Accession Number:

ADA161322

Title:

Piecewise Geometric Estimation of a Survival Function.

Descriptive Note:

Technical rept.,

Corporate Author:

FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s):

Report Date:

1985-04-01

Pagination or Media Count:

50.0

Abstract:

This document describes a statistical procedure that uses incomplete data to estimate failure rate and survival functions. Although the procedure is designed for discrete distributions, it applied in the continuous case also. This description is expository and therefore contains no proofs they are provided by Mimmack 1985. The procedure is based on the assumption of a piecewise constant failure rate. The resultant survival function estimator is a piecewise geometric function, denoted the Piecewise Geometric Estimator PEGE. The PEGE is the discrete version of the piecewise exponential estimators proposed independently by Kitchin, Langberg and Proschan 1983 and Whittemore and Keller 1983, and it is a generalization of an estimator of Umholtz 1984 who considers complete data taken from an exponential distribution. The PEGE is consistent and asymptotically normal under conditions more general than those of the model of random censorship. Although the PEGE and the widely used Kaplan-Meier estimator KME are asumptotically equivalent and generally interlace, the PEGE is expected to perform better than the KME in terms of small sample properties. The PEGE is attractive to users because it is computationally simple and realistic in that it decreases at every possible failure time it therefore no only has the appearance of a survival function, but also provides a realistic estimate of the failure rate function. The KME, in contrast, is a step function. Keywords pilot studies Monte Carlo method.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE