Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions

• Published in: Biometrika Vol. 99; no. 2; p. 327
• Main Authors: Park, Yongseok, Taylor, Jeremy M G, Kalbfleisch, John D
• Format: Journal Article
• Language: English
• Published: England 01.06.2012
• Subjects: Censored data; Maximum likelihood estimator; Kaplan–Meier estimator; Constrained nonparametric maximum likelihood estimator; Order restriction
• ISSN: 0006-3444
• DOI: 10.1093/biomet/ass006

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 by the estimates of the survivor functions subject to constraints applied at time only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in , 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.