Maximum Likelihood Estimation of the Survival Functions of N Stochastically Ordered Random Variables.
Abstract
Very often, populations exist that, logically, should satisfy linear stochastic ordering requirements. For example if a mechanical device is improved through N stages, the corresponding survival functions should be linearly stochastically ordered. Nevertheless, estimates may not reflect this stochastic ordering because of the inherent variability of the observations. This document characterizes the maximum likelihood estimates of the survival functions subject to linear stochastic ordering requirements. These estimates may be expressed in terms of the well-known Kaplan-Meier product limit estimates. Also given is an iterative algorithm which must converge to the correct solution that depends only upon solving the pairwise problem. Finally the authors consider an example concerning survival times for people with squamous carcinoma in the oropharynx when classified by degree of lymph node deterioration at time of discovery. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1984
- Accession Number
- ADA145429
Entities
People
- C. J. Feltz
- R. L. Dykstra
Organizations
- University of Iowa