, social sciences
Bootstrap resampling
Censorship
Confidence interval
Data processing
Estimation methods
Estimators
Exact sciences and technology
General topics
Kaplan Meier estimator
Mathematical functions
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
Maximum likelihood method
Multivariate analysis
Nonparametric inference
Parameter estimation
Probability and statistics
Prostate cancer
Reliability functions
Sample size
Sciences and techniques of general use
Statistics
Stochastic models
Stochasticity
Studies
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Summary:In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method.
ISSN:0006-3444
1464-3510
1464-3510
0006-3444
DOI:10.1093/biomet/ass006