Generalized case-cohort analysis for constrained estimation in the Cox’s model

ABSTRACT

The generalized case-cohort sampling is a best choice to reduce study cost and time, which contains many sampling steps, each step takes a random sample of a certain size without replacement from a certain subset of the cohort, the number of steps, the choice of sample size and the sampling subset must not use the information about the observed covariates. The constrained estimation in the Cox’s model for the right-censored survival data has been studied by Ding, Tian, and Kam, who proposed a novel minorization-maximization (MM) algorithm for the constrained estimation. In this paper, we derive an estimating equation by a sample reuse and local average weight method based on generalized case-cohort data and generalize the MM algorithm to get the constrained estimator in the Cox’s model with parameter subject to box or linear inequality constraint. Asymptotic properties are presented. The small sample operating characteristics of the proposed method are examined via simulation studies and are illustrated on a dataset from Wilms tumor studies.

KEYWORDS:

• Constrained estimation
• Cox’s model
• generalized case-cohort sampling
• MM algorithm