A general algorithm for non-parametric maximum likelihood estimator of stochastically ordered survival functions from case 2 interval-censored data

• Published in: Communications in statistics. Simulation and computation Vol. 48; no. 3; pp. 807 - 818
• Main Authors: Son, W., Kim, Y., Lim, J., Kuo, H.-C.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 16.03.2019; Taylor & Francis Ltd
• Subjects: Algorithms; Economic models; Interval-censored data; Linear order constraints; Maximum likelihood estimators; Monte Carlo simulation; Non-parametric maximum likelihood estimator; Nonparametric statistics; Quadratic equations; Quadratic programming; Regression analysis; Stochastic ordering; Survival
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2017.1400052

In this paper, we study an algorithm to compute the non-parametric maximum likelihood estimator of stochastically ordered survival functions from case 2 interval-censored data. The algorithm, simply denoted by SQP (sequential quadratic programming), re-parameterizes the likelihood function to make the order constraints as a set of linear constraints, approximates the log-likelihood function as a quadratic function, and updates the estimate by solving a quadratic programming. We particularly consider two stochastic orderings, simple and uniform orderings, although the algorithm can also be applied to many other stochastic orderings. We illustrate the algorithm using the breast cancer data reported in Finkelstein and Wolfe ( 1985 ).