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

ABSTRACT

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).

KEYWORDS:

• Interval-censored data
• Linear order constraints
• Non-parametric maximum likelihood estimator
• Quadratic programming
• Stochastic ordering

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N02
• 62G99